The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules

Nicholas R Hutzler1 lowast Hsin-I Lu1 2 dagger and John M Doyle1 Dagger

1Harvard University Department of Physics 17 Oxford Street Cambridge MA 02138 USA2Harvard University School of Engineering and Applied Sciences 29 Oxford Street Cambridge MA 02138 USA

CONTENTS

I Introduction 1A Cold atoms and molecules 2B Buffer gas cooling and beam production 3

II Buffer Gas Cooled Beams 4A Species production thermalization diffusion

and extraction 41 Buffer gas flow through the cell 42 Introduction of species 53 Thermalization 64 Diffusion 75 Extraction from the buffer cell 8

B Properties of buffer gas cooled beams 81 Characterization of gas flow regimes 82 Forward velocity 103 Velocity spreads 124 Angular spread and divergence 135 Relationship of flow and extraction

regimes 146 Choice of buffer gas 14

C Additional cooling and slowing 141 Isentropic expansion 152 Slowing cells 163 Guiding and velocity filtering 16

D Effusive and supersonic beam properties 181 Effusive beams 182 Fully hydrodynamic or ldquosupersonicrdquo

beams 19E Technical details of source construction 20

1 The cell 202 Radiation shields 203 Cryopumps 214 Beam collimation 21

III Applications 21A Laser cooling of buffer gas beams 21

1 Direct loading of exotic atoms intomagneto-optical traps 22

B Precision measurements 231 Electric dipole moments 232 Parity violation and anapole moments 243 Time-variation of fundamental constants 25

C Cold collisions and trap loading 26

lowast nickcuaharvardedudagger hsin-icuaharvardeduDagger doylephysicsharvardedu

1 ND3 + OH collisions 262 Direct trap loading of molecules 27

IV Acknowledgments 28

References 28

I INTRODUCTION

Beams of atoms and molecules are stalwart tools forspectroscopy and studies of collisional processes[1 2]The supersonic expansion technique can create coldbeams of many species of atoms and molecules How-ever the resulting beam is typically moving at a speedof 300ndash600 m sminus1 in the lab frame and for a large classof species has insufficient flux (ie brightness) for im-portant applications In contrast buffer gas beams[3 4]can be a superior method in many cases producing coldand relatively slow molecules in the lab frame with highbrightness and great versatility There are basic differ-ences between supersonic and buffer gas cooled beamsregarding particular technological advantages and con-straints At present it is clear that not all of the possiblevariations on the buffer gas method have been studiedIn this review we will present a survey of the currentstate of the art in buffer gas beams and explore someof the possible future directions that these new methodsmight take

Compared to supersonic expansion the buffer gascooled beam method has a fundamentally different ap-proach to cooling molecules into the kelvin regimeThe production of cold molecules (starting from hotmolecules) is achieved by initially mixing two gases ina cold cell (with dimensions of typically a few cm) Thetwo gases are the hot ldquospecies of interestrdquo molecules (in-troduced at an initial temperature T0 typically between300ndash10000 K) and cold inert ldquobufferrdquo gas atoms (cooledto 2-20 K by the cold cell) The buffer gas in the cell iskept at a specifically tuned atom number density typi-cally n = 1014minus17 cmminus3 which is low enough to preventsimple three body collision cluster formation involvingthe target molecule yet high enough to provide enoughcollisions for thermalization before the molecules touchthe walls of the cold cell A beam of cold moleculescan be formed when the buffer gas and target moleculesescape the cell through a few-millimeter-sized orificeor a more complicated exit structure into a high vac-uum region as shown in Figure 2 For certain buffergas densities the buffer gas aids in the extraction ofmolecules into the beam via a process called ldquohydrody-

arX

iv1

111

2841

v1 [

phys

ics

atom

-ph]

11

Nov

201

1

2

namic enhancementrdquo[5] Finally in the case where themass of the molecule is higher than that of the buffergas atom there is a velocity-induced angular narrowingof the molecular beam which increases the on-axis beamintensity[5] Although such enhancement has long beenrecognized in room-temperature beams[6] it is seldomemployed because it requires intermediate Reynolds num-bers in conflict with the high Reynolds numbers neces-sary for full supersonic cooling of molecules in the beamIn buffer gas cooled beams on the other hand the inter-mediate Reynolds number regime is often ideal for cool-ing and allows this technique to take full advantage ofthe intensity enhancement from angular narrowing

With cryogenic cooling high gas densities are notneeded in the buffer cell to cool into the kelvin regimeIn the case of supersonic beams the high gas densitiesrequired in the source can be undesirable In the caseof buffer gas beams the cryogenic environment and rel-atively low flow of buffer gas into the high vacuum beamregion allows for 100 duty cycle (continuous) beamoperation without relying on external vacuum pumpsRather internal cryopumping provides excellent vacuumin the beam region This combination of characteristicshas led to high-brightness cold molecule sources (see Ta-bles I and II) for both chemically reactive (eg pulsedcold ThO producing 3 times 1011 ground state moleculesper steradian during a few ms long pulse[7]) and stablemolecules (eg continuous cold O2 producing asymp 3times1013

cold molecules per second[5 8])

A Cold atoms and molecules

In the past two decades the evaporative cooling ofatoms to ultracold temperatures at high phase spacedensity has opened new chapters for physics and led toexciting discoveries including the realization of Bose-Einstein condensation[20 21] strongly correlated sys-tems in dilute gases[22 23] and controlled quantumsimulation[24 25] Meanwhile the success of cold atommethods and new theory has inspired the vigorous pur-suit of molecule cooling Molecules are more complicatedthan atoms and possess two key features not present inatoms additional internal degrees of freedom in theform of molecular rotation and vibration and the pos-sibility (with polar molecules) to exhibit an atomic unitof electric dipole moment in the lab frame which canlead to systems with long range anisotropic and tunableinteractions The rich internal structure and chemical di-versity of molecules could provide platforms for explor-ing science in diverse fields ranging from fundamentalphysics cold chemistry molecular physics and quantumphysics[26] We will list just a few of these applicationshere

bull Molecules have enhanced sensitivity (as comparedto atoms) to violations of fundamental symmetriessuch as the possible existence of the electron electric

0 50 100 150 200 250 300 350 400 4500

01

02

03

04

05

06

07

08

09

1

Beam Forward Velocity [ms]

Num

ber [

arb]

Supersonic

Buer Gas

Eusive

FIG 1 Schematic velocity distributions for selected effusivesupersonic and buffer gas cooled beam sources The buffergas cooled beam properties are taken from a ThO source withneon buffer gas[7] The effusive beam is a simulated roomtemperature source of a species with mass of 100 amu andthe simulated supersonic source uses room temperature xenonas the carrier gas Compared to the effusive beam the buffergas beam has a much lower temperature (ie smaller veloc-ity spread) Compared to the supersonic beam the buffergas beam has a comparable temperature but lower forwardvelocity Supersonic sources typically have much higher aver-age forward velocity than the one presented above (asymp 600 msminus1 for room temperature argon or asymp 1800 m sminus1 for roomtemperature helium)[1] and effusive sources for many species(like ThO[7 14]) would require oven temperatures of gt 1000K making the distribution much wider with a much highermean The distributions above are normalized however thebuffer gas cooled source of many species has a considerablyhigher flux See Table I for data about experimentally realizedbuffer gas cooled beams

dipole moment[27 28] and parity-violating nuclearmoments[29 30]

bull The internal degrees of freedom of polar moleculeshave been proposed as qubits for quantumcomputers[31] and are ideal for storage of quan-tum information[26 32 33]

bull The long-range electric dipole-dipole interactionbetween polar molecules may give rise to novelquantum systems[34 35]

bull Precision spectroscopy performed on vibrational orhyperfine states of cold molecules can probe thetime variation of fundamental constants such asthe electron-to-proton mass ratio and the fine struc-ture constant [36ndash38]

bull Studies of cold molecular chemistry in the labora-tory play an important role in understanding gas-phase chemistry of interstellar clouds which can beas cold as 10 K [39ndash41]

3

Method Species Intensity [sminus1] Velocity [m sminus1]

Chemically reactive polar molecules

Buffer gas ThO[7] 3 times 1013 srminus1 170

Buffer gas SrF[9] 17 times 1012 srminus1 140

Buffer gas CaH[10] 5 times 109 srminus1 40

Supersonic YbF[11] 14 times 1010 srminus1 290

Supersonic BaF[12] 13 times 1010 srminus1 500

Effusive SrF[13] 5 times 1011 srminus1 650

Effusive ThO[7 14] 1 times 1011 srminus1 540

Stable molecule with significant vapor pressure at 300 K

Buffer gas ND3[15 16] 1 times 1011 65

Supersonic ND3[17 18] 1 times 108 280

Stark Decelerated ND3[17 18] 1 times 106 13

Effusive ND3[19] 2 times 1010 40

TABLE I A comparison of supersonic effusive and buffer gas cooled beams for selected molecules The intensity is the numberof molecules per quantum state per second and the velocity is reported in the forward direction If the angular spread of thebeam is known then the intensity per unit solid angle (ie brightness) is given The ND3 sources are velocity-selected Forpulsed sources the intensity is averaged over a time period that includes multiple pulses For chemically reactive moleculesbuffer gas sources can provide dramatically higher brightness and with a slower forward velocity In addition to brightness andforward velocity we shall see later in this article that other features of buffer gas beams also compare favorably to supersonicand effusive beams See Table II for more data about experimentally realized buffer gas cooled beams

bull Ultracold chemical reactions have been observed ata temperature of a few hundred nK with reactionrates controllable by external electric fields[42 43]

bull Molecular collisions in the few partial wave regimereveal the molecular interaction in great detail[44ndash46]

The most common (but not the only[47]) way to coolatoms to ultracold temperatures defined as the temper-ature (typically 1 mK) where only sminuswave collisionsoccur (for bosons) is laser cooling[48] This techniquerelies on continuously scattering photons from atoms todissipate the atomrsquos motional energy Typically sim 104

photon scattering events are needed to significantly re-duce the kinetic energy of the atom Molecules gen-erally lack closed transitions that can easily cycle thismany photons because the excited states of the moleculescan decay to many vibrational or rotational states Be-cause laser cooling molecules is more difficult than it iswith atoms (and has only been demonstrated relativelyrecently[49 50]) there continue to be broad efforts in de-veloping new molecule cooling methods in order to fullycontrol the internal and motional degrees of freedom ofmolecules[26 51ndash53] Additionally many of these newproposed methods could work well with laser cooling insome form

In general cooling techniques for molecules can bebroadly classified into two types indirect and direct[5152] Indirect cooling relies on assembling two laser-cooledatoms into a bound molecule using photoassociation ormagnetoassociation The resulting molecules have thesame translational temperature as their ultracold parentatoms but are typically in a highly excited vibrational

state which can be transferred (typically by a coher-ent transfer method such as STIRAP[54]) to the abso-lute ground state While indirect methods can accessultracold polar molecules with a high phase space den-sity these molecules are currently limited to a combina-tion of the small subset of atoms which have been laserand evaporatively cooled such as the alkali and alkalineearth atoms Currently high-density samples of ultra-cold polar molecules have only been demonstrated witha single species KRb[55] Since many atoms are not eas-ily amenable to laser cooling there is a large class ofmolecules that are the focus of direct cooling this classincludes many of the molecules that are desirable for theapplications listed above[26] In this paper we shall focuson beams of molecules that are cooled directly throughcollisions with cryogenically cooled atoms

B Buffer gas cooling and beam production

At the heart of the buffer gas beam technique isbuffer gas cooling a direct cooling technique used in thefirst magnetic trapping of polar molecules over a decadeago[56] The buffer gas cooling technique works by dis-sipating the energy of the species of interest via elasticcollisions with cold inert gas atoms such as helium orneon Since this cooling mechanism does not depend onthe internal structure of the species (unlike laser cooling)buffer gas cooling can be applied to nearly any atom orsmall molecule[4] and certain large molecules [57] He-lium maintains a sufficient vapor pressure down to a fewhundred mK[4 58] and the typical helium-molecule elas-tic cross section[4] of sim 10minus14 cm2 allows buffer gas cool-

4

(c)

(a)

Cold Cell

Buer Gas

daperture

dcell

Lcell

(b)

Ablation Laser

Ablation Target

Windows

FIG 2 A schematic of a buffer gas beam cell which is main-tained at a temperature of few K (a) The buffer gas (typicallyhelium or neon) enters the cell through a fill line and exits viaa cell aperture on the other side of the cell The importantphysical dimensions (cell length Lcell cell diameter dcell andaperture diameter daperture) are indicated (b) Introductionof species via laser ablation (c) Molecules thermalize to thebuffer gas and form a molecular beam with the flowing buffergas

ing and trap loading to be realized with modest cell sizes(few times few times few cm3) Buffer gas cooling (using bothhelium and neon) has been used to create beams loadmagnetic traps and perform spectroscopy in a cold buffergas cell[4] In this paper we shall focus only on one as-pect the creation (and characterization) of buffer gascooled beams

As shown in Figure 2 a buffer gas beam is formedsimply by adding an exit aperture to one side of a coldcell filled with a buffer gas A constant buffer gas den-sity is maintained by continuously flowing the buffer gasthrough a fill line on the other side of the cell Figure2(b) shows laser ablation one of several methods used tointroduce molecules of interest into the cell (see discus-sion in Section II A 2) After production and injection of

molecules in the buffer gas cell the molecules thermalizewith the buffer gas translationally and rotationally andare carried out of the cell with the flowing buffer gasforming a molecular beam (Figure 2(c))

Cold molecular beams created from a buffer gas cellare made in a few key steps the introduction of ldquohotrdquomolecules in a ldquocoldrdquo buffer gas cell the thermalizationof the molecules with the buffer gas and the extractionof molecules into a beam Each of these steps affectsthe properties of the resultant beam The detailed char-acteristics (forward velocity velocity spreads tempera-tures and fluxes) of buffer gas beams in several operatingregimes will be described in the next section Techniquesto manipulate the beam properties such as guiding fil-tering cooling by isentropic expansion and advanced cellgeometries will also be discussed The last part of thispaper will discuss the applications of buffer gas beamsincluding the search for the electron electric dipole mo-ment using ThO[59] the study of cold dipolar collisionswith ND3[60] and the realization of direct laser coolingof molecules with SrF[49 50]

II BUFFER GAS COOLED BEAMS

The details of buffer gas cooled beam production andproperties will be presented in this section In our treat-ment we shall assume that the buffer gas is a noble gasand that the species of interest is seeded in the buffer gasflow with a low fractional concentration about 1 orless We will often refer to the species of interest as ldquothemoleculerdquo even though buffer gas cooled beams of atoms(eg Yb) are also of interest As is typically the case weshall assume that the species of interest is heavier thanthe buffer gas (though the analysis is easily extended tolighter molecules)

A Species production thermalization diffusionand extraction

In this section we present estimates of physical param-eters that can be used to support an intuitive under-standing of the processes occurring in the buffer gas cellThese derivations will all be approximate and will varydepending on geometry species introduction methodtemperature range density range etc However theyare typically descriptive within an order of unity

1 Buffer gas flow through the cell

Consider a buffer gas cell as depicted in Figure 2 Thecell has a volume of Vcell = AcelltimesLcell where Lcell is thelength of the cell interior and Acell asymp d2

cell is the cross-sectional area (which may be round or square but has acharacteristic length of dcell) Lcell is typically a few cmand Acell is typically a few cm2 The cell is held at a fixed

5

temperature T0 by a cryogenic refrigerator typically be-tween 1 K and 20 K Buffer gas of mass mb is introducedinto the cell volume by a long thin tube or ldquofill linerdquoThe buffer gas exits the cell through an aperture of char-acteristic length daperture and area Aaperture (for the casewhere the aperture is a rectangle daperture is the shorterdimension) Typical values are daperture = 1 minus 5 mmand Aaperture = 5minus 25 mm2 A buffer gas flow rate f0b

into the cell can be set with a mass flow controller Herethe subscript ldquobrdquo refers to the buffer gas and ldquo0rdquo refersto conditions in the cell at steady-state or ldquostagnationrdquoconditions The most commonly used unit for flow is thestandard cubic centimeter per minute or SCCM whichequals approximately 45 times 1017 gas atoms per secondTypical flow rates for buffer gas beams are f0b = 1minus100SCCM Technical details of cell construction and con-struction of a buffer gas cooled beam apparatus in gen-eral are discussed in Section II E

At steady state the flow rate out of the cell is givenby the molecular conductance of the aperture fout =14n0bv0bAaperture where

v0b =

radic8kBT0

πmb(1)

is the mean thermal velocity of the buffer gas inside thecell (about 140 m sminus1 for 4 K helium or 17 K neon) kB isBoltzmannrsquos constant and n0b is the stagnation numberdensity of buffer gas atoms Therefore the number den-sity n0b is set by controlling the flow via the steady-staterelationship fout = f0b or

n0b =4f0b

Aaperturev0b (2)

With typical cell aperture sizes and temperatures a flowof 1 SCCM corresponds to a stagnation density of about1015 cmminus3 so typical values for the stagnation density are1015minus1017 cmminus3 Note that in the above equation we as-sume that the flow through the aperture is purely molec-ular At higher number densities the flow can becomemore fluid-like and then the flow rate out will changehowever the difference is about a factor of two [61] sothe above equation is suitable for approximation

2 Introduction of species

The species of interest can be introduced into the buffergas cell through a number of methods [4] including laserablation laser-induced atomic desorption (LIAD) beaminjection capillary filling and discharge etching Themost commonly used techniques for creation of buffergas cooled beams are laser ablation and capillary fillingso we will focus here on those two methods

Laser ablation In laser ablation (see Figure 2) a highenergy pulsed laser is focused onto a solid precursor tar-get After receiving the laser pulse the solid precur-sor can eject gas-phase atoms or molecules of the de-sired species often along with other detritus The actual

mechanism for how gas phase species results from the ab-lation of the solid precursor is not simple and dependson the relationship between the length of the laser pulseand the time constants for electronic and lattice heating[62 63] While pulsed ablation has been studied withpulse widths from femtoseconds to milliseconds the mostcommon ablation laser (used for the majority of experi-ments in Table II) is a pulsed NdYAG which can easilydeliver up to 100 mJ of energy in a few ns Either thefundamental (1064 nm) or first harmonic (532 nm) modesare used and neither seems to have a distinct advantageover the other except for certain technical conveniencesafforded by a visible laser

Vapors of metals such as Na [3] or Yb [5] can be easilyproduced by ablation of the solid metal however cre-ation of gas phase molecules by laser ablation can bemore complicated Molecules with a stable solid phase(such as PbO[3]) can be created by simply using the solidphase as a precursor but unstable molecules require care-ful choice of precursor It is often the case that the de-sired diatomic molecule MX has a stable solid form MaXb

which is a glass or ceramic as is the case with BaF CaHSrF YO and ThO (and others) In such cases experi-ence has shown that pressing (and sometimes sintering)a very fine powder of the stable solid often yields the bestablation target [7 9]

The most important advantage of laser ablation is thatit can be used to create a very wide variety of atomsand molecules with high flux [4] The main drawback isthat ablation is typically a ldquoviolentrdquo non-thermal pro-cess that can result in unusual behavior of the gases inthe buffer cell and in the resulting beam Ablation tendsto give fairly inconsistent yields[7 9] and can create plas-mas and complex plumes[64] with temperatures of severalthousand K[65] However buffer gas cells can be designedto allow proper thermalization (see Section II A 3) of thespecies which can mitigate many of these problems

Capillary filling If the species of interest has an ap-preciable vapor pressure at convenient temperatures onecan simply flow the species into the cell through a gas fillline just like the buffer gas[66] This method is simplein principle but in practice it introduces some technicalchallenges The cell and fill line must be carefully engi-neered to keep the fill line warm while keeping the cellcold and preventing freezing of the species at the pointwhere the fill line enters the cell For species with anappreciable vapor pressure at room temperature such asO2 [5] a properly-designed fill line can be attached di-rectly to the buffer gas cell to flow the species For speciesthat require higher temperatures to obtain an apprecia-ble vapor pressure for example a 600 K oven to produceatomic K vapor a complex multi-stage cell must be con-structed [67] to keep heat from the oven out of the cellas shown in Figure 3

The primary advantage of the capillary filling methodis that it can be used to create high-flux beams that arecontinuous and robust The main drawback is the limitednumber of species of interest that have appreciable vapor

6

300 K

Neon buffer gas inputs

Potassium oven 550 K

Intermediate region 100 K

Cell15 K

Liquid potassium

Thermal standoffs

20 K

Needle 550 K

Potassium Beam

Buffer gas inSpecies in

Beam

Cold cell

FIG 3 Left simple capillary filling scheme for loading a molecule (large red circles) with vapor pressure at 300 K such asO2[5] or ND3[15 67] The species flows down a warm gas line and is mixed with the buffer gas (small blue circles) which flowsdown a cold gas line Right Scheme for capillary injection of K atoms (large red circles) from a 550 K oven into a 15 K neon(small blue circles) buffer gas cell Unlike the simple capillary scheme K atoms cannot simply flow down a warm gas line intothe buffer gas cell as the thermal conduction and blackbody heat loads would heat the cell too much Instead a multi-stagecell with thermal standoffs heat links at each stage must be used to reduce the heat load on the cell to acceptable levels Theamount of neon buffer gas introduced into the intermediate temperature regions must be sufficiently large to ensure that theK atoms are entrained in the flow and make it into the cold cell Reproduced from [Patterson D Rasmussen J amp Doyle JM New J Phys 11(5) 055018 (2009) httpdxdoiorg1010881367-2630115055018] with permission from the Instituteof Physics

pressure at temperatures low enough so that the methodis feasible As the required temperature increases thetechnical challenges rapidly multiply (see Figure 3)

It should be noted that regardless of technique thedensity of the species is typically (though not in the caseof some capillary filling schemes[15 16]) lt 1 of thenumber density of the buffer gas This fact will be im-portant later on because it allows us to treat the the gasflow properties as being determined solely by the buffergas with the species as a trace component

3 Thermalization

Before the species flows out of the cell it must undergoenough collisions with the cold buffer gas to become ther-malized to the cell temperature A simple estimate of thenecessary number of collisions can be obtained by ap-proximating the species and buffer gases as hard spheres[68 69] The mean loss in kinetic energy of the speciesper collision with a buffer gas atom results in a meantemperature change of

∆Ts = minus(Ts minus Tb)κ where κ equiv (mb +ms)2

2mbms (3)

Here T denotes temperature m denotes mass and thesubscripts ldquobrdquo and ldquosrdquo refer to the buffer gas and speciesof interest respectively Therefore the temperature ofthe species after N collisions Ts(N ) will vary as

Ts(N )minus Ts(N minus 1) = minus(Ts(N minus 1)minus Tb)κ (4)

If we treat N as large and the temperature change percollision as small we can approximate this discrete equa-

tion as a differential equation

dTs(N )

dN= minus(Ts(N )minus Tb)κ (5)

Solving this differential equation yields the ratio betweenthe species and buffer gas temperatures

Ts(N )

Tb= 1 +

(Ts(0)

Tbminus 1

)eminusNκ (6)

asymp 1 +Ts(0)

TbeminusNκ (7)

where in the last equality we have assumed that thespecies is introduced at a temperature much larger thanthe cell (and therefore buffer gas) temperature ieTs(0) Tb If we estimate mb sim 10 amu ms sim 100amu Tb sim 10 K and Ts(0) sim 1000 K the species shouldbe within a few percent of the buffer gas temperature af-ter sim 50 collisions Under typical cell geometry and flowconditions the thermalization time is a few millisecondsas shown in Figure 4

While this simple model is good enough to obtain anestimate of the thermalization it is not exact In ana-lyzing thermalization of ablation-loaded YbF moleculesin a helium buffer gas Skoff et al [70] found that themodel above did not fit the data however replacing theconstant buffer gas temperature with an initially largertemperature which then exponentially decays to the celltemperature resulted in good fits The physical moti-vation for this model is that the buffer gas is initiallyheated by the ablation and then cools as the buffer gasre-thermalizes with the cell walls Skoff et al presentdetailed analysis of thermalization in a buffer gas andthe reader is referred to their work for details

3

Method Species Intensity [sminus1] Velocity [m sminus1]

Chemically reactive polar molecules

Buffer gas ThO[7] 3 times 1013 srminus1 170

Buffer gas SrF[9] 17 times 1012 srminus1 140

Buffer gas CaH[10] 5 times 109 srminus1 40

Supersonic YbF[11] 14 times 1010 srminus1 290

Supersonic BaF[12] 13 times 1010 srminus1 500

Effusive SrF[13] 5 times 1011 srminus1 650

Effusive ThO[7 14] 1 times 1011 srminus1 540

Stable molecule with significant vapor pressure at 300 K

Buffer gas ND3[15 16] 1 times 1011 65

Supersonic ND3[17 18] 1 times 108 280

Stark Decelerated ND3[17 18] 1 times 106 13

Effusive ND3[19] 2 times 1010 40

TABLE I A comparison of supersonic effusive and buffer gas cooled beams for selected molecules The intensity is the numberof molecules per quantum state per second and the velocity is reported in the forward direction If the angular spread of thebeam is known then the intensity per unit solid angle (ie brightness) is given The ND3 sources are velocity-selected Forpulsed sources the intensity is averaged over a time period that includes multiple pulses For chemically reactive moleculesbuffer gas sources can provide dramatically higher brightness and with a slower forward velocity In addition to brightness andforward velocity we shall see later in this article that other features of buffer gas beams also compare favorably to supersonicand effusive beams See Table II for more data about experimentally realized buffer gas cooled beams

bull Ultracold chemical reactions have been observed ata temperature of a few hundred nK with reactionrates controllable by external electric fields[42 43]

bull Molecular collisions in the few partial wave regimereveal the molecular interaction in great detail[44ndash46]

The most common (but not the only[47]) way to coolatoms to ultracold temperatures defined as the temper-ature (typically 1 mK) where only sminuswave collisionsoccur (for bosons) is laser cooling[48] This techniquerelies on continuously scattering photons from atoms todissipate the atomrsquos motional energy Typically sim 104

photon scattering events are needed to significantly re-duce the kinetic energy of the atom Molecules gen-erally lack closed transitions that can easily cycle thismany photons because the excited states of the moleculescan decay to many vibrational or rotational states Be-cause laser cooling molecules is more difficult than it iswith atoms (and has only been demonstrated relativelyrecently[49 50]) there continue to be broad efforts in de-veloping new molecule cooling methods in order to fullycontrol the internal and motional degrees of freedom ofmolecules[26 51ndash53] Additionally many of these newproposed methods could work well with laser cooling insome form

In general cooling techniques for molecules can bebroadly classified into two types indirect and direct[5152] Indirect cooling relies on assembling two laser-cooledatoms into a bound molecule using photoassociation ormagnetoassociation The resulting molecules have thesame translational temperature as their ultracold parentatoms but are typically in a highly excited vibrational

state which can be transferred (typically by a coher-ent transfer method such as STIRAP[54]) to the abso-lute ground state While indirect methods can accessultracold polar molecules with a high phase space den-sity these molecules are currently limited to a combina-tion of the small subset of atoms which have been laserand evaporatively cooled such as the alkali and alkalineearth atoms Currently high-density samples of ultra-cold polar molecules have only been demonstrated witha single species KRb[55] Since many atoms are not eas-ily amenable to laser cooling there is a large class ofmolecules that are the focus of direct cooling this classincludes many of the molecules that are desirable for theapplications listed above[26] In this paper we shall focuson beams of molecules that are cooled directly throughcollisions with cryogenically cooled atoms

B Buffer gas cooling and beam production

At the heart of the buffer gas beam technique isbuffer gas cooling a direct cooling technique used in thefirst magnetic trapping of polar molecules over a decadeago[56] The buffer gas cooling technique works by dis-sipating the energy of the species of interest via elasticcollisions with cold inert gas atoms such as helium orneon Since this cooling mechanism does not depend onthe internal structure of the species (unlike laser cooling)buffer gas cooling can be applied to nearly any atom orsmall molecule[4] and certain large molecules [57] He-lium maintains a sufficient vapor pressure down to a fewhundred mK[4 58] and the typical helium-molecule elas-tic cross section[4] of sim 10minus14 cm2 allows buffer gas cool-

4

(c)

(a)

Cold Cell

Buer Gas

daperture

dcell

Lcell

(b)

Ablation Laser

Ablation Target

Windows

FIG 2 A schematic of a buffer gas beam cell which is main-tained at a temperature of few K (a) The buffer gas (typicallyhelium or neon) enters the cell through a fill line and exits viaa cell aperture on the other side of the cell The importantphysical dimensions (cell length Lcell cell diameter dcell andaperture diameter daperture) are indicated (b) Introductionof species via laser ablation (c) Molecules thermalize to thebuffer gas and form a molecular beam with the flowing buffergas

ing and trap loading to be realized with modest cell sizes(few times few times few cm3) Buffer gas cooling (using bothhelium and neon) has been used to create beams loadmagnetic traps and perform spectroscopy in a cold buffergas cell[4] In this paper we shall focus only on one as-pect the creation (and characterization) of buffer gascooled beams

As shown in Figure 2 a buffer gas beam is formedsimply by adding an exit aperture to one side of a coldcell filled with a buffer gas A constant buffer gas den-sity is maintained by continuously flowing the buffer gasthrough a fill line on the other side of the cell Figure2(b) shows laser ablation one of several methods used tointroduce molecules of interest into the cell (see discus-sion in Section II A 2) After production and injection of

molecules in the buffer gas cell the molecules thermalizewith the buffer gas translationally and rotationally andare carried out of the cell with the flowing buffer gasforming a molecular beam (Figure 2(c))

Cold molecular beams created from a buffer gas cellare made in a few key steps the introduction of ldquohotrdquomolecules in a ldquocoldrdquo buffer gas cell the thermalizationof the molecules with the buffer gas and the extractionof molecules into a beam Each of these steps affectsthe properties of the resultant beam The detailed char-acteristics (forward velocity velocity spreads tempera-tures and fluxes) of buffer gas beams in several operatingregimes will be described in the next section Techniquesto manipulate the beam properties such as guiding fil-tering cooling by isentropic expansion and advanced cellgeometries will also be discussed The last part of thispaper will discuss the applications of buffer gas beamsincluding the search for the electron electric dipole mo-ment using ThO[59] the study of cold dipolar collisionswith ND3[60] and the realization of direct laser coolingof molecules with SrF[49 50]

II BUFFER GAS COOLED BEAMS

The details of buffer gas cooled beam production andproperties will be presented in this section In our treat-ment we shall assume that the buffer gas is a noble gasand that the species of interest is seeded in the buffer gasflow with a low fractional concentration about 1 orless We will often refer to the species of interest as ldquothemoleculerdquo even though buffer gas cooled beams of atoms(eg Yb) are also of interest As is typically the case weshall assume that the species of interest is heavier thanthe buffer gas (though the analysis is easily extended tolighter molecules)

A Species production thermalization diffusionand extraction

In this section we present estimates of physical param-eters that can be used to support an intuitive under-standing of the processes occurring in the buffer gas cellThese derivations will all be approximate and will varydepending on geometry species introduction methodtemperature range density range etc However theyare typically descriptive within an order of unity

1 Buffer gas flow through the cell

Consider a buffer gas cell as depicted in Figure 2 Thecell has a volume of Vcell = AcelltimesLcell where Lcell is thelength of the cell interior and Acell asymp d2

cell is the cross-sectional area (which may be round or square but has acharacteristic length of dcell) Lcell is typically a few cmand Acell is typically a few cm2 The cell is held at a fixed

5

temperature T0 by a cryogenic refrigerator typically be-tween 1 K and 20 K Buffer gas of mass mb is introducedinto the cell volume by a long thin tube or ldquofill linerdquoThe buffer gas exits the cell through an aperture of char-acteristic length daperture and area Aaperture (for the casewhere the aperture is a rectangle daperture is the shorterdimension) Typical values are daperture = 1 minus 5 mmand Aaperture = 5minus 25 mm2 A buffer gas flow rate f0b

into the cell can be set with a mass flow controller Herethe subscript ldquobrdquo refers to the buffer gas and ldquo0rdquo refersto conditions in the cell at steady-state or ldquostagnationrdquoconditions The most commonly used unit for flow is thestandard cubic centimeter per minute or SCCM whichequals approximately 45 times 1017 gas atoms per secondTypical flow rates for buffer gas beams are f0b = 1minus100SCCM Technical details of cell construction and con-struction of a buffer gas cooled beam apparatus in gen-eral are discussed in Section II E

At steady state the flow rate out of the cell is givenby the molecular conductance of the aperture fout =14n0bv0bAaperture where

v0b =

radic8kBT0

πmb(1)

is the mean thermal velocity of the buffer gas inside thecell (about 140 m sminus1 for 4 K helium or 17 K neon) kB isBoltzmannrsquos constant and n0b is the stagnation numberdensity of buffer gas atoms Therefore the number den-sity n0b is set by controlling the flow via the steady-staterelationship fout = f0b or

n0b =4f0b

Aaperturev0b (2)

With typical cell aperture sizes and temperatures a flowof 1 SCCM corresponds to a stagnation density of about1015 cmminus3 so typical values for the stagnation density are1015minus1017 cmminus3 Note that in the above equation we as-sume that the flow through the aperture is purely molec-ular At higher number densities the flow can becomemore fluid-like and then the flow rate out will changehowever the difference is about a factor of two [61] sothe above equation is suitable for approximation

2 Introduction of species

The species of interest can be introduced into the buffergas cell through a number of methods [4] including laserablation laser-induced atomic desorption (LIAD) beaminjection capillary filling and discharge etching Themost commonly used techniques for creation of buffergas cooled beams are laser ablation and capillary fillingso we will focus here on those two methods

Laser ablation In laser ablation (see Figure 2) a highenergy pulsed laser is focused onto a solid precursor tar-get After receiving the laser pulse the solid precur-sor can eject gas-phase atoms or molecules of the de-sired species often along with other detritus The actual

mechanism for how gas phase species results from the ab-lation of the solid precursor is not simple and dependson the relationship between the length of the laser pulseand the time constants for electronic and lattice heating[62 63] While pulsed ablation has been studied withpulse widths from femtoseconds to milliseconds the mostcommon ablation laser (used for the majority of experi-ments in Table II) is a pulsed NdYAG which can easilydeliver up to 100 mJ of energy in a few ns Either thefundamental (1064 nm) or first harmonic (532 nm) modesare used and neither seems to have a distinct advantageover the other except for certain technical conveniencesafforded by a visible laser

Vapors of metals such as Na [3] or Yb [5] can be easilyproduced by ablation of the solid metal however cre-ation of gas phase molecules by laser ablation can bemore complicated Molecules with a stable solid phase(such as PbO[3]) can be created by simply using the solidphase as a precursor but unstable molecules require care-ful choice of precursor It is often the case that the de-sired diatomic molecule MX has a stable solid form MaXb

which is a glass or ceramic as is the case with BaF CaHSrF YO and ThO (and others) In such cases experi-ence has shown that pressing (and sometimes sintering)a very fine powder of the stable solid often yields the bestablation target [7 9]

The most important advantage of laser ablation is thatit can be used to create a very wide variety of atomsand molecules with high flux [4] The main drawback isthat ablation is typically a ldquoviolentrdquo non-thermal pro-cess that can result in unusual behavior of the gases inthe buffer cell and in the resulting beam Ablation tendsto give fairly inconsistent yields[7 9] and can create plas-mas and complex plumes[64] with temperatures of severalthousand K[65] However buffer gas cells can be designedto allow proper thermalization (see Section II A 3) of thespecies which can mitigate many of these problems

Capillary filling If the species of interest has an ap-preciable vapor pressure at convenient temperatures onecan simply flow the species into the cell through a gas fillline just like the buffer gas[66] This method is simplein principle but in practice it introduces some technicalchallenges The cell and fill line must be carefully engi-neered to keep the fill line warm while keeping the cellcold and preventing freezing of the species at the pointwhere the fill line enters the cell For species with anappreciable vapor pressure at room temperature such asO2 [5] a properly-designed fill line can be attached di-rectly to the buffer gas cell to flow the species For speciesthat require higher temperatures to obtain an apprecia-ble vapor pressure for example a 600 K oven to produceatomic K vapor a complex multi-stage cell must be con-structed [67] to keep heat from the oven out of the cellas shown in Figure 3

The primary advantage of the capillary filling methodis that it can be used to create high-flux beams that arecontinuous and robust The main drawback is the limitednumber of species of interest that have appreciable vapor

6

300 K

Neon buffer gas inputs

Potassium oven 550 K

Intermediate region 100 K

Cell15 K

Liquid potassium

Thermal standoffs

20 K

Needle 550 K

Potassium Beam

Buffer gas inSpecies in

Beam

Cold cell

FIG 3 Left simple capillary filling scheme for loading a molecule (large red circles) with vapor pressure at 300 K such asO2[5] or ND3[15 67] The species flows down a warm gas line and is mixed with the buffer gas (small blue circles) which flowsdown a cold gas line Right Scheme for capillary injection of K atoms (large red circles) from a 550 K oven into a 15 K neon(small blue circles) buffer gas cell Unlike the simple capillary scheme K atoms cannot simply flow down a warm gas line intothe buffer gas cell as the thermal conduction and blackbody heat loads would heat the cell too much Instead a multi-stagecell with thermal standoffs heat links at each stage must be used to reduce the heat load on the cell to acceptable levels Theamount of neon buffer gas introduced into the intermediate temperature regions must be sufficiently large to ensure that theK atoms are entrained in the flow and make it into the cold cell Reproduced from [Patterson D Rasmussen J amp Doyle JM New J Phys 11(5) 055018 (2009) httpdxdoiorg1010881367-2630115055018] with permission from the Instituteof Physics

pressure at temperatures low enough so that the methodis feasible As the required temperature increases thetechnical challenges rapidly multiply (see Figure 3)

It should be noted that regardless of technique thedensity of the species is typically (though not in the caseof some capillary filling schemes[15 16]) lt 1 of thenumber density of the buffer gas This fact will be im-portant later on because it allows us to treat the the gasflow properties as being determined solely by the buffergas with the species as a trace component

3 Thermalization

Before the species flows out of the cell it must undergoenough collisions with the cold buffer gas to become ther-malized to the cell temperature A simple estimate of thenecessary number of collisions can be obtained by ap-proximating the species and buffer gases as hard spheres[68 69] The mean loss in kinetic energy of the speciesper collision with a buffer gas atom results in a meantemperature change of

∆Ts = minus(Ts minus Tb)κ where κ equiv (mb +ms)2

2mbms (3)

Here T denotes temperature m denotes mass and thesubscripts ldquobrdquo and ldquosrdquo refer to the buffer gas and speciesof interest respectively Therefore the temperature ofthe species after N collisions Ts(N ) will vary as

Ts(N )minus Ts(N minus 1) = minus(Ts(N minus 1)minus Tb)κ (4)

If we treat N as large and the temperature change percollision as small we can approximate this discrete equa-

tion as a differential equation

dTs(N )

dN= minus(Ts(N )minus Tb)κ (5)

Solving this differential equation yields the ratio betweenthe species and buffer gas temperatures

Ts(N )

Tb= 1 +

(Ts(0)

Tbminus 1

)eminusNκ (6)

asymp 1 +Ts(0)

TbeminusNκ (7)

where in the last equality we have assumed that thespecies is introduced at a temperature much larger thanthe cell (and therefore buffer gas) temperature ieTs(0) Tb If we estimate mb sim 10 amu ms sim 100amu Tb sim 10 K and Ts(0) sim 1000 K the species shouldbe within a few percent of the buffer gas temperature af-ter sim 50 collisions Under typical cell geometry and flowconditions the thermalization time is a few millisecondsas shown in Figure 4

While this simple model is good enough to obtain anestimate of the thermalization it is not exact In ana-lyzing thermalization of ablation-loaded YbF moleculesin a helium buffer gas Skoff et al [70] found that themodel above did not fit the data however replacing theconstant buffer gas temperature with an initially largertemperature which then exponentially decays to the celltemperature resulted in good fits The physical moti-vation for this model is that the buffer gas is initiallyheated by the ablation and then cools as the buffer gasre-thermalizes with the cell walls Skoff et al presentdetailed analysis of thermalization in a buffer gas andthe reader is referred to their work for details

4

(c)

(a)

Cold Cell

Buer Gas

daperture

dcell

Lcell

(b)

Ablation Laser

Ablation Target

Windows

FIG 2 A schematic of a buffer gas beam cell which is main-tained at a temperature of few K (a) The buffer gas (typicallyhelium or neon) enters the cell through a fill line and exits viaa cell aperture on the other side of the cell The importantphysical dimensions (cell length Lcell cell diameter dcell andaperture diameter daperture) are indicated (b) Introductionof species via laser ablation (c) Molecules thermalize to thebuffer gas and form a molecular beam with the flowing buffergas

ing and trap loading to be realized with modest cell sizes(few times few times few cm3) Buffer gas cooling (using bothhelium and neon) has been used to create beams loadmagnetic traps and perform spectroscopy in a cold buffergas cell[4] In this paper we shall focus only on one as-pect the creation (and characterization) of buffer gascooled beams

As shown in Figure 2 a buffer gas beam is formedsimply by adding an exit aperture to one side of a coldcell filled with a buffer gas A constant buffer gas den-sity is maintained by continuously flowing the buffer gasthrough a fill line on the other side of the cell Figure2(b) shows laser ablation one of several methods used tointroduce molecules of interest into the cell (see discus-sion in Section II A 2) After production and injection of

molecules in the buffer gas cell the molecules thermalizewith the buffer gas translationally and rotationally andare carried out of the cell with the flowing buffer gasforming a molecular beam (Figure 2(c))

Cold molecular beams created from a buffer gas cellare made in a few key steps the introduction of ldquohotrdquomolecules in a ldquocoldrdquo buffer gas cell the thermalizationof the molecules with the buffer gas and the extractionof molecules into a beam Each of these steps affectsthe properties of the resultant beam The detailed char-acteristics (forward velocity velocity spreads tempera-tures and fluxes) of buffer gas beams in several operatingregimes will be described in the next section Techniquesto manipulate the beam properties such as guiding fil-tering cooling by isentropic expansion and advanced cellgeometries will also be discussed The last part of thispaper will discuss the applications of buffer gas beamsincluding the search for the electron electric dipole mo-ment using ThO[59] the study of cold dipolar collisionswith ND3[60] and the realization of direct laser coolingof molecules with SrF[49 50]

II BUFFER GAS COOLED BEAMS

The details of buffer gas cooled beam production andproperties will be presented in this section In our treat-ment we shall assume that the buffer gas is a noble gasand that the species of interest is seeded in the buffer gasflow with a low fractional concentration about 1 orless We will often refer to the species of interest as ldquothemoleculerdquo even though buffer gas cooled beams of atoms(eg Yb) are also of interest As is typically the case weshall assume that the species of interest is heavier thanthe buffer gas (though the analysis is easily extended tolighter molecules)

A Species production thermalization diffusionand extraction

In this section we present estimates of physical param-eters that can be used to support an intuitive under-standing of the processes occurring in the buffer gas cellThese derivations will all be approximate and will varydepending on geometry species introduction methodtemperature range density range etc However theyare typically descriptive within an order of unity

1 Buffer gas flow through the cell

Consider a buffer gas cell as depicted in Figure 2 Thecell has a volume of Vcell = AcelltimesLcell where Lcell is thelength of the cell interior and Acell asymp d2

cell is the cross-sectional area (which may be round or square but has acharacteristic length of dcell) Lcell is typically a few cmand Acell is typically a few cm2 The cell is held at a fixed

5

temperature T0 by a cryogenic refrigerator typically be-tween 1 K and 20 K Buffer gas of mass mb is introducedinto the cell volume by a long thin tube or ldquofill linerdquoThe buffer gas exits the cell through an aperture of char-acteristic length daperture and area Aaperture (for the casewhere the aperture is a rectangle daperture is the shorterdimension) Typical values are daperture = 1 minus 5 mmand Aaperture = 5minus 25 mm2 A buffer gas flow rate f0b

into the cell can be set with a mass flow controller Herethe subscript ldquobrdquo refers to the buffer gas and ldquo0rdquo refersto conditions in the cell at steady-state or ldquostagnationrdquoconditions The most commonly used unit for flow is thestandard cubic centimeter per minute or SCCM whichequals approximately 45 times 1017 gas atoms per secondTypical flow rates for buffer gas beams are f0b = 1minus100SCCM Technical details of cell construction and con-struction of a buffer gas cooled beam apparatus in gen-eral are discussed in Section II E

At steady state the flow rate out of the cell is givenby the molecular conductance of the aperture fout =14n0bv0bAaperture where

v0b =

radic8kBT0

πmb(1)

is the mean thermal velocity of the buffer gas inside thecell (about 140 m sminus1 for 4 K helium or 17 K neon) kB isBoltzmannrsquos constant and n0b is the stagnation numberdensity of buffer gas atoms Therefore the number den-sity n0b is set by controlling the flow via the steady-staterelationship fout = f0b or

n0b =4f0b

Aaperturev0b (2)

With typical cell aperture sizes and temperatures a flowof 1 SCCM corresponds to a stagnation density of about1015 cmminus3 so typical values for the stagnation density are1015minus1017 cmminus3 Note that in the above equation we as-sume that the flow through the aperture is purely molec-ular At higher number densities the flow can becomemore fluid-like and then the flow rate out will changehowever the difference is about a factor of two [61] sothe above equation is suitable for approximation

2 Introduction of species

The species of interest can be introduced into the buffergas cell through a number of methods [4] including laserablation laser-induced atomic desorption (LIAD) beaminjection capillary filling and discharge etching Themost commonly used techniques for creation of buffergas cooled beams are laser ablation and capillary fillingso we will focus here on those two methods

Laser ablation In laser ablation (see Figure 2) a highenergy pulsed laser is focused onto a solid precursor tar-get After receiving the laser pulse the solid precur-sor can eject gas-phase atoms or molecules of the de-sired species often along with other detritus The actual

mechanism for how gas phase species results from the ab-lation of the solid precursor is not simple and dependson the relationship between the length of the laser pulseand the time constants for electronic and lattice heating[62 63] While pulsed ablation has been studied withpulse widths from femtoseconds to milliseconds the mostcommon ablation laser (used for the majority of experi-ments in Table II) is a pulsed NdYAG which can easilydeliver up to 100 mJ of energy in a few ns Either thefundamental (1064 nm) or first harmonic (532 nm) modesare used and neither seems to have a distinct advantageover the other except for certain technical conveniencesafforded by a visible laser

Vapors of metals such as Na [3] or Yb [5] can be easilyproduced by ablation of the solid metal however cre-ation of gas phase molecules by laser ablation can bemore complicated Molecules with a stable solid phase(such as PbO[3]) can be created by simply using the solidphase as a precursor but unstable molecules require care-ful choice of precursor It is often the case that the de-sired diatomic molecule MX has a stable solid form MaXb

which is a glass or ceramic as is the case with BaF CaHSrF YO and ThO (and others) In such cases experi-ence has shown that pressing (and sometimes sintering)a very fine powder of the stable solid often yields the bestablation target [7 9]

The most important advantage of laser ablation is thatit can be used to create a very wide variety of atomsand molecules with high flux [4] The main drawback isthat ablation is typically a ldquoviolentrdquo non-thermal pro-cess that can result in unusual behavior of the gases inthe buffer cell and in the resulting beam Ablation tendsto give fairly inconsistent yields[7 9] and can create plas-mas and complex plumes[64] with temperatures of severalthousand K[65] However buffer gas cells can be designedto allow proper thermalization (see Section II A 3) of thespecies which can mitigate many of these problems

Capillary filling If the species of interest has an ap-preciable vapor pressure at convenient temperatures onecan simply flow the species into the cell through a gas fillline just like the buffer gas[66] This method is simplein principle but in practice it introduces some technicalchallenges The cell and fill line must be carefully engi-neered to keep the fill line warm while keeping the cellcold and preventing freezing of the species at the pointwhere the fill line enters the cell For species with anappreciable vapor pressure at room temperature such asO2 [5] a properly-designed fill line can be attached di-rectly to the buffer gas cell to flow the species For speciesthat require higher temperatures to obtain an apprecia-ble vapor pressure for example a 600 K oven to produceatomic K vapor a complex multi-stage cell must be con-structed [67] to keep heat from the oven out of the cellas shown in Figure 3

The primary advantage of the capillary filling methodis that it can be used to create high-flux beams that arecontinuous and robust The main drawback is the limitednumber of species of interest that have appreciable vapor

6

300 K

Neon buffer gas inputs

Potassium oven 550 K

Intermediate region 100 K

Cell15 K

Liquid potassium

Thermal standoffs

20 K

Needle 550 K

Potassium Beam

Buffer gas inSpecies in

Beam

Cold cell

FIG 3 Left simple capillary filling scheme for loading a molecule (large red circles) with vapor pressure at 300 K such asO2[5] or ND3[15 67] The species flows down a warm gas line and is mixed with the buffer gas (small blue circles) which flowsdown a cold gas line Right Scheme for capillary injection of K atoms (large red circles) from a 550 K oven into a 15 K neon(small blue circles) buffer gas cell Unlike the simple capillary scheme K atoms cannot simply flow down a warm gas line intothe buffer gas cell as the thermal conduction and blackbody heat loads would heat the cell too much Instead a multi-stagecell with thermal standoffs heat links at each stage must be used to reduce the heat load on the cell to acceptable levels Theamount of neon buffer gas introduced into the intermediate temperature regions must be sufficiently large to ensure that theK atoms are entrained in the flow and make it into the cold cell Reproduced from [Patterson D Rasmussen J amp Doyle JM New J Phys 11(5) 055018 (2009) httpdxdoiorg1010881367-2630115055018] with permission from the Instituteof Physics

pressure at temperatures low enough so that the methodis feasible As the required temperature increases thetechnical challenges rapidly multiply (see Figure 3)

It should be noted that regardless of technique thedensity of the species is typically (though not in the caseof some capillary filling schemes[15 16]) lt 1 of thenumber density of the buffer gas This fact will be im-portant later on because it allows us to treat the the gasflow properties as being determined solely by the buffergas with the species as a trace component

3 Thermalization

Before the species flows out of the cell it must undergoenough collisions with the cold buffer gas to become ther-malized to the cell temperature A simple estimate of thenecessary number of collisions can be obtained by ap-proximating the species and buffer gases as hard spheres[68 69] The mean loss in kinetic energy of the speciesper collision with a buffer gas atom results in a meantemperature change of

∆Ts = minus(Ts minus Tb)κ where κ equiv (mb +ms)2

2mbms (3)

Here T denotes temperature m denotes mass and thesubscripts ldquobrdquo and ldquosrdquo refer to the buffer gas and speciesof interest respectively Therefore the temperature ofthe species after N collisions Ts(N ) will vary as

Ts(N )minus Ts(N minus 1) = minus(Ts(N minus 1)minus Tb)κ (4)

If we treat N as large and the temperature change percollision as small we can approximate this discrete equa-

tion as a differential equation

dTs(N )

dN= minus(Ts(N )minus Tb)κ (5)

Solving this differential equation yields the ratio betweenthe species and buffer gas temperatures

Ts(N )

Tb= 1 +

(Ts(0)

Tbminus 1

)eminusNκ (6)

asymp 1 +Ts(0)

TbeminusNκ (7)

where in the last equality we have assumed that thespecies is introduced at a temperature much larger thanthe cell (and therefore buffer gas) temperature ieTs(0) Tb If we estimate mb sim 10 amu ms sim 100amu Tb sim 10 K and Ts(0) sim 1000 K the species shouldbe within a few percent of the buffer gas temperature af-ter sim 50 collisions Under typical cell geometry and flowconditions the thermalization time is a few millisecondsas shown in Figure 4

While this simple model is good enough to obtain anestimate of the thermalization it is not exact In ana-lyzing thermalization of ablation-loaded YbF moleculesin a helium buffer gas Skoff et al [70] found that themodel above did not fit the data however replacing theconstant buffer gas temperature with an initially largertemperature which then exponentially decays to the celltemperature resulted in good fits The physical moti-vation for this model is that the buffer gas is initiallyheated by the ablation and then cools as the buffer gasre-thermalizes with the cell walls Skoff et al presentdetailed analysis of thermalization in a buffer gas andthe reader is referred to their work for details

5

temperature T0 by a cryogenic refrigerator typically be-tween 1 K and 20 K Buffer gas of mass mb is introducedinto the cell volume by a long thin tube or ldquofill linerdquoThe buffer gas exits the cell through an aperture of char-acteristic length daperture and area Aaperture (for the casewhere the aperture is a rectangle daperture is the shorterdimension) Typical values are daperture = 1 minus 5 mmand Aaperture = 5minus 25 mm2 A buffer gas flow rate f0b

into the cell can be set with a mass flow controller Herethe subscript ldquobrdquo refers to the buffer gas and ldquo0rdquo refersto conditions in the cell at steady-state or ldquostagnationrdquoconditions The most commonly used unit for flow is thestandard cubic centimeter per minute or SCCM whichequals approximately 45 times 1017 gas atoms per secondTypical flow rates for buffer gas beams are f0b = 1minus100SCCM Technical details of cell construction and con-struction of a buffer gas cooled beam apparatus in gen-eral are discussed in Section II E

At steady state the flow rate out of the cell is givenby the molecular conductance of the aperture fout =14n0bv0bAaperture where

v0b =

radic8kBT0

πmb(1)

is the mean thermal velocity of the buffer gas inside thecell (about 140 m sminus1 for 4 K helium or 17 K neon) kB isBoltzmannrsquos constant and n0b is the stagnation numberdensity of buffer gas atoms Therefore the number den-sity n0b is set by controlling the flow via the steady-staterelationship fout = f0b or

n0b =4f0b

Aaperturev0b (2)

With typical cell aperture sizes and temperatures a flowof 1 SCCM corresponds to a stagnation density of about1015 cmminus3 so typical values for the stagnation density are1015minus1017 cmminus3 Note that in the above equation we as-sume that the flow through the aperture is purely molec-ular At higher number densities the flow can becomemore fluid-like and then the flow rate out will changehowever the difference is about a factor of two [61] sothe above equation is suitable for approximation

2 Introduction of species

The species of interest can be introduced into the buffergas cell through a number of methods [4] including laserablation laser-induced atomic desorption (LIAD) beaminjection capillary filling and discharge etching Themost commonly used techniques for creation of buffergas cooled beams are laser ablation and capillary fillingso we will focus here on those two methods

Laser ablation In laser ablation (see Figure 2) a highenergy pulsed laser is focused onto a solid precursor tar-get After receiving the laser pulse the solid precur-sor can eject gas-phase atoms or molecules of the de-sired species often along with other detritus The actual

mechanism for how gas phase species results from the ab-lation of the solid precursor is not simple and dependson the relationship between the length of the laser pulseand the time constants for electronic and lattice heating[62 63] While pulsed ablation has been studied withpulse widths from femtoseconds to milliseconds the mostcommon ablation laser (used for the majority of experi-ments in Table II) is a pulsed NdYAG which can easilydeliver up to 100 mJ of energy in a few ns Either thefundamental (1064 nm) or first harmonic (532 nm) modesare used and neither seems to have a distinct advantageover the other except for certain technical conveniencesafforded by a visible laser

Vapors of metals such as Na [3] or Yb [5] can be easilyproduced by ablation of the solid metal however cre-ation of gas phase molecules by laser ablation can bemore complicated Molecules with a stable solid phase(such as PbO[3]) can be created by simply using the solidphase as a precursor but unstable molecules require care-ful choice of precursor It is often the case that the de-sired diatomic molecule MX has a stable solid form MaXb

which is a glass or ceramic as is the case with BaF CaHSrF YO and ThO (and others) In such cases experi-ence has shown that pressing (and sometimes sintering)a very fine powder of the stable solid often yields the bestablation target [7 9]

The most important advantage of laser ablation is thatit can be used to create a very wide variety of atomsand molecules with high flux [4] The main drawback isthat ablation is typically a ldquoviolentrdquo non-thermal pro-cess that can result in unusual behavior of the gases inthe buffer cell and in the resulting beam Ablation tendsto give fairly inconsistent yields[7 9] and can create plas-mas and complex plumes[64] with temperatures of severalthousand K[65] However buffer gas cells can be designedto allow proper thermalization (see Section II A 3) of thespecies which can mitigate many of these problems

Capillary filling If the species of interest has an ap-preciable vapor pressure at convenient temperatures onecan simply flow the species into the cell through a gas fillline just like the buffer gas[66] This method is simplein principle but in practice it introduces some technicalchallenges The cell and fill line must be carefully engi-neered to keep the fill line warm while keeping the cellcold and preventing freezing of the species at the pointwhere the fill line enters the cell For species with anappreciable vapor pressure at room temperature such asO2 [5] a properly-designed fill line can be attached di-rectly to the buffer gas cell to flow the species For speciesthat require higher temperatures to obtain an apprecia-ble vapor pressure for example a 600 K oven to produceatomic K vapor a complex multi-stage cell must be con-structed [67] to keep heat from the oven out of the cellas shown in Figure 3

The primary advantage of the capillary filling methodis that it can be used to create high-flux beams that arecontinuous and robust The main drawback is the limitednumber of species of interest that have appreciable vapor

6

300 K

Neon buffer gas inputs

Potassium oven 550 K

Intermediate region 100 K

Cell15 K

Liquid potassium

Thermal standoffs

20 K

Needle 550 K

Potassium Beam

Buffer gas inSpecies in

Beam

Cold cell

FIG 3 Left simple capillary filling scheme for loading a molecule (large red circles) with vapor pressure at 300 K such asO2[5] or ND3[15 67] The species flows down a warm gas line and is mixed with the buffer gas (small blue circles) which flowsdown a cold gas line Right Scheme for capillary injection of K atoms (large red circles) from a 550 K oven into a 15 K neon(small blue circles) buffer gas cell Unlike the simple capillary scheme K atoms cannot simply flow down a warm gas line intothe buffer gas cell as the thermal conduction and blackbody heat loads would heat the cell too much Instead a multi-stagecell with thermal standoffs heat links at each stage must be used to reduce the heat load on the cell to acceptable levels Theamount of neon buffer gas introduced into the intermediate temperature regions must be sufficiently large to ensure that theK atoms are entrained in the flow and make it into the cold cell Reproduced from [Patterson D Rasmussen J amp Doyle JM New J Phys 11(5) 055018 (2009) httpdxdoiorg1010881367-2630115055018] with permission from the Instituteof Physics

pressure at temperatures low enough so that the methodis feasible As the required temperature increases thetechnical challenges rapidly multiply (see Figure 3)

It should be noted that regardless of technique thedensity of the species is typically (though not in the caseof some capillary filling schemes[15 16]) lt 1 of thenumber density of the buffer gas This fact will be im-portant later on because it allows us to treat the the gasflow properties as being determined solely by the buffergas with the species as a trace component

3 Thermalization

Before the species flows out of the cell it must undergoenough collisions with the cold buffer gas to become ther-malized to the cell temperature A simple estimate of thenecessary number of collisions can be obtained by ap-proximating the species and buffer gases as hard spheres[68 69] The mean loss in kinetic energy of the speciesper collision with a buffer gas atom results in a meantemperature change of

∆Ts = minus(Ts minus Tb)κ where κ equiv (mb +ms)2

2mbms (3)

Here T denotes temperature m denotes mass and thesubscripts ldquobrdquo and ldquosrdquo refer to the buffer gas and speciesof interest respectively Therefore the temperature ofthe species after N collisions Ts(N ) will vary as

Ts(N )minus Ts(N minus 1) = minus(Ts(N minus 1)minus Tb)κ (4)

If we treat N as large and the temperature change percollision as small we can approximate this discrete equa-

tion as a differential equation

dTs(N )

dN= minus(Ts(N )minus Tb)κ (5)

Solving this differential equation yields the ratio betweenthe species and buffer gas temperatures

Ts(N )

Tb= 1 +

(Ts(0)

Tbminus 1

)eminusNκ (6)

asymp 1 +Ts(0)

TbeminusNκ (7)

where in the last equality we have assumed that thespecies is introduced at a temperature much larger thanthe cell (and therefore buffer gas) temperature ieTs(0) Tb If we estimate mb sim 10 amu ms sim 100amu Tb sim 10 K and Ts(0) sim 1000 K the species shouldbe within a few percent of the buffer gas temperature af-ter sim 50 collisions Under typical cell geometry and flowconditions the thermalization time is a few millisecondsas shown in Figure 4

While this simple model is good enough to obtain anestimate of the thermalization it is not exact In ana-lyzing thermalization of ablation-loaded YbF moleculesin a helium buffer gas Skoff et al [70] found that themodel above did not fit the data however replacing theconstant buffer gas temperature with an initially largertemperature which then exponentially decays to the celltemperature resulted in good fits The physical moti-vation for this model is that the buffer gas is initiallyheated by the ablation and then cools as the buffer gasre-thermalizes with the cell walls Skoff et al presentdetailed analysis of thermalization in a buffer gas andthe reader is referred to their work for details

6

300 K

Neon buffer gas inputs

Potassium oven 550 K

Intermediate region 100 K

Cell15 K

Liquid potassium

Thermal standoffs

20 K

Needle 550 K

Potassium Beam

Buffer gas inSpecies in

Beam

Cold cell

FIG 3 Left simple capillary filling scheme for loading a molecule (large red circles) with vapor pressure at 300 K such asO2[5] or ND3[15 67] The species flows down a warm gas line and is mixed with the buffer gas (small blue circles) which flowsdown a cold gas line Right Scheme for capillary injection of K atoms (large red circles) from a 550 K oven into a 15 K neon(small blue circles) buffer gas cell Unlike the simple capillary scheme K atoms cannot simply flow down a warm gas line intothe buffer gas cell as the thermal conduction and blackbody heat loads would heat the cell too much Instead a multi-stagecell with thermal standoffs heat links at each stage must be used to reduce the heat load on the cell to acceptable levels Theamount of neon buffer gas introduced into the intermediate temperature regions must be sufficiently large to ensure that theK atoms are entrained in the flow and make it into the cold cell Reproduced from [Patterson D Rasmussen J amp Doyle JM New J Phys 11(5) 055018 (2009) httpdxdoiorg1010881367-2630115055018] with permission from the Instituteof Physics

pressure at temperatures low enough so that the methodis feasible As the required temperature increases thetechnical challenges rapidly multiply (see Figure 3)

It should be noted that regardless of technique thedensity of the species is typically (though not in the caseof some capillary filling schemes[15 16]) lt 1 of thenumber density of the buffer gas This fact will be im-portant later on because it allows us to treat the the gasflow properties as being determined solely by the buffergas with the species as a trace component

3 Thermalization

Before the species flows out of the cell it must undergoenough collisions with the cold buffer gas to become ther-malized to the cell temperature A simple estimate of thenecessary number of collisions can be obtained by ap-proximating the species and buffer gases as hard spheres[68 69] The mean loss in kinetic energy of the speciesper collision with a buffer gas atom results in a meantemperature change of

∆Ts = minus(Ts minus Tb)κ where κ equiv (mb +ms)2

2mbms (3)

Here T denotes temperature m denotes mass and thesubscripts ldquobrdquo and ldquosrdquo refer to the buffer gas and speciesof interest respectively Therefore the temperature ofthe species after N collisions Ts(N ) will vary as

Ts(N )minus Ts(N minus 1) = minus(Ts(N minus 1)minus Tb)κ (4)

If we treat N as large and the temperature change percollision as small we can approximate this discrete equa-

tion as a differential equation

dTs(N )

dN= minus(Ts(N )minus Tb)κ (5)

Solving this differential equation yields the ratio betweenthe species and buffer gas temperatures

Ts(N )

Tb= 1 +

(Ts(0)

Tbminus 1

)eminusNκ (6)

asymp 1 +Ts(0)

TbeminusNκ (7)

where in the last equality we have assumed that thespecies is introduced at a temperature much larger thanthe cell (and therefore buffer gas) temperature ieTs(0) Tb If we estimate mb sim 10 amu ms sim 100amu Tb sim 10 K and Ts(0) sim 1000 K the species shouldbe within a few percent of the buffer gas temperature af-ter sim 50 collisions Under typical cell geometry and flowconditions the thermalization time is a few millisecondsas shown in Figure 4

While this simple model is good enough to obtain anestimate of the thermalization it is not exact In ana-lyzing thermalization of ablation-loaded YbF moleculesin a helium buffer gas Skoff et al [70] found that themodel above did not fit the data however replacing theconstant buffer gas temperature with an initially largertemperature which then exponentially decays to the celltemperature resulted in good fits The physical moti-vation for this model is that the buffer gas is initiallyheated by the ablation and then cools as the buffer gasre-thermalizes with the cell walls Skoff et al presentdetailed analysis of thermalization in a buffer gas andthe reader is referred to their work for details

7

(b)

abs

sig

() (a)

minus2 0 2 4 6 8 10 12 140

5

10

15

time (ms)

sigτexp=16ms

05 1 15 2 25 3 3522242628

332343638

442

time after ablation (ms)

FIG 4 Thermalization of CaH in a helium buffer gascell of temperature sim 2 K[10] (a) The absorption sig-nal from a single ablation pulse (b) Temperature of theCaH molecules vs time after ablation determined byDoppler spectroscopy Reproduced from [Lu H et alPhys Chem Chem Phys 13 18986-18990 (2011)httpdxdoiorg101039c1cp21206k] by permission of thePCCP Owner Societies

Thus the cryogenic cell should be designed such thatthe species experiences at least 100 collisions or so beforeexiting the cell To find the thermalization length iethe typical distance that the species will travel beforebeing thermalized we need the mean free path of thespecies in the buffer gas which is given approximatelyby[71]

λsminusb0 =(n0bσbminuss)

minus1radic1 +msmb

asymp Aaperturev0b

4f0bσbminussradicmsmb

(8)

where σbminuss is the thermally averaged elastic collisioncross section (since the cross section typically varies withtemperature) we assume ms mb and have used Eq(2) in the second step For typical values of σbminuss asymp 10minus14

cm2 this mean free path is sim 01 mm Therefore thethermalization length for the species in the buffer gascell is typically no more than 100times 01 mm = 1 cm

Note that the above discussion has pertained only totranslational temperatures yet buffer gas cooling is alsoeffective at thermalization of internal states Typical ro-tational relaxation cross sections for molecules with he-lium buffer gas are typically of order σrot sim 10minus(15minus16)

cm2 which means that around σbminussσrot sim 10 minus 100collisions are required to relax (or ldquoquenchrdquo) a rota-tional state[4] Since this is a typical number of col-lisions required for motional thermalization buffer gascooling can be used to make samples of molecules whichare both translationally and rotationally cold Vibra-tional relaxation is less efficient since the cross sectionsfor vibrational quenching are typically several order ofmagnitude smaller than those for translational or rota-tional relaxation[4] Several experiments[9 56 72] haveseen the vibrational degree of freedom not in thermalequilibrium with the rotational or translational degrees

of freedom Further discussion of internal relaxation ofmolecules may be found elsewhere[1 4 61]

4 Diffusion

Once the species of interest is introduced into the celland thermalized we must consider the diffusion of thespecies in the buffer gas Understanding the diffusionis crucial since the buffer gas cell is typically kept at atemperature where the species of interest has essentiallyno vapor pressure and if it is allowed to diffuse to thecell walls before exiting the cell it will freeze and be lostThe diffusion constant for the species diffusing into thebuffer gas is[71]

D =3

16(n0s + n0b)σbminuss

(2πkBT0

micro

)12

(9)

where micro = msmb(ms + mb) is the reduced mass Itshould be noted that different works use different formsfor the diffusion coefficient [4] though they agree towithin factors of order unity and are all suitable for mak-ing estimates Making the approximations n0s n0b

and ms mb we find

D =3

16n0bσbminuss

(2πkBT0

mb

)12

=3π

32

v0b

n0bσbminuss (10)

After a time t a species molecule will have a mean-squared displacement of

〈∆x2〉(t) = 6Dt =9π

16

v0b

n0bσbminusst (11)

from its starting point[73] Since the characteristic lengthof the cell interior is the cross-sectional length dcell wecan define the diffusion timescale τdiff as 〈∆x2〉(τdiff ) =d2cell asymp Acell or

τdiff =16

9π

Acelln0bσbminussv0b

(12)

The diffusion time is typically 1-10 msSkoff et al [70] performed a detailed theoretical anal-

ysis and compared the results to measured absorptionimages in order to understand diffusion of YbF and Li ina helium buffer gas The diffusion behavior was studiedas a function of both helium density and cell temperaturefor both species At low densities they verified the linearrelationship between τdiff and n0b from Eq (12) and adeparture from linearity at high density While this wasnot the first time that this relationship was observed[74]their data and analysis allows for an informative possi-ble explanation At low buffer gas densities the ablationejects the YbF molecules so that they are distributed allacross the cell and the diffusion model discussed aboveis valid At high density the YbF molecules are local-ized near the target and therefore diffuse only through

8

higher-order modes with shorter timescales Previousmodels for this behavior included formation of dimersor clusters[74] however the model proposed by Skoff etal[70] seems reasonable considering that this behaviorhas been seen for several species including both atomsand molecules[56 70 74ndash76]

5 Extraction from the buffer cell

So far we have not considered the beam at all havingfocused entirely on the in-cell dynamics Once the speciesof interest is created in the gas phase and cooled in thebuffer gas cell it is necessary that the species flow outof the cell so that it can create a beam As discussedabove extraction of the species from the cell must occurfaster than the diffusion timescale τdiff so letrsquos work outan estimate of the extraction or ldquopumpoutrdquo time Therate at which the buffer gas out of the cell is given by themolecular conductance of the cell aperture

Nb =1

4Nbv0bAapertureVcell (13)

where Nb indicates the total number of buffer gas atomsin the cell and Nb is the rate at which they are flowingout of the cell The solution is an exponential decay withtimescale τpump the pumpout time given by

τpump =4Vcell

v0bAaperture (14)

The pumpout time is typically around 1-10 ms Notethat the pumpout time also sets the duration of themolecular pulse in the case of a beam with pulsed load-ing If the buffer gas density in the cell is high enoughthat the species of interest follows the buffer gas flowthen this is a good estimate for the pumpout time for thespecies of interest as well We now define[5] a dimension-less parameter to characterize the extraction behavior ofthe cell

γcell equivτdiffτpump

=4

9π

n0bσbminussAapertureLcell

asymp σbminussf0b

Lcellv0b (15)

where in the last approximation we dropped the order-unity prefactor as this is simply an estimate This pa-rameter γcell characterizes the extraction behavior andcan be divided into two limits (see Figure 5)

For γcell 1 the diffusion to the walls is faster thanthe extraction from the cell so the majority of speciesmolecules will stick to the cell walls and be lost Thisldquodiffusion limitrdquo [5] is characterized by low output fluxof the molecular species and is typically accompaniedby a velocity distribution in the beam that is similarto that inside the cell [3] In this limit increasing theflow (thereby increasing γcell) has the effect of increasingthe extraction efficiency fext defined as the fraction ofmolecules created in the cell which escape into the beam

The precise dependence of fext on γcell is highly variableand has been observed to be approximately linear expo-nential or cubic for the various species which have beenexamined[3 5 7 9]

For γcell amp 1 the molecules are mostly extractedfrom the cell before sticking to the walls resulting in abeam of increased brightness This limit called ldquohydro-dynamic entrainmentrdquo or ldquohydrodynamic enhancementrdquo[5] is characterized by high output flux of the molecularspecies and is typically accompanied by velocity distri-bution which can vary considerably from that presentinside the cell In this regime the extraction efficiencyplateaus and can be as high as gt40[5 9] but is typi-cally observed to be around 10

It should be noted that while the parameter γcell canbe used to estimate the extraction efficiency quite well[5 7 9] there have been instances where this simple esti-mate breaks down According to Eq (15) the parameterγcell has no explicit dependence on the aperture diame-ter however Hutzler et al [7] found that while varyingthe cell aperture diameter in situ without varying otherparameters the extraction efficiency of a ThO beam in aneon buffer gas began to decrease with decreasing aper-ture size as shown in Figure 5 These measurementssuggest that the cell aperture diameter should not betoo small ( 3 mm) in order to achieve good extraction

Regardless of the value for γcell thermalization (seeSection II A 3) must occur on a timescale faster than ei-ther τpump or τdiff to cool the species Since neither τdiffnor τpump impose strict constraints on the cell geometryit is possible to have both good thermalization and effi-cient extraction as demonstrated by the large number ofhigh flux cold beams created with the buffer gas method(see Table II)

B Properties of buffer gas cooled beams

Now that we have reviewed the requirements for intro-duction of the species thermalization and extraction wemay focus on the properties of the resulting beam

1 Characterization of gas flow regimes

As mentioned earlier the species of interest typicallyconstitutes lt 1 of the number density of the buffergas so the flow properties are determined entirely bythe buffer gas In this section we will introduce theReynolds number which we will use to characterize gasflow Note that the Reynolds (and Knudsen) numberrefers exclusively to the buffer gas and not the speciesof interest (for our treatment) For a more thorough dis-cussion about gas flow see texts about beams and gasdynamics[1 61 81]

The Reynolds number is defined as the ratio of inertial

9

Species OutputBrightness v||[m sminus1] ∆v[m sminus1]

Molecules

BaF[12] 16 times 1011 srminus1 pulseminus1 ndash ndash

CaH[10]A 5 minus 500 times 108 srminus1 pulseminus1 40ndash95 65

CH3F[16]B ndash 45 35

CF3H [16]B ndash 40 35

H2CO[15]B ndash ndash ndash

ND3[67]B 3 minus 200 times 108 sminus1 60ndash150 25ndash100

ND3[15 16]B 1 minus 10 times 1010 sminus1 65 50

ND3[60]B 1 times 1011 sminus1 100 ndash

O2[5]B 3 times 1012 sminus1 ndash ndash

PbO[3] 3 minus 100 times 108 srminus1 pulseminus1 40ndash80 30ndash40

SrF[9] 1 minus 12 times 1010 srminus1 pulseminus1 125ndash200 60ndash80

SrO[77] 3 minus 100 times 109 srminus1 pulseminus1 65ndash180 35ndash50

ThO[7] 1 minus 100 times 1010 pulseminus1 120ndash200 30ndash45

YbF[70 78] ndash ndash ndash

YO[79] ndash 160 ndash

Atoms

K[67]D 1 times 1016 srminus1 sminus1 130 120

Na[3] 2 minus 400 times 108 srminus1 pulseminus1 80ndash135 60-120

Rb[80]CD 3 times 1010 sminus1 190 25ndash30

Yb[5] 5 times 1013 srminus1 pulseminus1 130 ndash

Yb[5]A 5 times 1010 pulseminus1 35 ndash

TABLE II A list of molecules which have been cooled in buffer gas beams along with any measured properties The output iseither reported as molecules per state per pulse for pulsed beams or per second for continous beams If an angular spread wasmeasured the brightness is reported as molecules per state per unit steradian (sr) per pulse or per second v is the forwardvelocity and ∆v is the full-width at half-maximum of the forward velocity distribution Beams are ablation loaded and pulsedunless otherwise noted A dash (ndash) means that the beam property was not reported in the indicated references Notes A =slowing cell (see Section II C 2) B = continuous beam velocity selected or guided by electromagnetic fields C = flux reportedis after beam collimation D = continuous beam loaded via capillary

to viscous forces in a fluid flow[82 83]

Re =FintertialFviscous

=ρw2d2

microwd=ρwd

micro (16)

where ρ is the density w is the flow velocity micro isthe (dynamic) viscosity and d is a characteristic lengthscale In terms of kinetic quantities we make use ofthe relationship between mean free path density andviscosity[81 83]

micro asymp 1

2ρλv (17)

where v is the mean thermal velocity and λ is the meanfree path to express the Reynolds number as

Re =ρw

12ρλvd

asymp 2wv

λdasymp 2

Ma

Kn (18)

where wv asymp Ma is the Mach number and Kn = λdis the Knudsen number The Mach number for a gas ofatomic weight m is defined as Ma = wc where

c equivradicγkBT

m(19)

is the speed of sound in the gas and γ is the specific heatratio The value of γ for a monoatomic gas (the relevantcase for buffer gas beams) is γ = 53 so in this case

c = v

radic5π

8asymp 08v (20)

and we are justified in approximating Ma asymp wv Thisgives us the important von Karman relation [81 83]

Ma asymp 1

2KnRe (21)

To relate these quantities to the case under consider-ation we must mention two important facts about gasflow from an aperture into a vacuum [1] First themost relevant geometrical length scale which governs theflow behavior is the aperture diameter since the prop-erties of the beam are set almost entirely by collisionsthat occur near the aperture Therefore the characteris-tic length scale appearing in the formula for Re shouldbe d = daperture Second near the aperture the gasatoms are traveling near their mean thermal velocity soMa asymp 1 Combining these facts with Eqs (2) and (8)

10

0 05 10 15 20 25

06

05

04

03

02

01

0

Frac

tion

Extr

acte

d in

toBe

am

15 2 25 3 35 4 4510minus2

10minus1

100

Aperture Size [mm]

Frac

tion

Ext

ract

ed in

to B

eam

Neon Buffer GasHelium Buffer Gas

FIG 5 Extraction from a buffer gas cell Top Frac-tion of Yb atoms extracted into a helium cooled buffer gasbeam vs the parameter γcell (Eq (15)) Reproducedfrom [Patterson D amp Doyle J M J Chem Phys 126154307 (2007) httpdxdoiorg10106312717178] Copy-right (2007) American Institute of Physics Bottom Frac-tion of ThO molecules extracted into a helium (times) andneon () buffer gas vs the cell aperture size with afixed flow rate Reproduced from [Hutzler N et alPhys Chem Chem Phys 13 18976-18985 (2011)httpdxdoiorg101039c1cp20901a (2011)] by permissionof the PCCP Owner Societies

allows us to write the relevant expression for Re in oursituation

Re asymp 2dapertureλbminusb0

asymp 8radic

2f0bσbminusbdaperturev0b

(22)

We shall parameterize the beam by the Reynolds num-ber Re of the buffer gas flow at the aperture Ac-cording to Eq (22) Re is approximately 2Knminus1 =2dapertureλbminusb or twice the number of collisions withinone aperture diameter of the aperture ie ldquonearrdquo theaperture From Eqs (22) and (2) we can see that thein-cell buffer gas density buffer gas flow rate Reynolds

number and number of collisions near the aperture areall linearly related The possible types of flow can beroughly divided into three Reynolds number regimeseach of which will be discussed in the remainder of thissection

bull Effusive regime Re 1 In this regime there aretypically no collisions near the aperture so thebeam properties are simply a sampling of the ther-mal distribution present in the cell This regime isdiscussed further in Section II D 1

bull Intermediate or partially hydrodynamic regime1 Re 100 Here there are enough collisionsnear the aperture to change the beam propertiesfrom those present in the cell but not enough sothat the flow is fluid-like Buffer gas beams typi-cally operate in this regime however we will seeexamples of buffer gas beams in all three regimes

bull Fully hydrodynamic or ldquosupersonicrdquo regime 100 Re In this regime the buffer gas begins to behavemore like a fluid and the beam properties becomesimilar to those of a beam cooled via supersonic ex-pansion This regime is discussed further in SectionII D 2

2 Forward velocity

asymp1 asymp10 asymp100Reynolds Number Re

Forw

ard

Velo

city

v ||

14v0b

12v0s

Effusive Intermediate Supersonic

FIG 6 A schematic representation of beam forward veloc-ity vs Reynolds number In the effusive regime (Re 1)the forward velocity is the thermal velocity of the (heavy)species In the intermediate regime collisions of the specieswith the buffer gas near the aperture accelerate the speciesthe velocity increase is linear with the Reynolds number untilRe asymp 10 and then begins to asymptote to the final value Inthe supersonic regime (Re amp 100) the species has been fullyaccelerated to the forward velocity of the (light) buffer gasEach of these regimes is discussed in detail below

If the beam is in the effusive regime then there aretypically no collisions near the aperture and the forwardvelocity of the beam vs is given by the forward velocity

9

Species OutputBrightness v||[m sminus1] ∆v[m sminus1]

Molecules

BaF[12] 16 times 1011 srminus1 pulseminus1 ndash ndash

CaH[10]A 5 minus 500 times 108 srminus1 pulseminus1 40ndash95 65

CH3F[16]B ndash 45 35

CF3H [16]B ndash 40 35

H2CO[15]B ndash ndash ndash

ND3[67]B 3 minus 200 times 108 sminus1 60ndash150 25ndash100

ND3[15 16]B 1 minus 10 times 1010 sminus1 65 50

ND3[60]B 1 times 1011 sminus1 100 ndash

O2[5]B 3 times 1012 sminus1 ndash ndash

PbO[3] 3 minus 100 times 108 srminus1 pulseminus1 40ndash80 30ndash40

SrF[9] 1 minus 12 times 1010 srminus1 pulseminus1 125ndash200 60ndash80

SrO[77] 3 minus 100 times 109 srminus1 pulseminus1 65ndash180 35ndash50

ThO[7] 1 minus 100 times 1010 pulseminus1 120ndash200 30ndash45

YbF[70 78] ndash ndash ndash

YO[79] ndash 160 ndash

Atoms

K[67]D 1 times 1016 srminus1 sminus1 130 120

Na[3] 2 minus 400 times 108 srminus1 pulseminus1 80ndash135 60-120

Rb[80]CD 3 times 1010 sminus1 190 25ndash30

Yb[5] 5 times 1013 srminus1 pulseminus1 130 ndash

Yb[5]A 5 times 1010 pulseminus1 35 ndash

TABLE II A list of molecules which have been cooled in buffer gas beams along with any measured properties The output iseither reported as molecules per state per pulse for pulsed beams or per second for continous beams If an angular spread wasmeasured the brightness is reported as molecules per state per unit steradian (sr) per pulse or per second v is the forwardvelocity and ∆v is the full-width at half-maximum of the forward velocity distribution Beams are ablation loaded and pulsedunless otherwise noted A dash (ndash) means that the beam property was not reported in the indicated references Notes A =slowing cell (see Section II C 2) B = continuous beam velocity selected or guided by electromagnetic fields C = flux reportedis after beam collimation D = continuous beam loaded via capillary

to viscous forces in a fluid flow[82 83]

Re =FintertialFviscous

=ρw2d2

microwd=ρwd

micro (16)

where ρ is the density w is the flow velocity micro isthe (dynamic) viscosity and d is a characteristic lengthscale In terms of kinetic quantities we make use ofthe relationship between mean free path density andviscosity[81 83]

micro asymp 1

2ρλv (17)

where v is the mean thermal velocity and λ is the meanfree path to express the Reynolds number as

Re =ρw

12ρλvd

asymp 2wv

λdasymp 2

Ma

Kn (18)

where wv asymp Ma is the Mach number and Kn = λdis the Knudsen number The Mach number for a gas ofatomic weight m is defined as Ma = wc where

c equivradicγkBT

m(19)

is the speed of sound in the gas and γ is the specific heatratio The value of γ for a monoatomic gas (the relevantcase for buffer gas beams) is γ = 53 so in this case

c = v

radic5π

8asymp 08v (20)

and we are justified in approximating Ma asymp wv Thisgives us the important von Karman relation [81 83]

Ma asymp 1

2KnRe (21)

To relate these quantities to the case under consider-ation we must mention two important facts about gasflow from an aperture into a vacuum [1] First themost relevant geometrical length scale which governs theflow behavior is the aperture diameter since the prop-erties of the beam are set almost entirely by collisionsthat occur near the aperture Therefore the characteris-tic length scale appearing in the formula for Re shouldbe d = daperture Second near the aperture the gasatoms are traveling near their mean thermal velocity soMa asymp 1 Combining these facts with Eqs (2) and (8)

10

0 05 10 15 20 25

06

05

04

03

02

01

0

Frac

tion

Extr

acte

d in

toBe

am

15 2 25 3 35 4 4510minus2

10minus1

100

Aperture Size [mm]

Frac

tion

Ext

ract

ed in

to B

eam

Neon Buffer GasHelium Buffer Gas

FIG 5 Extraction from a buffer gas cell Top Frac-tion of Yb atoms extracted into a helium cooled buffer gasbeam vs the parameter γcell (Eq (15)) Reproducedfrom [Patterson D amp Doyle J M J Chem Phys 126154307 (2007) httpdxdoiorg10106312717178] Copy-right (2007) American Institute of Physics Bottom Frac-tion of ThO molecules extracted into a helium (times) andneon () buffer gas vs the cell aperture size with afixed flow rate Reproduced from [Hutzler N et alPhys Chem Chem Phys 13 18976-18985 (2011)httpdxdoiorg101039c1cp20901a (2011)] by permissionof the PCCP Owner Societies

allows us to write the relevant expression for Re in oursituation

Re asymp 2dapertureλbminusb0

asymp 8radic

2f0bσbminusbdaperturev0b

(22)

We shall parameterize the beam by the Reynolds num-ber Re of the buffer gas flow at the aperture Ac-cording to Eq (22) Re is approximately 2Knminus1 =2dapertureλbminusb or twice the number of collisions withinone aperture diameter of the aperture ie ldquonearrdquo theaperture From Eqs (22) and (2) we can see that thein-cell buffer gas density buffer gas flow rate Reynolds

number and number of collisions near the aperture areall linearly related The possible types of flow can beroughly divided into three Reynolds number regimeseach of which will be discussed in the remainder of thissection

bull Effusive regime Re 1 In this regime there aretypically no collisions near the aperture so thebeam properties are simply a sampling of the ther-mal distribution present in the cell This regime isdiscussed further in Section II D 1

bull Intermediate or partially hydrodynamic regime1 Re 100 Here there are enough collisionsnear the aperture to change the beam propertiesfrom those present in the cell but not enough sothat the flow is fluid-like Buffer gas beams typi-cally operate in this regime however we will seeexamples of buffer gas beams in all three regimes

bull Fully hydrodynamic or ldquosupersonicrdquo regime 100 Re In this regime the buffer gas begins to behavemore like a fluid and the beam properties becomesimilar to those of a beam cooled via supersonic ex-pansion This regime is discussed further in SectionII D 2

2 Forward velocity

asymp1 asymp10 asymp100Reynolds Number Re

Forw

ard

Velo

city

v ||

14v0b

12v0s

Effusive Intermediate Supersonic

FIG 6 A schematic representation of beam forward veloc-ity vs Reynolds number In the effusive regime (Re 1)the forward velocity is the thermal velocity of the (heavy)species In the intermediate regime collisions of the specieswith the buffer gas near the aperture accelerate the speciesthe velocity increase is linear with the Reynolds number untilRe asymp 10 and then begins to asymptote to the final value Inthe supersonic regime (Re amp 100) the species has been fullyaccelerated to the forward velocity of the (light) buffer gasEach of these regimes is discussed in detail below

If the beam is in the effusive regime then there aretypically no collisions near the aperture and the forwardvelocity of the beam vs is given by the forward velocity

10

0 05 10 15 20 25

06

05

04

03

02

01

0

Frac

tion

Extr

acte

d in

toBe

am

15 2 25 3 35 4 4510minus2

10minus1

100

Aperture Size [mm]

Frac

tion

Ext

ract

ed in

to B

eam

Neon Buffer GasHelium Buffer Gas

FIG 5 Extraction from a buffer gas cell Top Frac-tion of Yb atoms extracted into a helium cooled buffer gasbeam vs the parameter γcell (Eq (15)) Reproducedfrom [Patterson D amp Doyle J M J Chem Phys 126154307 (2007) httpdxdoiorg10106312717178] Copy-right (2007) American Institute of Physics Bottom Frac-tion of ThO molecules extracted into a helium (times) andneon () buffer gas vs the cell aperture size with afixed flow rate Reproduced from [Hutzler N et alPhys Chem Chem Phys 13 18976-18985 (2011)httpdxdoiorg101039c1cp20901a (2011)] by permissionof the PCCP Owner Societies

allows us to write the relevant expression for Re in oursituation

Re asymp 2dapertureλbminusb0

asymp 8radic

2f0bσbminusbdaperturev0b

(22)

We shall parameterize the beam by the Reynolds num-ber Re of the buffer gas flow at the aperture Ac-cording to Eq (22) Re is approximately 2Knminus1 =2dapertureλbminusb or twice the number of collisions withinone aperture diameter of the aperture ie ldquonearrdquo theaperture From Eqs (22) and (2) we can see that thein-cell buffer gas density buffer gas flow rate Reynolds

number and number of collisions near the aperture areall linearly related The possible types of flow can beroughly divided into three Reynolds number regimeseach of which will be discussed in the remainder of thissection

bull Effusive regime Re 1 In this regime there aretypically no collisions near the aperture so thebeam properties are simply a sampling of the ther-mal distribution present in the cell This regime isdiscussed further in Section II D 1

bull Intermediate or partially hydrodynamic regime1 Re 100 Here there are enough collisionsnear the aperture to change the beam propertiesfrom those present in the cell but not enough sothat the flow is fluid-like Buffer gas beams typi-cally operate in this regime however we will seeexamples of buffer gas beams in all three regimes

bull Fully hydrodynamic or ldquosupersonicrdquo regime 100 Re In this regime the buffer gas begins to behavemore like a fluid and the beam properties becomesimilar to those of a beam cooled via supersonic ex-pansion This regime is discussed further in SectionII D 2

2 Forward velocity

asymp1 asymp10 asymp100Reynolds Number Re

Forw

ard

Velo

city

v ||

14v0b

12v0s

Effusive Intermediate Supersonic

FIG 6 A schematic representation of beam forward veloc-ity vs Reynolds number In the effusive regime (Re 1)the forward velocity is the thermal velocity of the (heavy)species In the intermediate regime collisions of the specieswith the buffer gas near the aperture accelerate the speciesthe velocity increase is linear with the Reynolds number untilRe asymp 10 and then begins to asymptote to the final value Inthe supersonic regime (Re amp 100) the species has been fullyaccelerated to the forward velocity of the (light) buffer gasEach of these regimes is discussed in detail below

If the beam is in the effusive regime then there aretypically no collisions near the aperture and the forwardvelocity of the beam vs is given by the forward velocity

11

of an effusive beam (Eq (47)) where the appropriatethermal velocity is that of the species ie

vs asymp3π

8v0s asymp 12v0s (Re 1) (23)

As we will discuss creating a purely effusive buffer gasbeam without using advanced cell geometries (SectionII C 2) can be challenging

In the intermediate regime the molecules undergo col-lisions with the buffer gas atoms near (ie within oneaperture diameter of) the cell aperture whose averagevelocity is v0b This is larger than that of the (typically)

heavier species v0s by a factor ofradicmsmb Since the

collisions near the aperture are primarily in the forwarddirection the species can be accelerated or ldquoboostedrdquoto a forward velocity vs which is larger than the ther-mal velocity of the molecules (just as with supersonicbeams[1])

If there are few collisions we can estimate the rela-tionship between Re and vs with a simple model fromMaxwell et al[3] Near the aperture the molecules un-dergo approximately Re2 collisions Each of these col-lisions gives the molecules a momentum kick in the for-ward direction of about asymp mbvb so the net velocity boostis asymp vbmbRe2mmol Since there are a small number ofcollisions the forward velocity of the buffer gas is approx-imately given by the mean forward velocity of an effusivebeam (Eq (47)) vb asymp 12v0b so for 1 Re 10 (weshall justify the Re 10 cutoff later on)

vs asymp 12v0s + 06v0bRemb

mmol (24)

Therefore the forward velocity should increase linearlywith Re (and therefore with in-cell buffer gas density orbuffer gas flow) Several papers [3 7 9] have consideredthe behavior of vs vs Re and have seen this linear de-pendence at low Re The more recent papers [7 9] showdata where the Reynolds number is large enough that adeparture from the linear regime can be seen Hutzler etal [7] calculated the slope of the vs vs Re relationshipat low flow and found good agreement with the abovemodel

This model necessarily breaks down as vs approachessim v0b since the maximum possible forward velocity is14v0b (from Eq (54)) the forward velocity of a fullyhydrodynamic buffer gas expansion We therefore expectthat the forward velocity should saturate to this value atlarge enough Re To model the behavior outside of thelinear regime considered above Hutzler et al [7] used theldquosudden freezerdquo model [61] where it is assumed that thespecies molecules are in equilibrium with the buffer gasuntil the point along the beam where the buffer density isdecreased enough such that there are no more collisionsand the beam properties stop changing or ldquofreezerdquo Thefunctional form for this model is (for Re amp 10)

vs(Re) asymp 14v0b

radic1minus 4Reminus45 (25)

and fits the data fairly well[7] The estimate for wherethe linear to sudden-freeze model transition occurs is byfinding at which flow there are collisions at a distancelarger than one aperture diameter from the aperturewhich happens for Re amp 10 [7]

Finally for large enough Re there should be enoughcollisions to fully boost the molecules to the forward ve-locity of the buffer gas

vs asymp vb asymp 14v0b (Re amp 100) (26)

where the cutoff Re amp 100 means that vs(100) asymp 95timesvb according to Eq (25) and from experiment [7 9]This limit corresponds to the supersonic flow regime

0 4 8 12 16 200

20

40

60

80

100

120

140

160

Reynolds Number

Mean velocity of an eusive He beam

Mean velocity of an eusive Na beam

Mean velocity of an eusive PbO beam

NaPbO

0 10 20 30 40 50 60 70120

130

140

150

160

170

180

190

200

210

Reynolds Number

Forw

ard

Vel

ocity

[ms

]

DataSudden FreezeLinear

Forw

ard

Vel

ocity

[ms

]

FIG 7 Forward velocity of extracted beam vs buffergas flow rate Top Forward velocity for Na and PbOin a helium cooled buffer gas beam Reproduced from[Maxwell et al Phys Rev Lett Vol 95 173201 (2005)httpdxdoiorg101103PhysRevLett95173201] Copy-right (2005) by the American Physical Society BottomForward velocity for ThO in a neon cooled buffer gas beamHere the beam starts in the linear regime and then fully sat-urates at the neon supersonic forward velocity Reproducedfrom [Hutzler N et al Phys Chem Chem Phys 1318976-18985 (2011) httpdxdoiorg101039c1cp20901a(2011)] by permission of the PCCP Owner Societies

12

3 Velocity spreads

Forward or longitudinal velocity spread In the effu-sive regime the longitudinal velocity spread is the spread(FWHM) of the thermal 1D Maxwell-Boltzmann distri-bution

∆vs =

radic8 ln(2)kbT0

ms= v0s

radicπ ln(2) asymp 15v0s (27)

Maxwell et al[3] operated a buffer gas beam of PbOin this regime and found that the longitudinal velocityspread (as well as the transverse velocity spread and ro-tational level distribution) were all in agreement with athermal distribution at the cell temperature

If the Reynolds number of the flow is high enough thenthe forward velocity spread can begin to decrease due toisentropic expansion of the buffer gas into the vacuumregion The translational temperature in the longitudinal(ie forward) direction can be decreased below the celltemperature as will be discussed in Section II C 1

Transverse velocity spread Similarly the transversespread in the effusive regime is

∆vperps asymp 15v0s (28)

Also similar to the case with forward velocity in theintermediate regime there will be collisions between thespecies and buffer gas near the aperture which can in-crease the transverse velocity spread For low Re we canestimate the transverse velocity spread near the aperturewith a that is similar to the model for forward velocity

∆vperps asymp 15v0s + (Re2)v0bd2cell

d2aperture

mb

mmol (29)

Hutzler et al [7] used this model to describe the behaviorof the transverse spread of a ThO beam in neon buffergas and found it approximated the ratio ∆vperpsRe well

Experimentally we are less concerned with the trans-verse velocity spread near the aperture than with thefinal velocity spread downstream after collisions haveceased This is more complicated to model since it con-flates the dynamics discussed above with the dynamicsof the expansion However a similar argument showsthat the transverse spread should increase linearly (abovesome Re) with increasing Re This was examined indetail[7 9] and a linear relationship was seen with aratio ∆vperpsRe that was sim 2 times the ratio near theaperture[7]

Finally as Re is further increased the transverse ve-locity spread should saturate at the transverse spread ofthe buffer gas Barry et al[9] started to see this satura-tion behavior for SrF in a helium buffer gas start aroundRe asymp 100

We have seen that the shape of the Re vs ∆vperps re-lationship (see Figure 8) is very similar to that whichis plotted in Figure 6 However as we shall see in the

following section the Reynoldrsquos numbers where the tran-sitions occur do not have to be the same as in the caseof forward velocity

0 5 10 15 20 25 30 35 4045

50

55

60

65

70

75

80

85

90

Reynolds Number

Vel

ocity

FW

HM

[ms

]

DataLinear Fits

Vel

ocity

FW

HM

[ms

]

Reynolds Number

Velocity for Effusive 5K Beam of SrF

Flow [SCCM]

FIG 8 Behavior of transverse velocity spread vs Reynoldsnumber Top transverse velocity spread of SrF in a he-lium buffer gas cooled beam vs Re at a fixed distance of20 mm (asymp 7daperture) from the cell aperture[9] At low Rethe transverse spread is in the linear regime but it beginsto saturate around Re asymp 50 Reproduced from [Barry etal Phys Chem Chem Phys 13 18936-18947 (2011)httpdxdoiorg101039c1cp20335e] by permission of thePCCP Owner Societies Bottom transverse velocity spreadof ThO in a neon buffer gas[7] vs Re at a fixed distanceof 1 mm (lt daperture) from the cell aperture The transi-tion from flat (and approximately equal to the spread froma thermal distribution at T0) to linearly increasing occursaround Re asymp 10 The data is well described by the modelmentioned in the text Reproduced from [Hutzler N etal Phys Chem Chem Phys 13 18976-18985 (2011)httpdxdoiorg101039c1cp20901a] by permission of thePCCP Owner Societies

Typically the transverse velocity spread is not a di-rectly important parameter Actual experiments per-formed with atomic and molecular beams are generallyperformed at a distance from the cell aperture that ismany times larger than daperture and only sample a very

13

small solid angle of the output beam This is both toreduce the gas load on the vacuum apparatus (the un-used portions of the beam can be differentially pumpedto maintain a good vacuum) and to select atoms ormolecules with nearly-identical directions of flight to re-duce Doppler broadening of transversely probed spec-troscopic transitions However the transverse velocityspread is important because it factors in to the diver-gence of the molecular beam which will be discussed inthe next section

4 Angular spread and divergence

As mentioned earlier the experimentally useful por-tion of an atomic or molecular beam is the portion thatmakes it through a typically small detection region at alarge distance away For this reason an important char-acteristic of a beam is the value of the angular densitydistribution of the molecular beam A parameter thatcan be used to characterize the angular spread of thebeam is the full-width at half-maximum (FWHM) of theangular distribution ∆θ This parameter is defined byequating N(∆θ) = 1

2Ntotal where N(θ) is the density atan angle of θ from the aperture normal at a fixed distancefrom the aperture (see Section II D 1) This parameter isvery simple to calculate from transverse and longitudinalDoppler spectroscopic data if a beam has a transversevelocity spread ∆vperp and forward velocity v then (seeFigure 9)

tan(∆θ2) =∆vperp2

v(30)

rArr ∆θ = 2 arctan

(∆vperp2

v

)(31)

∆vperpv||

θFWHM

Cell Aperture

Molecular Beam Expansion

FIG 9 An illustration showing the relationship between theforward velocity v transverse velocity spread ∆vperp and an-gular spread ∆θ from Eq (31) tan(∆θ2) = (∆vperp2)vThe gray shaded region indicates the spatial extent of themolecular beam with darker indicating higher density

We can then also define the solid angle spread ∆Ω asthe solid angle subtended by ∆θ ie

∆Ω = 2π(1minus cos(∆θ2)) (32)

Note that this definition ignores the fact that at eachpoint in the beam there is a velocity spread due tothe non-zero temperature of the beam so the measuredtransverse Doppler spread is a convolution of both beamtranslational temperature and the actual shape of thebeam However if we measure this spread far enoughaway from the aperture that collisions have stopped sothat the aperture can be regarded as a point source fromwhich the molecules are ballistically expanding then in-ferring a spatial spread from the velocity spread is a validapproximation

For a buffer gas beam in the effusive regime the angu-lar spread is given by Eq (48) as ∆θ = 120 and solidangle spread is given by ∆Ω = π

In the range 1 Re 10 the forward velocity beginsto increase linearly with Re yet the transverse velocity re-mains constant at ∆vperps = 15v0s from Eq (28) There-fore Eq (31) tells us that the divergence will begin todecrease As the molecules begin to be boosted to theforward velocity of the buffer gas vs asymp vb asymp v0b thedivergence should approach

∆θ = 2 arctan

(∆vperps2

vs

)(33)

asymp 2 arctan

(15v0s2

v0b

)(34)

asymp 2

radicmb

ms (35)

where in the last approximation we assumed that ms mb The solid angle spread is then approximated by

∆Ω = 2π(1minus cos(2radicmbms)) asymp πmbms (36)

Notice that this can be much smaller than the corre-sponding spreads of π for an effusive beam (Eq (49)) or14 for a supersonic beam (Eq (56)) Both Maxwell etal[3] (with helium buffer gas) and Hutzler et al[7] (withneon buffer gas) have operated beams in this regime andhave been able to see the linearly decreasing divergence

As Re is increased to the point where the transversespread begins to increase the divergence will stop de-creasing Hutzler et al[7] were able to see this transitionfor a ThO beam in neon buffer gas shown in Figure 10With helium buffer gas both Hutzler et al[7] and Barryet al[9] observed that the divergence was constant overa combined range of Reynolds numbers 1 Re 150This was due to the fact that the increases in transverseand forward velocities canceled each other almost exactlyThis indicates that while there is some proposed ldquouniver-sal shaperdquo for the relationships of Re vs v and vs ∆vperpthe Reynolds numbers where transitions in behavior oc-cur for the two relationships need not overlap and thereis not a similar universal shape for Re vs ∆Ω

14

0 10 20 30 40 50 60 7020

30

40

50

60

80

100

120

140

Ang

ular

FW

HM

∆θ

[deg

rees

]

Reynolds Number

ThO in NeonThO in HeliumSupersonicEffusive

010

021

038

059

084

147

224

314

413

Sol

id A

ngle

FW

HM

∆Ω

[sr]

FIG 10 Divergence of a ThO beam in both a helium andneon cooled buffer gas beam[7] For low Reynolds num-ber with neon buffer gas we are in the regime of linearlyincreasing forward velocity but constant transverse veloc-ity spread (see Figures 7 and 8) Eventually the forwardvelocity stops increasing and the transverse velocity startsincreasing which results in the divergence ceasing to de-crease With helium buffer gas the divergence is essentiallyconstant similar to what was seen with SrF in a heliumbuffer gas cooled beam[9] Reproduced from [Hutzler Net al Phys Chem Chem Phys 13 18976-18985 (2011)httpdxdoiorg101039c1cp20901a (2011)] by permissionof the PCCP Owner Societies

5 Relationship of flow and extraction regimes

By examining Eq (22) for the Reynolds numberwhich governs the gas flow regime and Eq (15) for theextraction parameter γcell which governs the species ex-traction regime we can see that they are related by afactor which depends on the geometry

γcellReprop daperture

Lcell (37)

This means that at least in principle it should be pos-sible to design a buffer gas source which is any combi-nation of diffusive (low efficiency) or hydrodynamicallyextracted (high efficiency) and with effusive intermedi-ate or hydrodynamic flow Most buffer gas sources op-erate either in the effusive or intermediate regimes andit is experimentally challenging to design a beam whichis completely effusive has good extraction and sufficientthermalization A purely effusive beam should have aforward velocity which according to Eq (47) does notchange with source pressure however in buffer gas beamsources with good extraction [3 7 9 16] the forward ve-locity of the molecules indeed changes with source pres-sure Slowing cells (Section II C 2) can offer near-effusivevelocity distributions but typically havesim 1 extractionefficiency[5 10]

6 Choice of buffer gas

For many applications helium is a natural choice ofbuffer gas Helium has large vapor pressure at 4 K (thatcorresponds to an atom number density of gt 1019 cmminus3)which is a convenient temperature for cryogenics Manyrefrigerators can cool to sim 4 K as can a simple liquid he-lium cryostat Helium also has the advantage that it haslarge vapor pressure at even lower temperatures (lt 1 K)where operating the cell will result in a colder and slowerbeam[5 67] Simple cryogenic techniques can achievetemperatures of sim 2 K and still handle the necessaryheat loads lower temperatures require a more compli-cated setup

Neon has also been used as a buffer gas[7 67] and ithas some advantages of its own The thermal velocity ofthe buffer gas scales as

radicT0mb (Eq (1)) so as long as

the cell temperature is kept below 20 K with neon buffergas (whose mass is sim 20 amu) the thermal velocity (andtherefore forward velocity see Section II B 2) should becomparable to that of a 4 K helium-4 buffer gas beamsource Since neon has large enough vapor pressure downto sim 14 K (where the density drops below sim 1017 cmminus3)it can compare favorably to a 4 K helium source in termsof forward velocity

While the forward velocity of a neon or helium buffergas cooled beam can be comparable in certain situationsthe temperatures in the beam can be comparable as wellHutzler et al[7] found that operating a buffer gas cooledbeam resulted in isentropic cooling (see Section II C 1)that reduced the temperature of both a helium and aneon cooled beam of ThO to similar temperatures (seeTable II) even though the cell temperature was around17 K for the neon cooled beam and around 4 K for thehelium cooled beam This means that the beam proper-ties of a helium or neon cooled beam can be similar withthe neon beam offering some distinct technical advan-tages Neon can be efficiently cryopumped by a 4 K sur-face while helium requires a large-area adsorbent such asactivated charcoal as discussed in Section II E 3 Char-coal cryopumps are very effective however they mustbe emptied periodically have reduced pumping speed asthey begin to fill and can influence the resulting molec-ular beam properties[7 9] Cryopumping of neon ontoa cold surface does not display these properties[7] Ad-ditionally the properties of pulsed beams with heliumbuffer gas can show time-dependence not present withneon[7 9]

C Additional cooling and slowing

As discussed in the preceding sections the properties ofa buffer gas beam can be tuned considerably by alteringthe flow and aperture sizes to control the parameters Reand γcell However some applications require even finercontrol for example collision studies may require a verynarrow and tunable velocity distribution and trap load-

14

0 10 20 30 40 50 60 7020

30

40

50

60

80

100

120

140

Ang

ular

FW

HM

∆θ

[deg

rees

]

Reynolds Number

ThO in NeonThO in HeliumSupersonicEffusive

010

021

038

059

084

147

224

314

413

Sol

id A

ngle

FW

HM

∆Ω

[sr]

FIG 10 Divergence of a ThO beam in both a helium andneon cooled buffer gas beam[7] For low Reynolds num-ber with neon buffer gas we are in the regime of linearlyincreasing forward velocity but constant transverse veloc-ity spread (see Figures 7 and 8) Eventually the forwardvelocity stops increasing and the transverse velocity startsincreasing which results in the divergence ceasing to de-crease With helium buffer gas the divergence is essentiallyconstant similar to what was seen with SrF in a heliumbuffer gas cooled beam[9] Reproduced from [Hutzler Net al Phys Chem Chem Phys 13 18976-18985 (2011)httpdxdoiorg101039c1cp20901a (2011)] by permissionof the PCCP Owner Societies

5 Relationship of flow and extraction regimes

By examining Eq (22) for the Reynolds numberwhich governs the gas flow regime and Eq (15) for theextraction parameter γcell which governs the species ex-traction regime we can see that they are related by afactor which depends on the geometry

γcellReprop daperture

Lcell (37)

This means that at least in principle it should be pos-sible to design a buffer gas source which is any combi-nation of diffusive (low efficiency) or hydrodynamicallyextracted (high efficiency) and with effusive intermedi-ate or hydrodynamic flow Most buffer gas sources op-erate either in the effusive or intermediate regimes andit is experimentally challenging to design a beam whichis completely effusive has good extraction and sufficientthermalization A purely effusive beam should have aforward velocity which according to Eq (47) does notchange with source pressure however in buffer gas beamsources with good extraction [3 7 9 16] the forward ve-locity of the molecules indeed changes with source pres-sure Slowing cells (Section II C 2) can offer near-effusivevelocity distributions but typically havesim 1 extractionefficiency[5 10]

6 Choice of buffer gas

For many applications helium is a natural choice ofbuffer gas Helium has large vapor pressure at 4 K (thatcorresponds to an atom number density of gt 1019 cmminus3)which is a convenient temperature for cryogenics Manyrefrigerators can cool to sim 4 K as can a simple liquid he-lium cryostat Helium also has the advantage that it haslarge vapor pressure at even lower temperatures (lt 1 K)where operating the cell will result in a colder and slowerbeam[5 67] Simple cryogenic techniques can achievetemperatures of sim 2 K and still handle the necessaryheat loads lower temperatures require a more compli-cated setup

Neon has also been used as a buffer gas[7 67] and ithas some advantages of its own The thermal velocity ofthe buffer gas scales as

radicT0mb (Eq (1)) so as long as

the cell temperature is kept below 20 K with neon buffergas (whose mass is sim 20 amu) the thermal velocity (andtherefore forward velocity see Section II B 2) should becomparable to that of a 4 K helium-4 buffer gas beamsource Since neon has large enough vapor pressure downto sim 14 K (where the density drops below sim 1017 cmminus3)it can compare favorably to a 4 K helium source in termsof forward velocity

While the forward velocity of a neon or helium buffergas cooled beam can be comparable in certain situationsthe temperatures in the beam can be comparable as wellHutzler et al[7] found that operating a buffer gas cooledbeam resulted in isentropic cooling (see Section II C 1)that reduced the temperature of both a helium and aneon cooled beam of ThO to similar temperatures (seeTable II) even though the cell temperature was around17 K for the neon cooled beam and around 4 K for thehelium cooled beam This means that the beam proper-ties of a helium or neon cooled beam can be similar withthe neon beam offering some distinct technical advan-tages Neon can be efficiently cryopumped by a 4 K sur-face while helium requires a large-area adsorbent such asactivated charcoal as discussed in Section II E 3 Char-coal cryopumps are very effective however they mustbe emptied periodically have reduced pumping speed asthey begin to fill and can influence the resulting molec-ular beam properties[7 9] Cryopumping of neon ontoa cold surface does not display these properties[7] Ad-ditionally the properties of pulsed beams with heliumbuffer gas can show time-dependence not present withneon[7 9]

C Additional cooling and slowing

As discussed in the preceding sections the properties ofa buffer gas beam can be tuned considerably by alteringthe flow and aperture sizes to control the parameters Reand γcell However some applications require even finercontrol for example collision studies may require a verynarrow and tunable velocity distribution and trap load-

15

0 50 100 150 200minus02

0

02

04

06

08

1

12

Beam forward velocity (m sndash1)

Rel

ativ

e io

n si

gnal

12 K neon buffer gas12 K helium buffer gas

0 50 100 150 200 250 3000

005

01

015

02

025

03

035

04

42 K helium

14 K neon

40 K argon

Beam forward velocity (m s )minus1

Rel

ativ

e de

nsity

FIG 11 Plots comparing the forward velocity distributionsusing different buffer gasses[67] Top Calculated distribu-tions for noble gases at a temperature where there is suffi-cient vapor pressure for beam operation While helium hassufficient vapor pressure below 42 K (and even 1 K) 42K is a typical temperature for both cryogenic refrigeratorsand liquid helium cooled cryostats While the neon distri-bution is broader (ie hotter) for applications where onlythe slowest molecules are used (such as in trap loading seeSection III C) neon has an advantage Bottom measuredvelocity distributions of beam of ND3 in helium and neonbuffer gas at 12 K If the cell must be operated at a highertemperature for technical reasons (for example if there isa large heat load on the buffer cell from a capillary load-ing scheme) this data shows that neon has the advantagein terms of creating slow molecules The data here is veloc-ity selected Reproduced from [Patterson D RasmussenJ amp Doyle J M New J Phys 11(5) 055018 (2009)httpdxdoiorg1010881367-2630115055018] with per-mission from the Institute of Physics

ing typically requires a very slow distribution (see SectionIII C) In this section we shall discuss some methods tomanipulate the output of a buffer gas beam to eitherreduce temperatures reduce forward velocities or selectvelocity classes These techniques help make buffer gasbeams highly versatile and allow the many applicationsdiscussed in Section III

1 Isentropic expansion

The boosting effect discussed in Section II B 2 can bedetrimental if one aims to produce a slow beam whichis one of the benefits of buffer gas beams over super-sonic beams and effusive ldquoovenrdquo beams One wouldtherefore prefer to operate the beam in the effusive flowregime ie at a low Reynolds number (Eq (22))It is possible to keep the Reynolds number fairly lowwhile maintaining good extraction (γcell gt 1) by usinga slit-shaped aperture as we will now discuss Considerthe aperture as having a short and long dimension soAaperture = dshort times dlong For a fixed internal cell ge-ometry buffer gas species and cell temperature we cansee from Eqs (22) and (15) that

Re prop dshortn0b (38)

γcell prop n0bAaperture (39)

rArr γcellReprop dlong (40)

Therefore by increasing dlong but keeping Aaperturefixed we can decrease Re without changing γcell or thebuffer gas density Note that simply changing the aper-ture size while leaving all other parameters fixed alsohas the effect of changing Re but not γcell (Eq (15))however this is not ideal for two reasons First the in-cell buffer gas density is constrained to be large enoughthat the species is thermalized but small enough that themolecules can diffuse away from the injection point[70]and this method would change the buffer gas densitySecond as mentioned in Section II A 5 reducing the aper-ture size can in fact have an effect on the extraction forsmall enough aperture sizes For these reasons earlierbuffer gas beam papers tended to use a slit[3] aperturetypically around 1times 5 mm

While performing buffer gas beam studies that re-quired high flow rates to sufficiently thermalize atomsfrom a hot oven[67 80] it was quickly realized that thedownside of high Re flows could also come with a ben-efit isentropic cooling from the free expansion of a gassimilar to what happens in supersonic beams[1] This ef-fect was first seen (though not published) in K and Rbatoms cooled by a neon buffer gas[67 80] and it wassubsequently fully characterized with ThO in neon andhelium buffer gas beams at cell temperatures of about17 K and 4 K (respectively)[7] and simultaneously withSrF in helium buffer gas at a cell temperature of 3 K[9]In each case the molecules were found to cool rotation-ally and translationally below the temperature of the celland the beam properties had very good qualitative agree-ment Selected properties of these beams are listed inTable II

The cell apertures for these studies were either roundor square and the studies were performed between Re asymp1 minus 150 In each case the Reynolds numbers were highenough that the rotational temperatures appeared to sat-urate around 2 K and 1 K for ThO and SrF respectivelyas shown in Figure 12 The translational temperatures

16

(in the forward direction) of ThO in neon buffer gas wasalso decreased below the temperature of the cell and isshown in Figure 12 However the translational temper-atures for both ThO and SrF in helium buffer gas werecomplicated by time-dependence of the temperature af-ter the ablation pulse though in each case it was reducedbelow the cell temperature

It is worth noting that even in these fully-boosted highReynolds number regimes where the forward velocity isfully saturated (see Section II B 2) the velocity still com-pares very favorably to supersonic or effusive beams (seeTables I and II) In the next section we shall see thatthere are additional techniques to further reduce the for-ward velocity of a buffer gas cooled beam

2 Slowing cells

As mentioned in the previous section the beam prop-erties can be manipulated by choice of aperture geometryThis control can be extended by using an advanced aper-ture geometry known as a ldquoslowing cellrdquo[5 10] shownin Figure 13 which is used to create a region of inter-mediate pressure between the cell and vacuum (beam)regions and acts as an effusive source that can still uti-lize the high extraction of the main cell

The main or ldquofirstrdquo cell is created like a typical buffergas cell and has the same typical buffer gas flow rates di-mensions etc A second or slowing cell is then attachedto the aperture of the main cell This second cell has avery large area through which the buffer gas can flowso the steady-state pressure inside it is low about 10of the pressure in the main cell This makes the typicalmean free path on the order of a few mm so the specieswill scatter only a few times while in the slowing cellIf the slowing cell is also kept cold these collisions willnot heat the molecules but will have the effect of reduc-ing their boosted forward velocity closer to the thermalvelocity (see Section II B 2)

Species T0 [K] v [m sminus1] N [pulseminus1]

Yb Boosted[5] 26 130 5 times 1012

Yb Slowed[5] 26 35 5 times 1010

CaH Boosted[10] 18 110 5 times 109

CaH Slowed[10] 18 65 1 times 109

CaH Slowed[10] 18 40 5 times 108

TABLE III A comparison of boosted buffer gas beam sources(ie with no slowing cell) to those with a slowing cellldquoBoostedrdquo means that collisions near the aperture acceleratethe beam above the thermal velocity as discussed in SectionII B 2 ldquoSlowedrdquo means a slowing cell was added to the maincell

Notice that operating a beam in the effusive regime canalso result in low forward velocities (see Section II B 2)however as mentioned earlier it is difficult to operatea fully effusive beam that also has significant extraction

0 10 20 30 40 5015

20

25

30

35

40

45

50

55

60

Reynolds Number

Vel

ocity

FW

HM

[ms

]

25 mm Aperture45 mm Aperture

12

21

34

48

66

86

109

134

162

193

Tem

pera

ture

[K]

0 5 10 15 20 25 30 35 400

2

4

6

8

10

12

Reynolds Number

Rot

atio

nal T

empe

ratu

re [K

]

Neon Buffer Gas 20 mm ApertureNeon Buffer Gas 45 mm ApertureHelium Buffer Gas 20 mm Aperture

FIG 12 Additional cooling from isentropic expansion ina buffer gas cooled ThO beam[7] The cell temperature isaround 17 K for neon buffer gas and around 4 K for heliumbuffer gas Top Longitudinal velocity spread (temperature)in a neon cooled buffer gas beam with two different aperturesizes Bottom Final rotational temperature in the beam forcomparing two different aperture sizes with neon buffer gasand a single aperture size for helium buffer gas The rotationaltemperature with helium buffer gas showed essentially no de-pendence on the aperture size Figures are reproduced from[Hutzler N et al Phys Chem Chem Phys 13 18976-18985 (2011) httpdxdoiorg101039c1cp20901a (2011)]by permission of the PCCP Owner Societies

The PbO beam of Maxwell et al[3] had a forward velocityof sim 40 m sminus1 at low flows comparable to those achievedwith Yb and CaH using slowing cells but with an extrac-tion fraction of fext lt 10minus4 compared to fext asymp 10minus2 forthe slowing cells

3 Guiding and velocity filtering

Although they may not technically constitute coolingor slowing electric or magnetic guides or velocity filters

17

Fill Line

1st Cell ldquoSlowing Cellrdquo

2nd Aperture

Gap Vents

1st Aperture

Species

He

FIG 13 A slowing cell adapted from Lu et al[10] Here thespecies is represented by red dots and the helium buffer gas isrepresented by blue shading where darker shading indicateshigher density The density in the slowing cell is kept low bygaps and vents so that the species suffers only a few collisionsin the slowing cell These collisions can reduce the forwardvelocity without heating while sacrificing flux The methodfor introducing the species is not indicated in this figure buthas been accomplished with both ablation[5 10] and capillaryfilling[5]

can be used to change the output of a buffer gas cooledbeam to suit a particular application[5 15 16 67 84]Guiding the species of interest can be useful for a numberof reasons First if the presence of the buffer gas will in-terfere with the experiment for example while perform-ing collision studies a guide can be used to transportthe species far from the buffer gas source where thereis no appreciable buffer gas pressure[60] Second if thebeam is to be studied in a room temperature appara-tus for example to perform laser cooling [50] or pre-cision measurements[59] the beam may have to travela long distance to exit the cryogenic apparatus beforepassing into the experimental region Without a guidethe molecule density will decrease with the square of thedistance from the cell which could result in significantreduction An electrostatic or magnetic guide or lens canhelp reduce this loss from beam divergence

Magnetic ~B or electric ~E fields can be used to guideor focus a molecular beam by creating a restoring forceperpendicular to the motion of the molecule[1] If themolecular state has a magnetic moment microB then the in-teraction (of a low-field seeking state) with a magnetic

field leads to a potential energy U = microB| ~B| If we assumethat the molecule is traveling in a cylindrically symmet-

ric field ~B(r) where r is the distance from the axis ofsymmetry then the field from a nminuspole configuration

is | ~B(r)| = B0r(nminus2)2 and the potential energy of the

molecule is U = microBB0r(nminus2)2 In addition to guiding

multipole fields can also be used to focus molecules bycreating a linear restoring force (U prop r2) which we cansee requires a hexapole (n = 6) field configuration

The situation is similar for polar molecules If amolecular state has a permanent electric dipole mo-

ment microE (as is the case for states with Λ gt 0 suchas Π or ∆ states[85]) then the potential energy of the(low-field seeking state) molecule in an nminuspole field isU = microEE0r(nminus2)2 However unlike the case with mag-netic dipole moments polar molecules can be in states(such as Σ states[85]) which have an induced dipole mo-ments leading to a quadratic shift in fields In this casethe dipole moment (for small fields) is proportional to the

electric field microE prop |~E| so potential energy of the molecule

is minusmicroE |~E| prop rnminus2 If we wish to focus polar moleculeswith a linear restoring force we can see that a hexapoleis required for states with a permanent dipole momentor a quadrupole (n = 4) for states with an induced dipolemoment

If the maximum electric field in the guide (typicallysim 10 minus 40 kV cmminus1) is Emax and the molecules haveStark shift W (E) in a field E then the transverse depthof the guide is defined as Wmax = W (Emax) which istypically sim 1 KtimeskB This sets the maximum transversevelocity spread in the guide vperpmax to be

1

2msv

2perpmax = Wmax rArr vperpmax =

radic2Wmaxms (41)

which is around 10-30 m sminus1

Electrostatic guide

Switchable electrostatic gate

Cell

Slow guided ND3

FIG 14 Electrostatic guide for ND3[67] The cell is keptat 15 K and contains neon buffer gas (small blue circles) andND3 (large red circles) introduced from a capillary As themolecules exit the cell an ldquoelectrostatic gaterdquo can be turnedon to direct molecules into the guide This guide will onlyadmit slow molecules around the bend faster molecules willsimply overcome the potential barrier and escape the guideAdapted from Patterson et al[67]

In addition to guiding or focusing to increase usefulflux electric or magnetic fields can be used to select par-ticular velocity ranges from the output of the molecularbeam which is useful for collision studies and trap load-ing experiments (see Section III C) as will be discussedMolecules of a particular forward velocity range can beselected by rotating mechanical objects [86] however us-ing fields is much less technically challenging especiallyin a cryogenic environment The first realization of thismethod[87] (and later realizations with buffer gas cooledbeams[5 15 16 67]) was to simply bend one of the guides

18

described above similar to what is shown in Figure 14Molecules with high enough kinetic energies in the for-ward direction will simply pass over the potential bar-rier and only the more slow-moving molecules will re-main in the guide More specifically for a guide of depthWmax guide radius ρ (ie distance from the center of theguide to the location of the maximum electric field) andguide radius of curvature R the cutoff for longitudinalvelocities which will remain in the guide is found[84] byequating the centrifugal force msv

2maxR to the restor-

ing force simWmaxρ caused by the molecule traveling upthe potential hill of length ρ or

msv2maxR asympWmaxρrArr vmax asymp

radicWmaxRρms

(42)This technique can be used to filter only slow moleculesfrom a pulsed or continuous buffer gas source for exam-ple to load a trap In fact this technique can also beapplied to thermal effusive sources Rangwala et al[87]filtered slow H2CO and ND3 molecules from a 300 K ef-fusive source and obtained distributions that had widthsand means similar to those of a 5 K thermal distributionwhile maintaining a high flux of asymp 109 sminus1 guided H2COmolecules

In addition to simply selecting slow molecules elec-trostatic guides can be used to select a window of ve-locities by using multiple switched guides Sommeret al[84] devised a three-stage switchable electrostaticguide fed by a helium buffer gas cooled source of ND3

molecules which could deliver controllable velocity-selected molecule pulses By switching the individualguide segments on or off at precise times both a lowerand upper velocity cutoff can be imposed on moleculesthat remain in the guide Velocity windows of FWHMsim 3 minus 20 m sminus1 wide with centers between 20 and 100m sminus1 could be efficiently selected with low losses asshown in Figure 15

D Effusive and supersonic beam properties

For the sake of comparison we will briefly review someproperties of effusive and supersonic beams Detaileddiscussions may be found in existing literature[1 61]

1 Effusive beams

In an effusive gas flow from an aperture the typicalescaping gas atom has no collisions near the aperture(Kn gt 1) Therefore the resulting beam can be consid-ered as a sampling of the velocity distribution in the cellA typical setup is a gas cell with a thin exit aperturewhere the thickness of the aperture and the aperture di-ameter daperture are both much smaller than the meanfree path of the gas at stagnation conditions Note thatthe effusive beams under discussion in this section areoven-type effusive sources ie where the vapor pressure

( )

FIG 15 Velocity-selected pulses of ND3 obtained using mul-tiple bent switchable guides[84] The pulse centered about60 m sminus1 contains approximately 105 molecules Reproducedfrom [Sommer C et al Phys Rev A 82(1) 013410 (2010)httpdxdoiorg101103PhysRevA82013410] Copyright(2010) by the American Physical Society

of the species of interest is large at the source temper-ature (as opposed to buffer gas cooled effusive sourceswhich can operate at temperatures where the species hasno appreciable vapor pressure)

The number density in the beam resulting from a dif-ferential aperture area dA is given by

n(R v θ) = n(R θ)f(v) where (43)

n(R θ) =n0 cos(θ)

4πR2dA (44)

f(v) =32

π2v3v2eminus4v2π(v)2 (45)

R is the distance from the aperture θ is the angle fromthe aperture normal n0 is the stagnation density in thecell n(R θ) is the total number density distribution inte-grated over velocity and f(v) is the normalized velocitydistribution in the cell The velocity distribution in thebeam is given by [61]

fbeam(v) = (vv)f(v) =32

π2v4v3eminus4v2π(v)2 (46)

From the velocity distribution we can extract the meanforward velocity of the beam

veff =

int infin0

vfbeam(v) dv =3π

8v asymp 12v (47)

From the total number density in the beam n(R θ)we can extract the FWHM (full-width at half-maximum)of the characteristic angular spread ∆θ by solvingn(R∆θ2) = 1

2n(R 0) which gives

∆θ =2π

3= 120 (48)

18

described above similar to what is shown in Figure 14Molecules with high enough kinetic energies in the for-ward direction will simply pass over the potential bar-rier and only the more slow-moving molecules will re-main in the guide More specifically for a guide of depthWmax guide radius ρ (ie distance from the center of theguide to the location of the maximum electric field) andguide radius of curvature R the cutoff for longitudinalvelocities which will remain in the guide is found[84] byequating the centrifugal force msv

2maxR to the restor-

ing force simWmaxρ caused by the molecule traveling upthe potential hill of length ρ or

msv2maxR asympWmaxρrArr vmax asymp

radicWmaxRρms

(42)This technique can be used to filter only slow moleculesfrom a pulsed or continuous buffer gas source for exam-ple to load a trap In fact this technique can also beapplied to thermal effusive sources Rangwala et al[87]filtered slow H2CO and ND3 molecules from a 300 K ef-fusive source and obtained distributions that had widthsand means similar to those of a 5 K thermal distributionwhile maintaining a high flux of asymp 109 sminus1 guided H2COmolecules

In addition to simply selecting slow molecules elec-trostatic guides can be used to select a window of ve-locities by using multiple switched guides Sommeret al[84] devised a three-stage switchable electrostaticguide fed by a helium buffer gas cooled source of ND3

molecules which could deliver controllable velocity-selected molecule pulses By switching the individualguide segments on or off at precise times both a lowerand upper velocity cutoff can be imposed on moleculesthat remain in the guide Velocity windows of FWHMsim 3 minus 20 m sminus1 wide with centers between 20 and 100m sminus1 could be efficiently selected with low losses asshown in Figure 15

D Effusive and supersonic beam properties

For the sake of comparison we will briefly review someproperties of effusive and supersonic beams Detaileddiscussions may be found in existing literature[1 61]

1 Effusive beams

In an effusive gas flow from an aperture the typicalescaping gas atom has no collisions near the aperture(Kn gt 1) Therefore the resulting beam can be consid-ered as a sampling of the velocity distribution in the cellA typical setup is a gas cell with a thin exit aperturewhere the thickness of the aperture and the aperture di-ameter daperture are both much smaller than the meanfree path of the gas at stagnation conditions Note thatthe effusive beams under discussion in this section areoven-type effusive sources ie where the vapor pressure

( )

FIG 15 Velocity-selected pulses of ND3 obtained using mul-tiple bent switchable guides[84] The pulse centered about60 m sminus1 contains approximately 105 molecules Reproducedfrom [Sommer C et al Phys Rev A 82(1) 013410 (2010)httpdxdoiorg101103PhysRevA82013410] Copyright(2010) by the American Physical Society

of the species of interest is large at the source temper-ature (as opposed to buffer gas cooled effusive sourceswhich can operate at temperatures where the species hasno appreciable vapor pressure)

The number density in the beam resulting from a dif-ferential aperture area dA is given by

n(R v θ) = n(R θ)f(v) where (43)

n(R θ) =n0 cos(θ)

4πR2dA (44)

f(v) =32

π2v3v2eminus4v2π(v)2 (45)

R is the distance from the aperture θ is the angle fromthe aperture normal n0 is the stagnation density in thecell n(R θ) is the total number density distribution inte-grated over velocity and f(v) is the normalized velocitydistribution in the cell The velocity distribution in thebeam is given by [61]

fbeam(v) = (vv)f(v) =32

π2v4v3eminus4v2π(v)2 (46)

From the velocity distribution we can extract the meanforward velocity of the beam

veff =

int infin0

vfbeam(v) dv =3π

8v asymp 12v (47)

From the total number density in the beam n(R θ)we can extract the FWHM (full-width at half-maximum)of the characteristic angular spread ∆θ by solvingn(R∆θ2) = 1

2n(R 0) which gives

∆θ =2π

3= 120 (48)

19

or the characteristic solid angle ∆Ω

∆Ω = 2π(1minus cos(∆θ2)) = π (49)

Note that this is the angular spread from a differentialarea of the aperture near the aperture we would haveto integrate over the area of the aperture to obtain thefull shape however this angular spread is valid in the farfield

The rate at which molecules escape the cell and there-fore enter the beam is simply the molecular flow ratethrough an aperture

N =1

4n0bv0Aaperture (50)

Effusive beams of certain species have very large fluxessuch as certain metal atoms or low-reactivity moleculeswith high vapor pressure For alkali metals [48] the cell(or oven) temperature required to achieve a vapor pres-sure of 1 torr is between around 500 and 1000 K The flowthrough a 1 mm2 aperture is then around 1014minus1015 sminus1Note that in this situation there is no buffer gas

The beam resulting from an effusive source is not im-mediately useful for many applications The large for-ward velocity (typically several hundred m sminus1) wouldlimit laser interrogation time and broad velocity dis-tributions would lead to significantly broadened spec-tral lines Some atoms can be slowed and cooled usingpowerful optical techniques[48] however until recentlymolecules have (with few exceptions [49 50]) resistedthese optical techniques due to their complex internalstructure In addition molecules have internal degreesof freedom which can be excited by the large temper-atures in an oven The rotational energy constant fordiatomic molecules is typically 1-10 K timeskB so at typicaloven temperatures the molecules can be distributed overhundreds of rotational states

2 Fully hydrodynamic or ldquosupersonicrdquo beams

In a fully hydrodynamic or ldquosupersonicrdquo beam thegas experiences many collisions near the exit apertureKn 1 (typically Kn lt 10minus3) and therefore the beamproperties are determined by the flow properties of thegas In this case we cannot apply simple gas kinetics asin the case of effusive beams but instead must considerthe dymanics of a compressible fluid We shall assumethat the gas is monoatomic

A typical supersonic source has P0 sim 1 atm anddaperture sim 1 mm2 Supersonic sources are often cooledso that the forward velocity is reduced and typicallyhave T0 = 200 minus 300 K Increasing the backing pres-sure P0 can be used to further reduce the temperatureof the molecules though at high enough pressures clus-ter formation can begin to negatively affect the beamproperties[1] On the other hand buffer gas beams canbe operated with high enough backing pressure such

that increasing the pressure further will no longer reducethe beam temperature without degradation of the beamproperties[7 9] Additionally for supersonic beams theintroduction of chemically reactive or refractory species ischallenging due to the short mean free path between col-lisions in the source and are typically introduced into theexpansion plume[11 88ndash90] This reduces the brightnessof the beam On the other hand beams of polar radicalscan be created with buffer gas cooling[7 9] with around100 times the brightness of supersonic beams of similarspecies (see Table I)

The gas flow rate from the aperture in a supersonicsource can be on the order of 1 standard liter per secondwhich would make keeping good vacuum in the appara-tus difficult if the beam were to operate continuously Forthis reason supersonic beams are often pulsed to reducetime-averaged gas load on the vacuum system Contin-uous or ldquoCamparguerdquo-type[1 91] supersonic beams arepossible although they introduce many technical chal-lenges On the other hand buffer gas cooled beams canbe operated continuously without considerable difficulty(see Table II for a list of continuous buffer gas cooledbeams)

For a monoatomic gas with specific heat ratio γ =53 the number density and temperature in a supersonicexpansion are related by[61]

n

n0=

(T

T0

)32

(51)

In the far field (typically more than four times theaperture diameter away from the aperture [61]) the num-ber density will fall off as a point source n(R) prop Rminus2where R is the distance to the aperture Therefore

n(R) prop Rminus2 T (R) prop Rminus43 (52)

Thus we see that unlike in the case of an effusivebeam as the beam expands the temperature decreasesThe temperature will continue to decrease until the gasdensity becomes low enough that collisions stop the gasceases to act like a fluid and the gas atoms simply flyballistically This transition is often called ldquofreezingrdquo orldquoquittingrdquo Even from a room-temperature supersonicsource it is not uncommon to have beam-frame temper-atures of around 1 K

The relationship between the forward velocity andtemperature of an ideal monoatomic gas expansion isgiven by [61]

v =

radic5kB(T0 minus T )

m (53)

If this gas is allowed to expand a long enough distancesuch that T T0 then the final forward velocity is

v =

radic5kBT0

m= v0

radic5π

8asymp 14v0 (54)

20

A standard supersonic source is argon expanding froma 300 K cell which has a forward velocity of about 600m sminus1 A more technically challenging source has argonexpanding from a 210 K cell which has a forward velocityof about 300 m sminus1 On the other hand buffer gas beamstypically have a forward velocity of lt 200 m sminus1 and canbe as slow as 40 m sminus1 (see section Section II B 2)

The label ldquosupersonicrdquo comes from the fact that as thegas expands from the aperture the temperature drops sothat the speed of sound (Eq (19)) decreases yet the for-ward (flow) velocity increases (Eq (53)) so that even-tually the Mach number becomes larger than 1 In factsetting the stagnation pressure and temperature so thatthe Mach number is exactly 1 at the aperture yields max-imum gas flow rate through the aperture [61]

The number density as a function of the distance Rand the angle θ from the aperture normal is given ap-proximately by [92]

n(R θ) = n(R 0) cos2

(πθ

2φ

) (55)

where φ asymp 14 for a monoatomic gas We can then findthe angular spread ∆θ and solid angle ∆Ω as in Eqs (48)and (49) to be

∆θ = φ asymp 14 = 79 ∆Ω asymp 14 (56)

If there is a small amount of a species of interest mixedin with the main (or carrier) gas there are enough col-lisions that the species will follow the carrier gas flowlines and always be in thermal equilibrium Thereforethe properties discussed for the carrier gas should be verysimilar for the species gas as well If the species has inter-nal structure (ie electonic vibrational and rotationalstates that can be thermally populated) then if there aresufficiently large inelastic internal-state-changing colli-sion cross sections with the carrier gas then the internaltemperatures can be thermalized as well[1] This is oftenthe case so supersonic beams are useful tools for creat-ing beams of translationally and internally cold molecularbeams albeit with a large forward velocity

E Technical details of source construction

The basic requirements for a buffer gas cell were out-lined in Section II A but in this section we will providesome technical details of source construction More de-tails may be found in existing literature [3 5 7 9 67]Here we shall focus purely on the design and engineeringaspects so readers not concerned with these details areencouraged to skip this section

1 The cell

Here we will describe the cell used by Hutzler et al[7]however the features are similar for other ablation-loaded

buffer gas cells[3 5 9] (we will not consider the technicaldetails of capillary loading[5 67]) A schematic of thecell is shown in Figure 2

The cell is a cryogenically cooled cylindrical coppercell with internal dimensions of 13 mm diameter and 75mm length A 2 mm inner diameter copper tube enter-ing on one end of the cylinder flows buffer gas into thecell A 150 mm length of the fill line tube is thermallyanchored to the cell ensuring that the buffer gas is coldbefore it flows into the cell volume An open aperture(or nozzle) on the other end of the cell lets the buffer gasspray out as a beam The aperture should be thin-walled(typically iexcl05 mm) to prevent the species of interest fromsticking to the sides of the aperture The ablation targetis located approximately 50 mm from the exit apertureA pulsed NdYAG laser (Continuum Minilite II 532 nm17 mJ per 6 ns pulse) focused with a converging lens isfired at the target

In addition to the main cylindrical internal volumetwo holes are drilled perpendicularly to the main vol-ume axis One hole (13 mm diameter) has the ablationtarget on one side and a window on the other anotherhole (10 mm diameter) has a window on both sides fora spectroscopy laser The windows are made of 3 mmthick borosilicate glass and are sealed to the holes in thecell with indium The window for the ablation laser ismounted on the end of a 38 mm long copper tube whichattaches to the cell this keeps the window far from theablation target If the window is too close to the abla-tion target the window will become coated with ablationdetritus into which the ablation laser can begin deposit-ing energy This both reduces the amount of energy de-posited into the ablation target and cause the windowto become damaged and unusable

2 Radiation shields

The blackbody heat load on a 4 K surface from a 300 Kenvironment is approximately 50 mW cmminus2 A cryogeniccell can easily have surface area of gt100 cm2 and wouldtherefore have to experience a heat load of several wattsThis would overwhelm most cryogenic refrigerators soit is necessary to surround the cell with cold surfacesSurrounding the cell by a blackbody shield cooled by aliquid nitrogen cryostat (77 K) or the first stage of apulse tube cooler (sim 30minus50 K) will reduce the blackbodyheat load on the cell to lt 1 of the 300 K blackbodyheat load This heat load will instead be deposited intothe blackbody shield however a typical liquid nitrogencryostat or pulse tube cooler can easily handle these heatloads at these temperatures The blackbody heat loadcan also be further reduced by covering the blackbodyshield with several layers of thin aluminum-coated mylarldquosuperinsulationrdquo

The cell is also sometimes additionally enclosed in aninner radiation shield typically around 4-5 K This canhelp reduce the heat load further since it could be eas-

21

ier to superinsulate a radiation shield instead of the cellitself Additionally the 4 K shield could help to protectcryopumps as discussed below

3 Cryopumps

Enclosing the cell in radiation shields means that thegas conductance to the external vacuum chamber is verylow If no pumping occurred inside the radiation shieldsthe buffer gas would build up to the point where theresidual pressure was too high to allow for a beam In thecase of neon buffer gas this can be solved by surroundingthe cell with a radiation shield kept at a temperaturewhere the vapor pressure of neon is acceptably low whichis simple to achieve with standard cryogenic refrigeratorsor liquid helium (for example the vapor pressure of neonis lt 10minus9 torr at 7 K) A neon cooled buffer gas beaminside a 4 K radiation shield can operate for extendedperiods of time Hutzler et al[7] operated such a beamcontinuously for over 24 hours without beam or vacuumdegradation

For helium this is not practical the radiation shieldwould have to be cooled to lt 05 K for similar vapor pres-sures which would require much more complex cryogenicsystems and superfluid film management Fortunatelythere is a solution which is to use activated charcoal asa cryopump[58] When cooled to 10 K activated char-coal becomes a cryopump for helium with up to severall sminus1 pumping speed per cm2 of charcoal and can holdalmost 1 STP liter of helium per gram (though thesevalues are highly dependent on temperature and otherparameters [58]) Covering the inside of a 4 K radiationshield with sim 100 cm2 of activated charcoal bonded tocopper plates can result in a cryopump with a pump-ing speed of several hundred liters per second that canlast for hours under typical gas loads[7 9] As the char-coal fills up with helium the pumping speed begins tochange which can result in a degradation of beam prop-erties [7 9] therefore it is necessary to warm up thecharcoal (typically to sim 20 K) and pump out the des-orbed helium with a mechanical pump Experience showsthat the beam properties are very sensitive to charcoalamount and placement[7 9] often in very non-intuitiveways

4 Beam collimation

Similar to supersonic beams buffer gas cooled beamstypically have collimators to create differentially pumpedregions and reduce the gas load on the part of the appa-ratus where the molecules are being probed With buffergas cooled beams this is especially advantageous sincecollimators can be kept in the cryogenic region and there-fore take advantage of the very large pumping speeds af-forded by cryopumping Hutzler et al[7] found that thebeam properties were largely insensitive to the placement

of a collimator when using a neon buffer gas however aswith the charcoal cryopumps the placement of the colli-mator has often been seen to strongly influence the beamproperties of the helium buffer gas cooled beam Cor-rect placement requires careful consideration and mayinvolve multiple attempts

III APPLICATIONS

In this section we will discuss some select applicationswhere buffer gas beams can offer significant advantagesLaser cooling precision measurements collisional stud-ies and trap loading

A Laser cooling of buffer gas beams

Laser cooling works by continuously scattering photonsoff of an atom or molecule in a manner that dissipatesenergy[48] The number of photon scattering events tostop an atom or a molecule is given by N = mv~kwhere m is the mass of the species v is its velocity andk = 2πλ where λ is the wavelength of the laser lightFor typical atoms or molecules moving at room temper-ature thermal velocities this number is about 104 Theelectronic ground state of an atom may contain multi-ple hyperfine states and off-resonance excitation some-times brings the atoms to different hyperfine states inthe excited state which can decay to an off-resonant (orldquodarkrdquo) hyperfine state in the electronic ground state Ifthis happens a ldquore-pumprdquo laser resonant with the otherhyperfine state can pump the atom back into the reso-nant state

In contrast the electronic ground state of moleculescontains multiple internal states including vibrationaland rotational as well as hyperfine states The num-ber of re-pump lasers needed to close the optical transi-tion grows accordingly Despite these challenges Di Rosa[93] pointed out that a set of molecules with strong sin-gle photon transitions and a highly diagonal vibrationaltransitions (Frank-Condon factors[85]) may be feasiblefor direct laser cooling The first criterion ensures a largephoton scattering rate meaning that a sufficient numberof photons can be scattered in the limited interactiontime (determined by the molecular beam velocity andgeometrical constraints on the length of the interactionregion) The second criterion implies a high probabilityof decaying back to the initial vibrational ground state(vprimeprime = 0) If p 1 is the probability of decaying into adark state after one optical transition then if there areno re-pump lasers the total number of photons scatteredfor each molecule Nscat is given by (1 minus p)Nscat sim eminus1yielding Nscat sim 1p Di Rosa[93] listed a few moleculesthat satisfied the above requirements including CaH andNH Most of these molecules can scatter sim 100 photonswithout any vibrational re-pump lasers and can scatterup to sim 104 photons with one vprimeprime = 1 re-pump laser

22

In contrast to vibrational leakage where no strict se-lection rules apply rotational transitions satisfy the totalangular momentum change selection rule ∆J = 0plusmn1Stuhl et al [94] noticed that the rotational leakage canbe mitigated by choosing a transition where the angu-lar momentum J primeprime of the ground state is larger than theangular momentum J prime of the lowest rotational state inthe excited electronic state For example consider amolecule with a ground electronic state containing ro-tational levels J primeprime = 1 2 3 and an excited electronicstate with rotational levels J prime = 0 1 2 (for examplethe X3∆1 rarr E3Π0 transition of TiO[94]) If a laserdrives the transition |X J primeprime = 1〉 rarr |E J prime = 0〉 then theselection rule |J primeprimeminusJ prime| le 1 means that the only radiativedecay allowed is |E J prime = 0〉 |XJ primeprime = 1〉 ie a ro-tationally closed transition The molecule may still havevibrational leakage but those channels can be closed withre-pump lasers in the usual way

Several of the diatomic molecules that satisfy the crite-ria for laser cooling as suggested by Di Rosa[93] and Stuhlet al[94] are radicals Since the number of photons andthe distance needed to stop molecules are proportional tov and v2

respectively where v is the forward velocity of

the molecules molecular radical sources with a low for-ward velocity as well as a high brightness are desirablefor direct laser cooling As mentioned earlier (see TableI) a buffer gas cooled beam can deliver higher brightnessand lower forward velocity for these types of species Asan example a boosted buffer gas beam has a typical for-ward velocity of sim 150 m sminus1 which reduces the numberof photons needed to stop a CaH molecule by a factorof sim 5 compared to a 1300 K oven source as initiallyproposed by Di Rosa[93]

The first demonstration of optical cycling in moleculeswas achieved by using a buffer gas cooled beam ofSrF[49] The X2Σ+

12 rarr A2Π12 transition of SrF has

relatively diagonal Franck-Condon factors[49] fvprime=0 vprimeprime f00 asymp 098 f01 asymp 002 f02 asymp 4 times 10minus4 and f03+ lt10minus5 Theoretically SrF could scatter Nscat = 1f03+ gt105 photons with two vibrational re-pump lasers assum-ing that other internal states are addressed as well Rota-tional leaking was prevented by using an N primeprime = 1rarr N prime =0 transition Since SrF has a nuclear spin of I = 12 andthe hyperfine splitting of |N prime = 0 J prime = 12 gt is small ev-ery hyperfine state in the N primeprime = 1 manifold would be pop-ulated during the transition and needs to be addressedThis was achieved using lasers with several sidebands(created using an electro-optic modulator) which were onresonance with the hyperfine states One important fea-ture of a transition with J primeprime gt J prime is that the ground statecontains more Zeeman states than the excited state lead-ing to dark Zeeman states[94] mJprimeprime = plusmnJ primeprime To addressthese dark states Shuman et al used a small magneticfield which was at an angle relative to the polarization ofthe cooling lasers to constantly remix the Zeeman states

With the beam source used in those first laser coolingexperiments the SrF molecules were produced by laserablation in a helium buffer gas cell at 4 K resulting in a

molecular beam with a total number of 109 SrF moleculesexiting the cell (per pulse) in the N primeprime = 1 state moving atv = 200 m sminus1 [49] The molecular beam was collimatedtransversely by a 6 mm diameter aperture before enteringthe laser interaction area which consisted of the maincooling laser one re-pump laser for vprimeprime = 1 and mag-netic field coils When the magnetic field was turned onin addition to the main cooling laser Shuman et al ob-served that the induced fluorescence signals increased bya factor of sim 35 Adding the vibrational re-pump laserfurther increased the fluorescence signals by another fac-tor of sim 35 corresponding to a total average numberof photons scattered per molecule of Nscat sim 170 Sinceboth lasers were applied perpendicularly to the molecu-lar beam from one transverse direction the net momen-tum transferred from the photons to SrF was sufficient tocreate a position shift or deflection of the beam The ob-served deflection indicated Nscat = 140 consistent withthe previous estimation based on the fluorescence mea-surement

In a subsequent experiment Shuman et al [50] demon-strated transverse cooling of the buffer gas cooled SrFbeam By incorporating an additional re-pump laser forthe vprimeprime = 2 state and arranging the cooling lasers to in-tersect the molecular beam multiple times at nearly 90the molecules scattered Nscat = 500 minus 1000 photons ina 15 cm long region When the cooling lasers were reddetuned with a magnetic field of 5 G the transverse tem-perature of the SrF beam was cooled from T0 = 50 mK(due to the geometry of the mechanical beam collima-tors) down to T sim 5 mK In this regime the mixingfield is large enough for rapidly remixing molecules inthe Zeeman states leading to Doppler cooling Shumanet al discovered that the molecular beam also obtaineda lower temperature when the lasers were blue detunedwith a relatively low field of 06 G In this case SrF inthe bright Zeeman state constantly experienced a peri-odic potential provided by the cooling lasers resulting inldquoSisyphusrdquo-like cooling[48 50]

1 Direct loading of exotic atoms into magneto-optical traps

Several exotic atoms have been successfully loadedinto magneto-optical traps (MOTs[48 95]) including Yb[96 97] Ag[98] Er[99] Dy [100] and Tm [101] Becausethese atoms have much higher melting points than alkaliatoms effusive oven sources used to create these atomicbeams operated at high temperatures between 700 and1500 K A Zeeman slower is typically needed to deceler-ate the fast-moving atoms (v sim 350 minus 580 m sminus1) forefficiently loading into MOT which has a typical cap-ture velocity lt 60 m sminus1 As discussed in Section II C 2a near effusive buffer gas cooled beam can be producedby adding one slowing cell to the typical buffer gas cellAlthough this type of beam has been found to have atypically lower extraction efficiency(sim 1) than a hydro-dynamically extracted beam without a slowing cell the

23

low forward velocity of the beam makes direct loading ofexotic atomic beams into MOTs feasible Additionallythe very high fluxes possible with ablation of certain met-als can lead to a superior beam system

The longitudinal and transverse temperatures of CaHmolecules in a beam produced with a slowing cell weremeasured to be sim 5 K and sim 25 K respectively [10]Since the cooling mechanism only relies on elastic col-lisions with the He buffer gas we expect atomic beamsproduced from such a slowing cell to have properties simi-lar to the beam of CaH (except of course for any possiblemass-related differences) For example the forward ve-locity of a slow Yb beam with a longitudinal temperatureof 5 K is sim 30 m sminus1 which is consistent with the forwardvelocity of a Yb beam demonstrated by Patterson [102]using a similar cell design Employing a one-dimensionallaser cooling model the capture velocity of a MOT isgiven by vc = (|∆|+ Γ)k [97] where ∆ is the detuningof the cooling laser and Γ is the natural linewidth ForYb assuming |∆| = Γ = 2πtimes28 MHz the capture veloc-ity is 22 m sminus1 implying a large fraction of a buffer gascooled Yb beam can be loaded without any longitudinallaser slowing (see Table IV)

Collisional heating from the buffer gas streamingthrough the MOT region could be a concern Typicallythe buffer density inside the slowing cell is on the orderof 1014 cmminus3 Although it is difficult to measure the Hebeam profile a good approximation is to assume thatthe He beam attains the same temperatures as the CaHmolecular beam Therefore the collisional heating fromthe buffer gas is negligible compared to the cooling powerfrom the scattered photons starting from a distance of10 cm away from the aperture where the He density islt 1012 cmminus3 Any potential loss due to the divergenceof the beam can be mitigated by employing transverselaser cooling to collimate the atomic beam between thecell aperture and MOT Assuming the transverse capturevelocity is given by vct = Γk we can estimate the load-ing efficiency of a buffer gas cooled beam into MOTs byconsidering the velocity distributions that are within vcttransversely and vc longitudinally

Table IV shows some exotic atoms that have beenloaded into MOTs from effusive oven sources and havealso been buffer gas cooled Of these species only Ybhas been realized as a buffer gas beam so far[5] Giventhe generality of the buffer gas beam technique we be-lieve that producing cold and slow exotic atomic beamswith beam properties similar to the CaH beam[10] isvery likely We can therefore estimate the loading effi-ciency of these atoms into MOTs from buffer gas beamsfload by assuming that these proposed atomic beamswould have the same longitudinal and transverse tem-peratures of the CaH beam 5 K and 25 K respectivelyBased on the ablation yields inside the buffer gas cellNablation reported in the past[4] and a typical extrac-tion efficiency of the slowing cell of fext sim 5 times 10minus3 wecan estimate potential loaded numbers per ablation pulseNload sim Nablationtimesfexttimesfload shown as the last column

Atom Ntrappedexp fload [] Nload [pulseminus1]

Yb [97] 107 21 2 times 1010

Ag [98] 3 times 106 17 3 times 109

Dy [100] 25 times 108 33 3 times 109

Er [99] 106 39 4 times 108

Tm [101] 7 times 104 03 3 times 106

TABLE IV Some exotic atoms which have been loaded into aMOT from an effusive oven source and also buffer gas cooledNtrappedexp is the number of atoms that were loaded into theMOT in the respective experiments fload is the projectedloading efficiency from a buffer gas beam source and Nload

is the projected number of atoms which could be trapped inthe MOT with a single pulse from a buffer gas source Adescription of these estimates may be found in the text

in Table IV The estimated numbers of atoms loaded perpulse are high compared to the reported trapped num-bers By loading 1minus 10 pulses the expected atom num-bers (or densities) accumulated in MOTs could approacha regime where the radiation pressure and collisions be-tween ground and excited state atoms would limit theatomic density[103] Co-loading multiple species with-out using high temperature ovens and Zeeman slowersinto a MOT is feasible by simply ablating several speciessimultaneously

B Precision measurements

Another application of molecular beams is the preci-sion determination of molecular properties This is madepossible by the lack of collisions in the beam regionand enhanced by the large volume of advanced molec-ular beam production manipulation and spectroscopytechniques[1 2] Precision spectroscopy with supersonicbeams is a workhorse in chemistry and physics As thereader can surely surmise by now many precision mea-surements can benefit from the high flux and low for-ward velocity afforded by buffer gas cooled beams Inthis section we will review some molecular beam preci-sion measurements and discuss how they could benefitfrom buffer gas cooled beam technology

1 Electric dipole moments

In 1950 Purcell and Ramsey[104] were the first to se-riously consider the possibility of a fundamental parti-cle (ie an electron or nucleon) possessing a permanentelectric dipole moment (EDM) Before this time it waswidely (though not universally[105]) believed that a fun-damental particle could not possess such a moment be-cause it would violate parity (P) and time-reversal (T)invariance in the following manner Since a dipole mo-ment is a vector quantity it must be aligned with the spinof the particle which is the only intrinsic vector associ-

24

ated with a fundamental particle However an electricdipole moment is a polar vector while spin is an axial(or pseudo-) vector so these two quantities must behaveoppositely under inversion of coordinate systems or rever-sal of time yet the previous argument requires them touniquely determine each other Although no permanentEDM of a fundamental particle has ever been measured(despite over 50 years of experimental searches[106])such a discovery would have a profound impact on ourunderstanding of particle physics and cosmology For anaccessible discussion about EDMs of fundamental par-ticles and their implications see the article by FortsonSandars and Barr[107] for more details see the book byKhriplovich and Lamoreaux[28]

The essential idea of nearly every EDM search isto look for a small shift in precession frequency of aspin in an electric field as the electric field direction is

reversed[28] For a particle with spin ~S magnetic dipolemoment micro and electric dipole moment d in a parallel

magnetic field ~B and electric field ~E the spin of the par-ticle (which is parallel to both the magnetic and electricdipole moment) will precess about the fields with angularfrequency

ω =d~E + micro~B

~middot~S

|~S| (57)

Consider an experiment where ~S and ~B are kept fixed

but the direction of ~E is reversed and then the frequency

ωplusmn is measured for the two different orientations plusmn~E The value of the electric dipole moment d can then beextracted by comparing these two measured values

d =~(ω+ minus ωminus)

2~E middot ~S|~S| (58)

The determination of d then reduces to a precision mea-surement of the frequencies ωplusmn Precise frequency mea-surements are best accomplished by the separated oscilla-tory field (or Ramsey) method[2] in which the spins areallowed to precess for a time (the ldquocoherence timerdquo) τbefore the accumulated phase angle is measured therebydetermining ω If such an experiment is repeated witha total of N spins the uncertainty in the EDM is givenby[28]

δd =~τ

|~E|radicN|~S|

(59)

From this equation we can see that an EDM ex-periment should have large electric fields long coher-ence times and large count rates Neutral objects suchas neutrons or atoms can simply be placed in largeelectric fields however charged particles like electronsor protons would simply accelerate out of the electricfield Sandars[108] realized that not only could an elec-tric dipole moment of a charged object be inferred bystudying a composite neutral object such as an atom or

molecule but the electric dipole moment could actuallybe enhanced For example Sandars calculated[109] thatan electric dipole moment of the electron de could in-duce an electric dipole moment of an atom dA with arelativistic ldquoenhancement factorrdquo dAde that can be over100 for Cs atoms The basic idea[110] is that the electroncan sample the atomic electric field which is typically oforder

Eatomic asympe2

4πε0a20

asymp 5 GV cmminus1 (60)

where a0 is the Bohr radius This is considerably largerthan a typical macroscopic lab field of 100 kV cmminus1Atoms cannot take full advantage of this enhancementbecause they cannot be fully polarized in laboratory elec-tric fields[111] however polar molecules can be polarizedin lab fields and for this reason most current electronEDM experiments use polar molecules[111]

The molecules which have the highest enhancementfactor have high-Z atoms with partially filled electronshells and tend to be chemically reactive have high melt-ing points and are often free radicals[111] For this rea-son effusive beam sources of these molecules are typ-ically not feasible the Boltzmann distribution of rota-tional states at temperatures where the species have ap-preciable vapor pressure put only a tiny fraction in anysingle rotational state (however performing an electronEDM experiment with molecules in a hot vapor cell is apossibility[112]) A molecular beam for an EDM searchshould therefore have low temperature and in light ofEq (59) a low forward velocity to allow the moleculesto interact with the fields for a long time giving largeτ For the types of molecules under consideration buffergas cooled beams[3 7 9] have considerable advantagesover the standard supersonic beam[11] As discussed ear-lier the brightness for refractory or chemically reactivespecies can be very high with buffer gas beams and theyhave considerably slower forward velocities In Table Iwe can see that a buffer gas cooled ThO beam has aslower forward velocity and over 100 times the bright-ness compared to a demonstrated state-of-the-art YbFsupersonic beam both of which are currently being usedfor an electron EDM search These reasons make buffergas cooled beams an attractive option for electron EDMsearches with some existing supersonic experiments con-sidering switching to buffer gas cooling[70]

Searches for the electron EDM are currently underwayin molecular beams of YbF[27] ThO[59] and WC[113]as well as several other atomic molecular and solid statesystems[111]

2 Parity violation and anapole moments

The exchange of weak neutral currents between theconstituent particles of an atom or molecule can lead toobservable parity violating effects in their spectra Pre-cision examinations of these effects known as atomic

25

parity violation (APV) allow the study of nuclear andelectroweak physics using atomic systems[29] An ex-perimentally feasible approach to using APV to probeelectroweak physics was first proposed in 1974[114] andsince then APV has been observed in a number ofatoms[29 115ndash117] Here we will briefly discuss howbuffer gas beams may improve experimental studies ofAPV detailed discussions of APV theory and experi-ments may be found elsewhere[29 30 115 118]

Weak neutral currents The exchange of a neutralZ0 boson between the nucleus and the electrons in anatom can give rise a parity-violating electronic contactpotential[114] This potential can mix atomic states ofopposite parity such as a valence electron in S12 andP12 atomic orbitals This mixing can either be mea-sured by searching for parity violating optical rotationin atomic emissionabsorption[114 117] or by lookingfor interference between the APV induced state mixingand the mixing provided by an external electric field (theStark-interference method[119]) APV has been mea-sured in a number of atoms[29 116] and comparison totheory gives tests of the standard model at low energies

Nuclear anapole moments Another parity violatingeffect in an atom is the anapole moment[29 118 120]which arises from an exchange of a Z0 or Wplusmn boson be-tween nucleons in a nucleus Like the parity-violatingpotential above the interaction is a contact potential be-tween the electrons and nuclear anapole moment Theobservable effect is very similar to that of the weak neu-tral currents discussed above with the important ex-ception that the size of the effect will vary dependingon the nuclear spin An experimental signature of ananapole moment is then a difference in parity violat-ing amplitudes between different hyperfine levels Sofar only a single anapole moment has been measuredin the 133Cs nucleus[121] though other experiments areunderway[30]

Enhancement of parity violation in diatomic moleculesParity-violating effects have thus far been observed onlyin atoms though the search has been extended to di-atomic molecules for very compelling reasons Moleculeshave states of opposite parity (rotational states and insome cases ΛΩ-doublets[85]) which are typically muchsmaller than the spacing between opposite parity elec-tronic states in atoms so the effects of nuclear-spin-dependent parity-violating violation (such as anapolemoments) can be greatly enhanced[122ndash125] This mix-ing can be increased even further by applying exter-nal magnetic fields to push rotational states to near-degeneracy DeMille et al[124] proposed (and are work-ing on) an experiment to use a supersonic beam of BaFfree radicals in a 2Σ electronic state to measure parity-violating amplitudes with high precision

Similar to the case with an EDM measurement theshot-noise limited uncertainty (Eq (59)) in the parity vi-olating amplitude scales as prop Nminus12Tminus1 where N is thetotal number of interrogated molecules and T is the timethat the molecules spend interacting with the electro-

magnetic fields Also similar to the EDM measurementsis the choice of molecules including[30] BiO BiS HgFLaO LaS LuO LuS PbF and YbF These are all freeradicals with heavy nuclei and are therefore prime candi-dates for production in a buffer gas cooled beam Thereare even some molecules which have already been dis-cussed such as YbF and BaF (Table I) for which usinga buffer gas beam can deliver over 100 times the bright-ness of a supersonic beam with a slower forward velocity(allowing for the same time T with a shorter apparatuseasing technical requirements) It is for this reason thata BaF anapole moment experiment (at Yale[124]) is pur-suing a buffer gas cooled beam source[12]

3 Time-variation of fundamental constants

There has been much recent interest in the ques-tion of whether or not fundamental constants are trulyldquoconstantrdquo or whether their values have changed overtime In particular the dimensionless fine structureconstant α = e24πε0~c and electron-proton mass ra-tio micro = memp have attracted special attention due tothe possibility of measuring their variation from mul-tiple independent sources Detailed discussions of thetheory and experiments discussed here may be found inreviews[38 126]

Searches for time-variation of fundamental constantstypically take one of two approaches One is to lookat data which may give information about α or micro froma very long time ago for example by examining astro-nomical spectra at large redshifts[38 127] but with lim-ited accuracy (though the search may be coupled with alaboratory precision spectroscopy experiment) Anothertechnique is to use measurements with high precision butover a comparatively short timescale for example by us-ing an atomic clock[128 129] The current limits on microand α are

micro

micro= (1plusmn 3)times 10minus16 yrminus1

from the inversion spectrum of ammonia measured insources with high redshift[127] and

α

α= (minus16plusmn 23)times 10minus17 yrminus1

from comparing optical clocks[128]As with EDMs and parity violation molecules can have

large enhancement factors which could allow for moresensitive measurements In particular the α and micro de-pendence of fine structure splitting ωf prop α2 rotational

splitting ωr prop micro and vibrational splitting ωv prop micro12 aredifferent[38] and if two levels with different hyperfinerotational or vibrational character are nearly degener-ate there can be significant sensitivity enhancement[130]in changes to both micro and α This enhancement can beseveral orders of magnitude (compared to atoms) and

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

20

A standard supersonic source is argon expanding froma 300 K cell which has a forward velocity of about 600m sminus1 A more technically challenging source has argonexpanding from a 210 K cell which has a forward velocityof about 300 m sminus1 On the other hand buffer gas beamstypically have a forward velocity of lt 200 m sminus1 and canbe as slow as 40 m sminus1 (see section Section II B 2)

The label ldquosupersonicrdquo comes from the fact that as thegas expands from the aperture the temperature drops sothat the speed of sound (Eq (19)) decreases yet the for-ward (flow) velocity increases (Eq (53)) so that even-tually the Mach number becomes larger than 1 In factsetting the stagnation pressure and temperature so thatthe Mach number is exactly 1 at the aperture yields max-imum gas flow rate through the aperture [61]

The number density as a function of the distance Rand the angle θ from the aperture normal is given ap-proximately by [92]

n(R θ) = n(R 0) cos2

(πθ

2φ

) (55)

where φ asymp 14 for a monoatomic gas We can then findthe angular spread ∆θ and solid angle ∆Ω as in Eqs (48)and (49) to be

∆θ = φ asymp 14 = 79 ∆Ω asymp 14 (56)

If there is a small amount of a species of interest mixedin with the main (or carrier) gas there are enough col-lisions that the species will follow the carrier gas flowlines and always be in thermal equilibrium Thereforethe properties discussed for the carrier gas should be verysimilar for the species gas as well If the species has inter-nal structure (ie electonic vibrational and rotationalstates that can be thermally populated) then if there aresufficiently large inelastic internal-state-changing colli-sion cross sections with the carrier gas then the internaltemperatures can be thermalized as well[1] This is oftenthe case so supersonic beams are useful tools for creat-ing beams of translationally and internally cold molecularbeams albeit with a large forward velocity

E Technical details of source construction

The basic requirements for a buffer gas cell were out-lined in Section II A but in this section we will providesome technical details of source construction More de-tails may be found in existing literature [3 5 7 9 67]Here we shall focus purely on the design and engineeringaspects so readers not concerned with these details areencouraged to skip this section

1 The cell

Here we will describe the cell used by Hutzler et al[7]however the features are similar for other ablation-loaded

buffer gas cells[3 5 9] (we will not consider the technicaldetails of capillary loading[5 67]) A schematic of thecell is shown in Figure 2

The cell is a cryogenically cooled cylindrical coppercell with internal dimensions of 13 mm diameter and 75mm length A 2 mm inner diameter copper tube enter-ing on one end of the cylinder flows buffer gas into thecell A 150 mm length of the fill line tube is thermallyanchored to the cell ensuring that the buffer gas is coldbefore it flows into the cell volume An open aperture(or nozzle) on the other end of the cell lets the buffer gasspray out as a beam The aperture should be thin-walled(typically iexcl05 mm) to prevent the species of interest fromsticking to the sides of the aperture The ablation targetis located approximately 50 mm from the exit apertureA pulsed NdYAG laser (Continuum Minilite II 532 nm17 mJ per 6 ns pulse) focused with a converging lens isfired at the target

In addition to the main cylindrical internal volumetwo holes are drilled perpendicularly to the main vol-ume axis One hole (13 mm diameter) has the ablationtarget on one side and a window on the other anotherhole (10 mm diameter) has a window on both sides fora spectroscopy laser The windows are made of 3 mmthick borosilicate glass and are sealed to the holes in thecell with indium The window for the ablation laser ismounted on the end of a 38 mm long copper tube whichattaches to the cell this keeps the window far from theablation target If the window is too close to the abla-tion target the window will become coated with ablationdetritus into which the ablation laser can begin deposit-ing energy This both reduces the amount of energy de-posited into the ablation target and cause the windowto become damaged and unusable

2 Radiation shields

The blackbody heat load on a 4 K surface from a 300 Kenvironment is approximately 50 mW cmminus2 A cryogeniccell can easily have surface area of gt100 cm2 and wouldtherefore have to experience a heat load of several wattsThis would overwhelm most cryogenic refrigerators soit is necessary to surround the cell with cold surfacesSurrounding the cell by a blackbody shield cooled by aliquid nitrogen cryostat (77 K) or the first stage of apulse tube cooler (sim 30minus50 K) will reduce the blackbodyheat load on the cell to lt 1 of the 300 K blackbodyheat load This heat load will instead be deposited intothe blackbody shield however a typical liquid nitrogencryostat or pulse tube cooler can easily handle these heatloads at these temperatures The blackbody heat loadcan also be further reduced by covering the blackbodyshield with several layers of thin aluminum-coated mylarldquosuperinsulationrdquo

The cell is also sometimes additionally enclosed in aninner radiation shield typically around 4-5 K This canhelp reduce the heat load further since it could be eas-

21

ier to superinsulate a radiation shield instead of the cellitself Additionally the 4 K shield could help to protectcryopumps as discussed below

3 Cryopumps

Enclosing the cell in radiation shields means that thegas conductance to the external vacuum chamber is verylow If no pumping occurred inside the radiation shieldsthe buffer gas would build up to the point where theresidual pressure was too high to allow for a beam In thecase of neon buffer gas this can be solved by surroundingthe cell with a radiation shield kept at a temperaturewhere the vapor pressure of neon is acceptably low whichis simple to achieve with standard cryogenic refrigeratorsor liquid helium (for example the vapor pressure of neonis lt 10minus9 torr at 7 K) A neon cooled buffer gas beaminside a 4 K radiation shield can operate for extendedperiods of time Hutzler et al[7] operated such a beamcontinuously for over 24 hours without beam or vacuumdegradation

For helium this is not practical the radiation shieldwould have to be cooled to lt 05 K for similar vapor pres-sures which would require much more complex cryogenicsystems and superfluid film management Fortunatelythere is a solution which is to use activated charcoal asa cryopump[58] When cooled to 10 K activated char-coal becomes a cryopump for helium with up to severall sminus1 pumping speed per cm2 of charcoal and can holdalmost 1 STP liter of helium per gram (though thesevalues are highly dependent on temperature and otherparameters [58]) Covering the inside of a 4 K radiationshield with sim 100 cm2 of activated charcoal bonded tocopper plates can result in a cryopump with a pump-ing speed of several hundred liters per second that canlast for hours under typical gas loads[7 9] As the char-coal fills up with helium the pumping speed begins tochange which can result in a degradation of beam prop-erties [7 9] therefore it is necessary to warm up thecharcoal (typically to sim 20 K) and pump out the des-orbed helium with a mechanical pump Experience showsthat the beam properties are very sensitive to charcoalamount and placement[7 9] often in very non-intuitiveways

4 Beam collimation

Similar to supersonic beams buffer gas cooled beamstypically have collimators to create differentially pumpedregions and reduce the gas load on the part of the appa-ratus where the molecules are being probed With buffergas cooled beams this is especially advantageous sincecollimators can be kept in the cryogenic region and there-fore take advantage of the very large pumping speeds af-forded by cryopumping Hutzler et al[7] found that thebeam properties were largely insensitive to the placement

of a collimator when using a neon buffer gas however aswith the charcoal cryopumps the placement of the colli-mator has often been seen to strongly influence the beamproperties of the helium buffer gas cooled beam Cor-rect placement requires careful consideration and mayinvolve multiple attempts

III APPLICATIONS

In this section we will discuss some select applicationswhere buffer gas beams can offer significant advantagesLaser cooling precision measurements collisional stud-ies and trap loading

A Laser cooling of buffer gas beams

Laser cooling works by continuously scattering photonsoff of an atom or molecule in a manner that dissipatesenergy[48] The number of photon scattering events tostop an atom or a molecule is given by N = mv~kwhere m is the mass of the species v is its velocity andk = 2πλ where λ is the wavelength of the laser lightFor typical atoms or molecules moving at room temper-ature thermal velocities this number is about 104 Theelectronic ground state of an atom may contain multi-ple hyperfine states and off-resonance excitation some-times brings the atoms to different hyperfine states inthe excited state which can decay to an off-resonant (orldquodarkrdquo) hyperfine state in the electronic ground state Ifthis happens a ldquore-pumprdquo laser resonant with the otherhyperfine state can pump the atom back into the reso-nant state

In contrast the electronic ground state of moleculescontains multiple internal states including vibrationaland rotational as well as hyperfine states The num-ber of re-pump lasers needed to close the optical transi-tion grows accordingly Despite these challenges Di Rosa[93] pointed out that a set of molecules with strong sin-gle photon transitions and a highly diagonal vibrationaltransitions (Frank-Condon factors[85]) may be feasiblefor direct laser cooling The first criterion ensures a largephoton scattering rate meaning that a sufficient numberof photons can be scattered in the limited interactiontime (determined by the molecular beam velocity andgeometrical constraints on the length of the interactionregion) The second criterion implies a high probabilityof decaying back to the initial vibrational ground state(vprimeprime = 0) If p 1 is the probability of decaying into adark state after one optical transition then if there areno re-pump lasers the total number of photons scatteredfor each molecule Nscat is given by (1 minus p)Nscat sim eminus1yielding Nscat sim 1p Di Rosa[93] listed a few moleculesthat satisfied the above requirements including CaH andNH Most of these molecules can scatter sim 100 photonswithout any vibrational re-pump lasers and can scatterup to sim 104 photons with one vprimeprime = 1 re-pump laser

22

In contrast to vibrational leakage where no strict se-lection rules apply rotational transitions satisfy the totalangular momentum change selection rule ∆J = 0plusmn1Stuhl et al [94] noticed that the rotational leakage canbe mitigated by choosing a transition where the angu-lar momentum J primeprime of the ground state is larger than theangular momentum J prime of the lowest rotational state inthe excited electronic state For example consider amolecule with a ground electronic state containing ro-tational levels J primeprime = 1 2 3 and an excited electronicstate with rotational levels J prime = 0 1 2 (for examplethe X3∆1 rarr E3Π0 transition of TiO[94]) If a laserdrives the transition |X J primeprime = 1〉 rarr |E J prime = 0〉 then theselection rule |J primeprimeminusJ prime| le 1 means that the only radiativedecay allowed is |E J prime = 0〉 |XJ primeprime = 1〉 ie a ro-tationally closed transition The molecule may still havevibrational leakage but those channels can be closed withre-pump lasers in the usual way

Several of the diatomic molecules that satisfy the crite-ria for laser cooling as suggested by Di Rosa[93] and Stuhlet al[94] are radicals Since the number of photons andthe distance needed to stop molecules are proportional tov and v2

respectively where v is the forward velocity of

the molecules molecular radical sources with a low for-ward velocity as well as a high brightness are desirablefor direct laser cooling As mentioned earlier (see TableI) a buffer gas cooled beam can deliver higher brightnessand lower forward velocity for these types of species Asan example a boosted buffer gas beam has a typical for-ward velocity of sim 150 m sminus1 which reduces the numberof photons needed to stop a CaH molecule by a factorof sim 5 compared to a 1300 K oven source as initiallyproposed by Di Rosa[93]

The first demonstration of optical cycling in moleculeswas achieved by using a buffer gas cooled beam ofSrF[49] The X2Σ+

12 rarr A2Π12 transition of SrF has

relatively diagonal Franck-Condon factors[49] fvprime=0 vprimeprime f00 asymp 098 f01 asymp 002 f02 asymp 4 times 10minus4 and f03+ lt10minus5 Theoretically SrF could scatter Nscat = 1f03+ gt105 photons with two vibrational re-pump lasers assum-ing that other internal states are addressed as well Rota-tional leaking was prevented by using an N primeprime = 1rarr N prime =0 transition Since SrF has a nuclear spin of I = 12 andthe hyperfine splitting of |N prime = 0 J prime = 12 gt is small ev-ery hyperfine state in the N primeprime = 1 manifold would be pop-ulated during the transition and needs to be addressedThis was achieved using lasers with several sidebands(created using an electro-optic modulator) which were onresonance with the hyperfine states One important fea-ture of a transition with J primeprime gt J prime is that the ground statecontains more Zeeman states than the excited state lead-ing to dark Zeeman states[94] mJprimeprime = plusmnJ primeprime To addressthese dark states Shuman et al used a small magneticfield which was at an angle relative to the polarization ofthe cooling lasers to constantly remix the Zeeman states

With the beam source used in those first laser coolingexperiments the SrF molecules were produced by laserablation in a helium buffer gas cell at 4 K resulting in a

molecular beam with a total number of 109 SrF moleculesexiting the cell (per pulse) in the N primeprime = 1 state moving atv = 200 m sminus1 [49] The molecular beam was collimatedtransversely by a 6 mm diameter aperture before enteringthe laser interaction area which consisted of the maincooling laser one re-pump laser for vprimeprime = 1 and mag-netic field coils When the magnetic field was turned onin addition to the main cooling laser Shuman et al ob-served that the induced fluorescence signals increased bya factor of sim 35 Adding the vibrational re-pump laserfurther increased the fluorescence signals by another fac-tor of sim 35 corresponding to a total average numberof photons scattered per molecule of Nscat sim 170 Sinceboth lasers were applied perpendicularly to the molecu-lar beam from one transverse direction the net momen-tum transferred from the photons to SrF was sufficient tocreate a position shift or deflection of the beam The ob-served deflection indicated Nscat = 140 consistent withthe previous estimation based on the fluorescence mea-surement

In a subsequent experiment Shuman et al [50] demon-strated transverse cooling of the buffer gas cooled SrFbeam By incorporating an additional re-pump laser forthe vprimeprime = 2 state and arranging the cooling lasers to in-tersect the molecular beam multiple times at nearly 90the molecules scattered Nscat = 500 minus 1000 photons ina 15 cm long region When the cooling lasers were reddetuned with a magnetic field of 5 G the transverse tem-perature of the SrF beam was cooled from T0 = 50 mK(due to the geometry of the mechanical beam collima-tors) down to T sim 5 mK In this regime the mixingfield is large enough for rapidly remixing molecules inthe Zeeman states leading to Doppler cooling Shumanet al discovered that the molecular beam also obtaineda lower temperature when the lasers were blue detunedwith a relatively low field of 06 G In this case SrF inthe bright Zeeman state constantly experienced a peri-odic potential provided by the cooling lasers resulting inldquoSisyphusrdquo-like cooling[48 50]

1 Direct loading of exotic atoms into magneto-optical traps

Several exotic atoms have been successfully loadedinto magneto-optical traps (MOTs[48 95]) including Yb[96 97] Ag[98] Er[99] Dy [100] and Tm [101] Becausethese atoms have much higher melting points than alkaliatoms effusive oven sources used to create these atomicbeams operated at high temperatures between 700 and1500 K A Zeeman slower is typically needed to deceler-ate the fast-moving atoms (v sim 350 minus 580 m sminus1) forefficiently loading into MOT which has a typical cap-ture velocity lt 60 m sminus1 As discussed in Section II C 2a near effusive buffer gas cooled beam can be producedby adding one slowing cell to the typical buffer gas cellAlthough this type of beam has been found to have atypically lower extraction efficiency(sim 1) than a hydro-dynamically extracted beam without a slowing cell the

23

low forward velocity of the beam makes direct loading ofexotic atomic beams into MOTs feasible Additionallythe very high fluxes possible with ablation of certain met-als can lead to a superior beam system

The longitudinal and transverse temperatures of CaHmolecules in a beam produced with a slowing cell weremeasured to be sim 5 K and sim 25 K respectively [10]Since the cooling mechanism only relies on elastic col-lisions with the He buffer gas we expect atomic beamsproduced from such a slowing cell to have properties simi-lar to the beam of CaH (except of course for any possiblemass-related differences) For example the forward ve-locity of a slow Yb beam with a longitudinal temperatureof 5 K is sim 30 m sminus1 which is consistent with the forwardvelocity of a Yb beam demonstrated by Patterson [102]using a similar cell design Employing a one-dimensionallaser cooling model the capture velocity of a MOT isgiven by vc = (|∆|+ Γ)k [97] where ∆ is the detuningof the cooling laser and Γ is the natural linewidth ForYb assuming |∆| = Γ = 2πtimes28 MHz the capture veloc-ity is 22 m sminus1 implying a large fraction of a buffer gascooled Yb beam can be loaded without any longitudinallaser slowing (see Table IV)

Collisional heating from the buffer gas streamingthrough the MOT region could be a concern Typicallythe buffer density inside the slowing cell is on the orderof 1014 cmminus3 Although it is difficult to measure the Hebeam profile a good approximation is to assume thatthe He beam attains the same temperatures as the CaHmolecular beam Therefore the collisional heating fromthe buffer gas is negligible compared to the cooling powerfrom the scattered photons starting from a distance of10 cm away from the aperture where the He density islt 1012 cmminus3 Any potential loss due to the divergenceof the beam can be mitigated by employing transverselaser cooling to collimate the atomic beam between thecell aperture and MOT Assuming the transverse capturevelocity is given by vct = Γk we can estimate the load-ing efficiency of a buffer gas cooled beam into MOTs byconsidering the velocity distributions that are within vcttransversely and vc longitudinally

Table IV shows some exotic atoms that have beenloaded into MOTs from effusive oven sources and havealso been buffer gas cooled Of these species only Ybhas been realized as a buffer gas beam so far[5] Giventhe generality of the buffer gas beam technique we be-lieve that producing cold and slow exotic atomic beamswith beam properties similar to the CaH beam[10] isvery likely We can therefore estimate the loading effi-ciency of these atoms into MOTs from buffer gas beamsfload by assuming that these proposed atomic beamswould have the same longitudinal and transverse tem-peratures of the CaH beam 5 K and 25 K respectivelyBased on the ablation yields inside the buffer gas cellNablation reported in the past[4] and a typical extrac-tion efficiency of the slowing cell of fext sim 5 times 10minus3 wecan estimate potential loaded numbers per ablation pulseNload sim Nablationtimesfexttimesfload shown as the last column

Atom Ntrappedexp fload [] Nload [pulseminus1]

Yb [97] 107 21 2 times 1010

Ag [98] 3 times 106 17 3 times 109

Dy [100] 25 times 108 33 3 times 109

Er [99] 106 39 4 times 108

Tm [101] 7 times 104 03 3 times 106

TABLE IV Some exotic atoms which have been loaded into aMOT from an effusive oven source and also buffer gas cooledNtrappedexp is the number of atoms that were loaded into theMOT in the respective experiments fload is the projectedloading efficiency from a buffer gas beam source and Nload

is the projected number of atoms which could be trapped inthe MOT with a single pulse from a buffer gas source Adescription of these estimates may be found in the text

in Table IV The estimated numbers of atoms loaded perpulse are high compared to the reported trapped num-bers By loading 1minus 10 pulses the expected atom num-bers (or densities) accumulated in MOTs could approacha regime where the radiation pressure and collisions be-tween ground and excited state atoms would limit theatomic density[103] Co-loading multiple species with-out using high temperature ovens and Zeeman slowersinto a MOT is feasible by simply ablating several speciessimultaneously

B Precision measurements

Another application of molecular beams is the preci-sion determination of molecular properties This is madepossible by the lack of collisions in the beam regionand enhanced by the large volume of advanced molec-ular beam production manipulation and spectroscopytechniques[1 2] Precision spectroscopy with supersonicbeams is a workhorse in chemistry and physics As thereader can surely surmise by now many precision mea-surements can benefit from the high flux and low for-ward velocity afforded by buffer gas cooled beams Inthis section we will review some molecular beam preci-sion measurements and discuss how they could benefitfrom buffer gas cooled beam technology

1 Electric dipole moments

In 1950 Purcell and Ramsey[104] were the first to se-riously consider the possibility of a fundamental parti-cle (ie an electron or nucleon) possessing a permanentelectric dipole moment (EDM) Before this time it waswidely (though not universally[105]) believed that a fun-damental particle could not possess such a moment be-cause it would violate parity (P) and time-reversal (T)invariance in the following manner Since a dipole mo-ment is a vector quantity it must be aligned with the spinof the particle which is the only intrinsic vector associ-

24

ated with a fundamental particle However an electricdipole moment is a polar vector while spin is an axial(or pseudo-) vector so these two quantities must behaveoppositely under inversion of coordinate systems or rever-sal of time yet the previous argument requires them touniquely determine each other Although no permanentEDM of a fundamental particle has ever been measured(despite over 50 years of experimental searches[106])such a discovery would have a profound impact on ourunderstanding of particle physics and cosmology For anaccessible discussion about EDMs of fundamental par-ticles and their implications see the article by FortsonSandars and Barr[107] for more details see the book byKhriplovich and Lamoreaux[28]

The essential idea of nearly every EDM search isto look for a small shift in precession frequency of aspin in an electric field as the electric field direction is

reversed[28] For a particle with spin ~S magnetic dipolemoment micro and electric dipole moment d in a parallel

magnetic field ~B and electric field ~E the spin of the par-ticle (which is parallel to both the magnetic and electricdipole moment) will precess about the fields with angularfrequency

ω =d~E + micro~B

~middot~S

|~S| (57)

Consider an experiment where ~S and ~B are kept fixed

but the direction of ~E is reversed and then the frequency

ωplusmn is measured for the two different orientations plusmn~E The value of the electric dipole moment d can then beextracted by comparing these two measured values

d =~(ω+ minus ωminus)

2~E middot ~S|~S| (58)

The determination of d then reduces to a precision mea-surement of the frequencies ωplusmn Precise frequency mea-surements are best accomplished by the separated oscilla-tory field (or Ramsey) method[2] in which the spins areallowed to precess for a time (the ldquocoherence timerdquo) τbefore the accumulated phase angle is measured therebydetermining ω If such an experiment is repeated witha total of N spins the uncertainty in the EDM is givenby[28]

δd =~τ

|~E|radicN|~S|

(59)

From this equation we can see that an EDM ex-periment should have large electric fields long coher-ence times and large count rates Neutral objects suchas neutrons or atoms can simply be placed in largeelectric fields however charged particles like electronsor protons would simply accelerate out of the electricfield Sandars[108] realized that not only could an elec-tric dipole moment of a charged object be inferred bystudying a composite neutral object such as an atom or

molecule but the electric dipole moment could actuallybe enhanced For example Sandars calculated[109] thatan electric dipole moment of the electron de could in-duce an electric dipole moment of an atom dA with arelativistic ldquoenhancement factorrdquo dAde that can be over100 for Cs atoms The basic idea[110] is that the electroncan sample the atomic electric field which is typically oforder

Eatomic asympe2

4πε0a20

asymp 5 GV cmminus1 (60)

where a0 is the Bohr radius This is considerably largerthan a typical macroscopic lab field of 100 kV cmminus1Atoms cannot take full advantage of this enhancementbecause they cannot be fully polarized in laboratory elec-tric fields[111] however polar molecules can be polarizedin lab fields and for this reason most current electronEDM experiments use polar molecules[111]

The molecules which have the highest enhancementfactor have high-Z atoms with partially filled electronshells and tend to be chemically reactive have high melt-ing points and are often free radicals[111] For this rea-son effusive beam sources of these molecules are typ-ically not feasible the Boltzmann distribution of rota-tional states at temperatures where the species have ap-preciable vapor pressure put only a tiny fraction in anysingle rotational state (however performing an electronEDM experiment with molecules in a hot vapor cell is apossibility[112]) A molecular beam for an EDM searchshould therefore have low temperature and in light ofEq (59) a low forward velocity to allow the moleculesto interact with the fields for a long time giving largeτ For the types of molecules under consideration buffergas cooled beams[3 7 9] have considerable advantagesover the standard supersonic beam[11] As discussed ear-lier the brightness for refractory or chemically reactivespecies can be very high with buffer gas beams and theyhave considerably slower forward velocities In Table Iwe can see that a buffer gas cooled ThO beam has aslower forward velocity and over 100 times the bright-ness compared to a demonstrated state-of-the-art YbFsupersonic beam both of which are currently being usedfor an electron EDM search These reasons make buffergas cooled beams an attractive option for electron EDMsearches with some existing supersonic experiments con-sidering switching to buffer gas cooling[70]

Searches for the electron EDM are currently underwayin molecular beams of YbF[27] ThO[59] and WC[113]as well as several other atomic molecular and solid statesystems[111]

2 Parity violation and anapole moments

The exchange of weak neutral currents between theconstituent particles of an atom or molecule can lead toobservable parity violating effects in their spectra Pre-cision examinations of these effects known as atomic

25

parity violation (APV) allow the study of nuclear andelectroweak physics using atomic systems[29] An ex-perimentally feasible approach to using APV to probeelectroweak physics was first proposed in 1974[114] andsince then APV has been observed in a number ofatoms[29 115ndash117] Here we will briefly discuss howbuffer gas beams may improve experimental studies ofAPV detailed discussions of APV theory and experi-ments may be found elsewhere[29 30 115 118]

Weak neutral currents The exchange of a neutralZ0 boson between the nucleus and the electrons in anatom can give rise a parity-violating electronic contactpotential[114] This potential can mix atomic states ofopposite parity such as a valence electron in S12 andP12 atomic orbitals This mixing can either be mea-sured by searching for parity violating optical rotationin atomic emissionabsorption[114 117] or by lookingfor interference between the APV induced state mixingand the mixing provided by an external electric field (theStark-interference method[119]) APV has been mea-sured in a number of atoms[29 116] and comparison totheory gives tests of the standard model at low energies

Nuclear anapole moments Another parity violatingeffect in an atom is the anapole moment[29 118 120]which arises from an exchange of a Z0 or Wplusmn boson be-tween nucleons in a nucleus Like the parity-violatingpotential above the interaction is a contact potential be-tween the electrons and nuclear anapole moment Theobservable effect is very similar to that of the weak neu-tral currents discussed above with the important ex-ception that the size of the effect will vary dependingon the nuclear spin An experimental signature of ananapole moment is then a difference in parity violat-ing amplitudes between different hyperfine levels Sofar only a single anapole moment has been measuredin the 133Cs nucleus[121] though other experiments areunderway[30]

Enhancement of parity violation in diatomic moleculesParity-violating effects have thus far been observed onlyin atoms though the search has been extended to di-atomic molecules for very compelling reasons Moleculeshave states of opposite parity (rotational states and insome cases ΛΩ-doublets[85]) which are typically muchsmaller than the spacing between opposite parity elec-tronic states in atoms so the effects of nuclear-spin-dependent parity-violating violation (such as anapolemoments) can be greatly enhanced[122ndash125] This mix-ing can be increased even further by applying exter-nal magnetic fields to push rotational states to near-degeneracy DeMille et al[124] proposed (and are work-ing on) an experiment to use a supersonic beam of BaFfree radicals in a 2Σ electronic state to measure parity-violating amplitudes with high precision

Similar to the case with an EDM measurement theshot-noise limited uncertainty (Eq (59)) in the parity vi-olating amplitude scales as prop Nminus12Tminus1 where N is thetotal number of interrogated molecules and T is the timethat the molecules spend interacting with the electro-

magnetic fields Also similar to the EDM measurementsis the choice of molecules including[30] BiO BiS HgFLaO LaS LuO LuS PbF and YbF These are all freeradicals with heavy nuclei and are therefore prime candi-dates for production in a buffer gas cooled beam Thereare even some molecules which have already been dis-cussed such as YbF and BaF (Table I) for which usinga buffer gas beam can deliver over 100 times the bright-ness of a supersonic beam with a slower forward velocity(allowing for the same time T with a shorter apparatuseasing technical requirements) It is for this reason thata BaF anapole moment experiment (at Yale[124]) is pur-suing a buffer gas cooled beam source[12]

3 Time-variation of fundamental constants

There has been much recent interest in the ques-tion of whether or not fundamental constants are trulyldquoconstantrdquo or whether their values have changed overtime In particular the dimensionless fine structureconstant α = e24πε0~c and electron-proton mass ra-tio micro = memp have attracted special attention due tothe possibility of measuring their variation from mul-tiple independent sources Detailed discussions of thetheory and experiments discussed here may be found inreviews[38 126]

Searches for time-variation of fundamental constantstypically take one of two approaches One is to lookat data which may give information about α or micro froma very long time ago for example by examining astro-nomical spectra at large redshifts[38 127] but with lim-ited accuracy (though the search may be coupled with alaboratory precision spectroscopy experiment) Anothertechnique is to use measurements with high precision butover a comparatively short timescale for example by us-ing an atomic clock[128 129] The current limits on microand α are

micro

micro= (1plusmn 3)times 10minus16 yrminus1

from the inversion spectrum of ammonia measured insources with high redshift[127] and

α

α= (minus16plusmn 23)times 10minus17 yrminus1

from comparing optical clocks[128]As with EDMs and parity violation molecules can have

large enhancement factors which could allow for moresensitive measurements In particular the α and micro de-pendence of fine structure splitting ωf prop α2 rotational

splitting ωr prop micro and vibrational splitting ωv prop micro12 aredifferent[38] and if two levels with different hyperfinerotational or vibrational character are nearly degener-ate there can be significant sensitivity enhancement[130]in changes to both micro and α This enhancement can beseveral orders of magnitude (compared to atoms) and

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

21

ier to superinsulate a radiation shield instead of the cellitself Additionally the 4 K shield could help to protectcryopumps as discussed below

3 Cryopumps

Enclosing the cell in radiation shields means that thegas conductance to the external vacuum chamber is verylow If no pumping occurred inside the radiation shieldsthe buffer gas would build up to the point where theresidual pressure was too high to allow for a beam In thecase of neon buffer gas this can be solved by surroundingthe cell with a radiation shield kept at a temperaturewhere the vapor pressure of neon is acceptably low whichis simple to achieve with standard cryogenic refrigeratorsor liquid helium (for example the vapor pressure of neonis lt 10minus9 torr at 7 K) A neon cooled buffer gas beaminside a 4 K radiation shield can operate for extendedperiods of time Hutzler et al[7] operated such a beamcontinuously for over 24 hours without beam or vacuumdegradation

For helium this is not practical the radiation shieldwould have to be cooled to lt 05 K for similar vapor pres-sures which would require much more complex cryogenicsystems and superfluid film management Fortunatelythere is a solution which is to use activated charcoal asa cryopump[58] When cooled to 10 K activated char-coal becomes a cryopump for helium with up to severall sminus1 pumping speed per cm2 of charcoal and can holdalmost 1 STP liter of helium per gram (though thesevalues are highly dependent on temperature and otherparameters [58]) Covering the inside of a 4 K radiationshield with sim 100 cm2 of activated charcoal bonded tocopper plates can result in a cryopump with a pump-ing speed of several hundred liters per second that canlast for hours under typical gas loads[7 9] As the char-coal fills up with helium the pumping speed begins tochange which can result in a degradation of beam prop-erties [7 9] therefore it is necessary to warm up thecharcoal (typically to sim 20 K) and pump out the des-orbed helium with a mechanical pump Experience showsthat the beam properties are very sensitive to charcoalamount and placement[7 9] often in very non-intuitiveways

4 Beam collimation

Similar to supersonic beams buffer gas cooled beamstypically have collimators to create differentially pumpedregions and reduce the gas load on the part of the appa-ratus where the molecules are being probed With buffergas cooled beams this is especially advantageous sincecollimators can be kept in the cryogenic region and there-fore take advantage of the very large pumping speeds af-forded by cryopumping Hutzler et al[7] found that thebeam properties were largely insensitive to the placement

of a collimator when using a neon buffer gas however aswith the charcoal cryopumps the placement of the colli-mator has often been seen to strongly influence the beamproperties of the helium buffer gas cooled beam Cor-rect placement requires careful consideration and mayinvolve multiple attempts

III APPLICATIONS

In this section we will discuss some select applicationswhere buffer gas beams can offer significant advantagesLaser cooling precision measurements collisional stud-ies and trap loading

A Laser cooling of buffer gas beams

Laser cooling works by continuously scattering photonsoff of an atom or molecule in a manner that dissipatesenergy[48] The number of photon scattering events tostop an atom or a molecule is given by N = mv~kwhere m is the mass of the species v is its velocity andk = 2πλ where λ is the wavelength of the laser lightFor typical atoms or molecules moving at room temper-ature thermal velocities this number is about 104 Theelectronic ground state of an atom may contain multi-ple hyperfine states and off-resonance excitation some-times brings the atoms to different hyperfine states inthe excited state which can decay to an off-resonant (orldquodarkrdquo) hyperfine state in the electronic ground state Ifthis happens a ldquore-pumprdquo laser resonant with the otherhyperfine state can pump the atom back into the reso-nant state

In contrast the electronic ground state of moleculescontains multiple internal states including vibrationaland rotational as well as hyperfine states The num-ber of re-pump lasers needed to close the optical transi-tion grows accordingly Despite these challenges Di Rosa[93] pointed out that a set of molecules with strong sin-gle photon transitions and a highly diagonal vibrationaltransitions (Frank-Condon factors[85]) may be feasiblefor direct laser cooling The first criterion ensures a largephoton scattering rate meaning that a sufficient numberof photons can be scattered in the limited interactiontime (determined by the molecular beam velocity andgeometrical constraints on the length of the interactionregion) The second criterion implies a high probabilityof decaying back to the initial vibrational ground state(vprimeprime = 0) If p 1 is the probability of decaying into adark state after one optical transition then if there areno re-pump lasers the total number of photons scatteredfor each molecule Nscat is given by (1 minus p)Nscat sim eminus1yielding Nscat sim 1p Di Rosa[93] listed a few moleculesthat satisfied the above requirements including CaH andNH Most of these molecules can scatter sim 100 photonswithout any vibrational re-pump lasers and can scatterup to sim 104 photons with one vprimeprime = 1 re-pump laser

22

In contrast to vibrational leakage where no strict se-lection rules apply rotational transitions satisfy the totalangular momentum change selection rule ∆J = 0plusmn1Stuhl et al [94] noticed that the rotational leakage canbe mitigated by choosing a transition where the angu-lar momentum J primeprime of the ground state is larger than theangular momentum J prime of the lowest rotational state inthe excited electronic state For example consider amolecule with a ground electronic state containing ro-tational levels J primeprime = 1 2 3 and an excited electronicstate with rotational levels J prime = 0 1 2 (for examplethe X3∆1 rarr E3Π0 transition of TiO[94]) If a laserdrives the transition |X J primeprime = 1〉 rarr |E J prime = 0〉 then theselection rule |J primeprimeminusJ prime| le 1 means that the only radiativedecay allowed is |E J prime = 0〉 |XJ primeprime = 1〉 ie a ro-tationally closed transition The molecule may still havevibrational leakage but those channels can be closed withre-pump lasers in the usual way

Several of the diatomic molecules that satisfy the crite-ria for laser cooling as suggested by Di Rosa[93] and Stuhlet al[94] are radicals Since the number of photons andthe distance needed to stop molecules are proportional tov and v2

respectively where v is the forward velocity of

the molecules molecular radical sources with a low for-ward velocity as well as a high brightness are desirablefor direct laser cooling As mentioned earlier (see TableI) a buffer gas cooled beam can deliver higher brightnessand lower forward velocity for these types of species Asan example a boosted buffer gas beam has a typical for-ward velocity of sim 150 m sminus1 which reduces the numberof photons needed to stop a CaH molecule by a factorof sim 5 compared to a 1300 K oven source as initiallyproposed by Di Rosa[93]

The first demonstration of optical cycling in moleculeswas achieved by using a buffer gas cooled beam ofSrF[49] The X2Σ+

12 rarr A2Π12 transition of SrF has

relatively diagonal Franck-Condon factors[49] fvprime=0 vprimeprime f00 asymp 098 f01 asymp 002 f02 asymp 4 times 10minus4 and f03+ lt10minus5 Theoretically SrF could scatter Nscat = 1f03+ gt105 photons with two vibrational re-pump lasers assum-ing that other internal states are addressed as well Rota-tional leaking was prevented by using an N primeprime = 1rarr N prime =0 transition Since SrF has a nuclear spin of I = 12 andthe hyperfine splitting of |N prime = 0 J prime = 12 gt is small ev-ery hyperfine state in the N primeprime = 1 manifold would be pop-ulated during the transition and needs to be addressedThis was achieved using lasers with several sidebands(created using an electro-optic modulator) which were onresonance with the hyperfine states One important fea-ture of a transition with J primeprime gt J prime is that the ground statecontains more Zeeman states than the excited state lead-ing to dark Zeeman states[94] mJprimeprime = plusmnJ primeprime To addressthese dark states Shuman et al used a small magneticfield which was at an angle relative to the polarization ofthe cooling lasers to constantly remix the Zeeman states

With the beam source used in those first laser coolingexperiments the SrF molecules were produced by laserablation in a helium buffer gas cell at 4 K resulting in a

molecular beam with a total number of 109 SrF moleculesexiting the cell (per pulse) in the N primeprime = 1 state moving atv = 200 m sminus1 [49] The molecular beam was collimatedtransversely by a 6 mm diameter aperture before enteringthe laser interaction area which consisted of the maincooling laser one re-pump laser for vprimeprime = 1 and mag-netic field coils When the magnetic field was turned onin addition to the main cooling laser Shuman et al ob-served that the induced fluorescence signals increased bya factor of sim 35 Adding the vibrational re-pump laserfurther increased the fluorescence signals by another fac-tor of sim 35 corresponding to a total average numberof photons scattered per molecule of Nscat sim 170 Sinceboth lasers were applied perpendicularly to the molecu-lar beam from one transverse direction the net momen-tum transferred from the photons to SrF was sufficient tocreate a position shift or deflection of the beam The ob-served deflection indicated Nscat = 140 consistent withthe previous estimation based on the fluorescence mea-surement

In a subsequent experiment Shuman et al [50] demon-strated transverse cooling of the buffer gas cooled SrFbeam By incorporating an additional re-pump laser forthe vprimeprime = 2 state and arranging the cooling lasers to in-tersect the molecular beam multiple times at nearly 90the molecules scattered Nscat = 500 minus 1000 photons ina 15 cm long region When the cooling lasers were reddetuned with a magnetic field of 5 G the transverse tem-perature of the SrF beam was cooled from T0 = 50 mK(due to the geometry of the mechanical beam collima-tors) down to T sim 5 mK In this regime the mixingfield is large enough for rapidly remixing molecules inthe Zeeman states leading to Doppler cooling Shumanet al discovered that the molecular beam also obtaineda lower temperature when the lasers were blue detunedwith a relatively low field of 06 G In this case SrF inthe bright Zeeman state constantly experienced a peri-odic potential provided by the cooling lasers resulting inldquoSisyphusrdquo-like cooling[48 50]

1 Direct loading of exotic atoms into magneto-optical traps

Several exotic atoms have been successfully loadedinto magneto-optical traps (MOTs[48 95]) including Yb[96 97] Ag[98] Er[99] Dy [100] and Tm [101] Becausethese atoms have much higher melting points than alkaliatoms effusive oven sources used to create these atomicbeams operated at high temperatures between 700 and1500 K A Zeeman slower is typically needed to deceler-ate the fast-moving atoms (v sim 350 minus 580 m sminus1) forefficiently loading into MOT which has a typical cap-ture velocity lt 60 m sminus1 As discussed in Section II C 2a near effusive buffer gas cooled beam can be producedby adding one slowing cell to the typical buffer gas cellAlthough this type of beam has been found to have atypically lower extraction efficiency(sim 1) than a hydro-dynamically extracted beam without a slowing cell the

23

low forward velocity of the beam makes direct loading ofexotic atomic beams into MOTs feasible Additionallythe very high fluxes possible with ablation of certain met-als can lead to a superior beam system

The longitudinal and transverse temperatures of CaHmolecules in a beam produced with a slowing cell weremeasured to be sim 5 K and sim 25 K respectively [10]Since the cooling mechanism only relies on elastic col-lisions with the He buffer gas we expect atomic beamsproduced from such a slowing cell to have properties simi-lar to the beam of CaH (except of course for any possiblemass-related differences) For example the forward ve-locity of a slow Yb beam with a longitudinal temperatureof 5 K is sim 30 m sminus1 which is consistent with the forwardvelocity of a Yb beam demonstrated by Patterson [102]using a similar cell design Employing a one-dimensionallaser cooling model the capture velocity of a MOT isgiven by vc = (|∆|+ Γ)k [97] where ∆ is the detuningof the cooling laser and Γ is the natural linewidth ForYb assuming |∆| = Γ = 2πtimes28 MHz the capture veloc-ity is 22 m sminus1 implying a large fraction of a buffer gascooled Yb beam can be loaded without any longitudinallaser slowing (see Table IV)

Collisional heating from the buffer gas streamingthrough the MOT region could be a concern Typicallythe buffer density inside the slowing cell is on the orderof 1014 cmminus3 Although it is difficult to measure the Hebeam profile a good approximation is to assume thatthe He beam attains the same temperatures as the CaHmolecular beam Therefore the collisional heating fromthe buffer gas is negligible compared to the cooling powerfrom the scattered photons starting from a distance of10 cm away from the aperture where the He density islt 1012 cmminus3 Any potential loss due to the divergenceof the beam can be mitigated by employing transverselaser cooling to collimate the atomic beam between thecell aperture and MOT Assuming the transverse capturevelocity is given by vct = Γk we can estimate the load-ing efficiency of a buffer gas cooled beam into MOTs byconsidering the velocity distributions that are within vcttransversely and vc longitudinally

Table IV shows some exotic atoms that have beenloaded into MOTs from effusive oven sources and havealso been buffer gas cooled Of these species only Ybhas been realized as a buffer gas beam so far[5] Giventhe generality of the buffer gas beam technique we be-lieve that producing cold and slow exotic atomic beamswith beam properties similar to the CaH beam[10] isvery likely We can therefore estimate the loading effi-ciency of these atoms into MOTs from buffer gas beamsfload by assuming that these proposed atomic beamswould have the same longitudinal and transverse tem-peratures of the CaH beam 5 K and 25 K respectivelyBased on the ablation yields inside the buffer gas cellNablation reported in the past[4] and a typical extrac-tion efficiency of the slowing cell of fext sim 5 times 10minus3 wecan estimate potential loaded numbers per ablation pulseNload sim Nablationtimesfexttimesfload shown as the last column

Atom Ntrappedexp fload [] Nload [pulseminus1]

Yb [97] 107 21 2 times 1010

Ag [98] 3 times 106 17 3 times 109

Dy [100] 25 times 108 33 3 times 109

Er [99] 106 39 4 times 108

Tm [101] 7 times 104 03 3 times 106

TABLE IV Some exotic atoms which have been loaded into aMOT from an effusive oven source and also buffer gas cooledNtrappedexp is the number of atoms that were loaded into theMOT in the respective experiments fload is the projectedloading efficiency from a buffer gas beam source and Nload

is the projected number of atoms which could be trapped inthe MOT with a single pulse from a buffer gas source Adescription of these estimates may be found in the text

in Table IV The estimated numbers of atoms loaded perpulse are high compared to the reported trapped num-bers By loading 1minus 10 pulses the expected atom num-bers (or densities) accumulated in MOTs could approacha regime where the radiation pressure and collisions be-tween ground and excited state atoms would limit theatomic density[103] Co-loading multiple species with-out using high temperature ovens and Zeeman slowersinto a MOT is feasible by simply ablating several speciessimultaneously

B Precision measurements

Another application of molecular beams is the preci-sion determination of molecular properties This is madepossible by the lack of collisions in the beam regionand enhanced by the large volume of advanced molec-ular beam production manipulation and spectroscopytechniques[1 2] Precision spectroscopy with supersonicbeams is a workhorse in chemistry and physics As thereader can surely surmise by now many precision mea-surements can benefit from the high flux and low for-ward velocity afforded by buffer gas cooled beams Inthis section we will review some molecular beam preci-sion measurements and discuss how they could benefitfrom buffer gas cooled beam technology

1 Electric dipole moments

In 1950 Purcell and Ramsey[104] were the first to se-riously consider the possibility of a fundamental parti-cle (ie an electron or nucleon) possessing a permanentelectric dipole moment (EDM) Before this time it waswidely (though not universally[105]) believed that a fun-damental particle could not possess such a moment be-cause it would violate parity (P) and time-reversal (T)invariance in the following manner Since a dipole mo-ment is a vector quantity it must be aligned with the spinof the particle which is the only intrinsic vector associ-

24

ated with a fundamental particle However an electricdipole moment is a polar vector while spin is an axial(or pseudo-) vector so these two quantities must behaveoppositely under inversion of coordinate systems or rever-sal of time yet the previous argument requires them touniquely determine each other Although no permanentEDM of a fundamental particle has ever been measured(despite over 50 years of experimental searches[106])such a discovery would have a profound impact on ourunderstanding of particle physics and cosmology For anaccessible discussion about EDMs of fundamental par-ticles and their implications see the article by FortsonSandars and Barr[107] for more details see the book byKhriplovich and Lamoreaux[28]

The essential idea of nearly every EDM search isto look for a small shift in precession frequency of aspin in an electric field as the electric field direction is

reversed[28] For a particle with spin ~S magnetic dipolemoment micro and electric dipole moment d in a parallel

magnetic field ~B and electric field ~E the spin of the par-ticle (which is parallel to both the magnetic and electricdipole moment) will precess about the fields with angularfrequency

ω =d~E + micro~B

~middot~S

|~S| (57)

Consider an experiment where ~S and ~B are kept fixed

but the direction of ~E is reversed and then the frequency

ωplusmn is measured for the two different orientations plusmn~E The value of the electric dipole moment d can then beextracted by comparing these two measured values

d =~(ω+ minus ωminus)

2~E middot ~S|~S| (58)

The determination of d then reduces to a precision mea-surement of the frequencies ωplusmn Precise frequency mea-surements are best accomplished by the separated oscilla-tory field (or Ramsey) method[2] in which the spins areallowed to precess for a time (the ldquocoherence timerdquo) τbefore the accumulated phase angle is measured therebydetermining ω If such an experiment is repeated witha total of N spins the uncertainty in the EDM is givenby[28]

δd =~τ

|~E|radicN|~S|

(59)

From this equation we can see that an EDM ex-periment should have large electric fields long coher-ence times and large count rates Neutral objects suchas neutrons or atoms can simply be placed in largeelectric fields however charged particles like electronsor protons would simply accelerate out of the electricfield Sandars[108] realized that not only could an elec-tric dipole moment of a charged object be inferred bystudying a composite neutral object such as an atom or

molecule but the electric dipole moment could actuallybe enhanced For example Sandars calculated[109] thatan electric dipole moment of the electron de could in-duce an electric dipole moment of an atom dA with arelativistic ldquoenhancement factorrdquo dAde that can be over100 for Cs atoms The basic idea[110] is that the electroncan sample the atomic electric field which is typically oforder

Eatomic asympe2

4πε0a20

asymp 5 GV cmminus1 (60)

where a0 is the Bohr radius This is considerably largerthan a typical macroscopic lab field of 100 kV cmminus1Atoms cannot take full advantage of this enhancementbecause they cannot be fully polarized in laboratory elec-tric fields[111] however polar molecules can be polarizedin lab fields and for this reason most current electronEDM experiments use polar molecules[111]

The molecules which have the highest enhancementfactor have high-Z atoms with partially filled electronshells and tend to be chemically reactive have high melt-ing points and are often free radicals[111] For this rea-son effusive beam sources of these molecules are typ-ically not feasible the Boltzmann distribution of rota-tional states at temperatures where the species have ap-preciable vapor pressure put only a tiny fraction in anysingle rotational state (however performing an electronEDM experiment with molecules in a hot vapor cell is apossibility[112]) A molecular beam for an EDM searchshould therefore have low temperature and in light ofEq (59) a low forward velocity to allow the moleculesto interact with the fields for a long time giving largeτ For the types of molecules under consideration buffergas cooled beams[3 7 9] have considerable advantagesover the standard supersonic beam[11] As discussed ear-lier the brightness for refractory or chemically reactivespecies can be very high with buffer gas beams and theyhave considerably slower forward velocities In Table Iwe can see that a buffer gas cooled ThO beam has aslower forward velocity and over 100 times the bright-ness compared to a demonstrated state-of-the-art YbFsupersonic beam both of which are currently being usedfor an electron EDM search These reasons make buffergas cooled beams an attractive option for electron EDMsearches with some existing supersonic experiments con-sidering switching to buffer gas cooling[70]

Searches for the electron EDM are currently underwayin molecular beams of YbF[27] ThO[59] and WC[113]as well as several other atomic molecular and solid statesystems[111]

2 Parity violation and anapole moments

The exchange of weak neutral currents between theconstituent particles of an atom or molecule can lead toobservable parity violating effects in their spectra Pre-cision examinations of these effects known as atomic

25

parity violation (APV) allow the study of nuclear andelectroweak physics using atomic systems[29] An ex-perimentally feasible approach to using APV to probeelectroweak physics was first proposed in 1974[114] andsince then APV has been observed in a number ofatoms[29 115ndash117] Here we will briefly discuss howbuffer gas beams may improve experimental studies ofAPV detailed discussions of APV theory and experi-ments may be found elsewhere[29 30 115 118]

Weak neutral currents The exchange of a neutralZ0 boson between the nucleus and the electrons in anatom can give rise a parity-violating electronic contactpotential[114] This potential can mix atomic states ofopposite parity such as a valence electron in S12 andP12 atomic orbitals This mixing can either be mea-sured by searching for parity violating optical rotationin atomic emissionabsorption[114 117] or by lookingfor interference between the APV induced state mixingand the mixing provided by an external electric field (theStark-interference method[119]) APV has been mea-sured in a number of atoms[29 116] and comparison totheory gives tests of the standard model at low energies

Nuclear anapole moments Another parity violatingeffect in an atom is the anapole moment[29 118 120]which arises from an exchange of a Z0 or Wplusmn boson be-tween nucleons in a nucleus Like the parity-violatingpotential above the interaction is a contact potential be-tween the electrons and nuclear anapole moment Theobservable effect is very similar to that of the weak neu-tral currents discussed above with the important ex-ception that the size of the effect will vary dependingon the nuclear spin An experimental signature of ananapole moment is then a difference in parity violat-ing amplitudes between different hyperfine levels Sofar only a single anapole moment has been measuredin the 133Cs nucleus[121] though other experiments areunderway[30]

Enhancement of parity violation in diatomic moleculesParity-violating effects have thus far been observed onlyin atoms though the search has been extended to di-atomic molecules for very compelling reasons Moleculeshave states of opposite parity (rotational states and insome cases ΛΩ-doublets[85]) which are typically muchsmaller than the spacing between opposite parity elec-tronic states in atoms so the effects of nuclear-spin-dependent parity-violating violation (such as anapolemoments) can be greatly enhanced[122ndash125] This mix-ing can be increased even further by applying exter-nal magnetic fields to push rotational states to near-degeneracy DeMille et al[124] proposed (and are work-ing on) an experiment to use a supersonic beam of BaFfree radicals in a 2Σ electronic state to measure parity-violating amplitudes with high precision

Similar to the case with an EDM measurement theshot-noise limited uncertainty (Eq (59)) in the parity vi-olating amplitude scales as prop Nminus12Tminus1 where N is thetotal number of interrogated molecules and T is the timethat the molecules spend interacting with the electro-

magnetic fields Also similar to the EDM measurementsis the choice of molecules including[30] BiO BiS HgFLaO LaS LuO LuS PbF and YbF These are all freeradicals with heavy nuclei and are therefore prime candi-dates for production in a buffer gas cooled beam Thereare even some molecules which have already been dis-cussed such as YbF and BaF (Table I) for which usinga buffer gas beam can deliver over 100 times the bright-ness of a supersonic beam with a slower forward velocity(allowing for the same time T with a shorter apparatuseasing technical requirements) It is for this reason thata BaF anapole moment experiment (at Yale[124]) is pur-suing a buffer gas cooled beam source[12]

3 Time-variation of fundamental constants

There has been much recent interest in the ques-tion of whether or not fundamental constants are trulyldquoconstantrdquo or whether their values have changed overtime In particular the dimensionless fine structureconstant α = e24πε0~c and electron-proton mass ra-tio micro = memp have attracted special attention due tothe possibility of measuring their variation from mul-tiple independent sources Detailed discussions of thetheory and experiments discussed here may be found inreviews[38 126]

Searches for time-variation of fundamental constantstypically take one of two approaches One is to lookat data which may give information about α or micro froma very long time ago for example by examining astro-nomical spectra at large redshifts[38 127] but with lim-ited accuracy (though the search may be coupled with alaboratory precision spectroscopy experiment) Anothertechnique is to use measurements with high precision butover a comparatively short timescale for example by us-ing an atomic clock[128 129] The current limits on microand α are

micro

micro= (1plusmn 3)times 10minus16 yrminus1

from the inversion spectrum of ammonia measured insources with high redshift[127] and

α

α= (minus16plusmn 23)times 10minus17 yrminus1

from comparing optical clocks[128]As with EDMs and parity violation molecules can have

large enhancement factors which could allow for moresensitive measurements In particular the α and micro de-pendence of fine structure splitting ωf prop α2 rotational

splitting ωr prop micro and vibrational splitting ωv prop micro12 aredifferent[38] and if two levels with different hyperfinerotational or vibrational character are nearly degener-ate there can be significant sensitivity enhancement[130]in changes to both micro and α This enhancement can beseveral orders of magnitude (compared to atoms) and

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

22

In contrast to vibrational leakage where no strict se-lection rules apply rotational transitions satisfy the totalangular momentum change selection rule ∆J = 0plusmn1Stuhl et al [94] noticed that the rotational leakage canbe mitigated by choosing a transition where the angu-lar momentum J primeprime of the ground state is larger than theangular momentum J prime of the lowest rotational state inthe excited electronic state For example consider amolecule with a ground electronic state containing ro-tational levels J primeprime = 1 2 3 and an excited electronicstate with rotational levels J prime = 0 1 2 (for examplethe X3∆1 rarr E3Π0 transition of TiO[94]) If a laserdrives the transition |X J primeprime = 1〉 rarr |E J prime = 0〉 then theselection rule |J primeprimeminusJ prime| le 1 means that the only radiativedecay allowed is |E J prime = 0〉 |XJ primeprime = 1〉 ie a ro-tationally closed transition The molecule may still havevibrational leakage but those channels can be closed withre-pump lasers in the usual way

Several of the diatomic molecules that satisfy the crite-ria for laser cooling as suggested by Di Rosa[93] and Stuhlet al[94] are radicals Since the number of photons andthe distance needed to stop molecules are proportional tov and v2

respectively where v is the forward velocity of

the molecules molecular radical sources with a low for-ward velocity as well as a high brightness are desirablefor direct laser cooling As mentioned earlier (see TableI) a buffer gas cooled beam can deliver higher brightnessand lower forward velocity for these types of species Asan example a boosted buffer gas beam has a typical for-ward velocity of sim 150 m sminus1 which reduces the numberof photons needed to stop a CaH molecule by a factorof sim 5 compared to a 1300 K oven source as initiallyproposed by Di Rosa[93]

The first demonstration of optical cycling in moleculeswas achieved by using a buffer gas cooled beam ofSrF[49] The X2Σ+

12 rarr A2Π12 transition of SrF has

relatively diagonal Franck-Condon factors[49] fvprime=0 vprimeprime f00 asymp 098 f01 asymp 002 f02 asymp 4 times 10minus4 and f03+ lt10minus5 Theoretically SrF could scatter Nscat = 1f03+ gt105 photons with two vibrational re-pump lasers assum-ing that other internal states are addressed as well Rota-tional leaking was prevented by using an N primeprime = 1rarr N prime =0 transition Since SrF has a nuclear spin of I = 12 andthe hyperfine splitting of |N prime = 0 J prime = 12 gt is small ev-ery hyperfine state in the N primeprime = 1 manifold would be pop-ulated during the transition and needs to be addressedThis was achieved using lasers with several sidebands(created using an electro-optic modulator) which were onresonance with the hyperfine states One important fea-ture of a transition with J primeprime gt J prime is that the ground statecontains more Zeeman states than the excited state lead-ing to dark Zeeman states[94] mJprimeprime = plusmnJ primeprime To addressthese dark states Shuman et al used a small magneticfield which was at an angle relative to the polarization ofthe cooling lasers to constantly remix the Zeeman states

With the beam source used in those first laser coolingexperiments the SrF molecules were produced by laserablation in a helium buffer gas cell at 4 K resulting in a

molecular beam with a total number of 109 SrF moleculesexiting the cell (per pulse) in the N primeprime = 1 state moving atv = 200 m sminus1 [49] The molecular beam was collimatedtransversely by a 6 mm diameter aperture before enteringthe laser interaction area which consisted of the maincooling laser one re-pump laser for vprimeprime = 1 and mag-netic field coils When the magnetic field was turned onin addition to the main cooling laser Shuman et al ob-served that the induced fluorescence signals increased bya factor of sim 35 Adding the vibrational re-pump laserfurther increased the fluorescence signals by another fac-tor of sim 35 corresponding to a total average numberof photons scattered per molecule of Nscat sim 170 Sinceboth lasers were applied perpendicularly to the molecu-lar beam from one transverse direction the net momen-tum transferred from the photons to SrF was sufficient tocreate a position shift or deflection of the beam The ob-served deflection indicated Nscat = 140 consistent withthe previous estimation based on the fluorescence mea-surement

In a subsequent experiment Shuman et al [50] demon-strated transverse cooling of the buffer gas cooled SrFbeam By incorporating an additional re-pump laser forthe vprimeprime = 2 state and arranging the cooling lasers to in-tersect the molecular beam multiple times at nearly 90the molecules scattered Nscat = 500 minus 1000 photons ina 15 cm long region When the cooling lasers were reddetuned with a magnetic field of 5 G the transverse tem-perature of the SrF beam was cooled from T0 = 50 mK(due to the geometry of the mechanical beam collima-tors) down to T sim 5 mK In this regime the mixingfield is large enough for rapidly remixing molecules inthe Zeeman states leading to Doppler cooling Shumanet al discovered that the molecular beam also obtaineda lower temperature when the lasers were blue detunedwith a relatively low field of 06 G In this case SrF inthe bright Zeeman state constantly experienced a peri-odic potential provided by the cooling lasers resulting inldquoSisyphusrdquo-like cooling[48 50]

1 Direct loading of exotic atoms into magneto-optical traps

Several exotic atoms have been successfully loadedinto magneto-optical traps (MOTs[48 95]) including Yb[96 97] Ag[98] Er[99] Dy [100] and Tm [101] Becausethese atoms have much higher melting points than alkaliatoms effusive oven sources used to create these atomicbeams operated at high temperatures between 700 and1500 K A Zeeman slower is typically needed to deceler-ate the fast-moving atoms (v sim 350 minus 580 m sminus1) forefficiently loading into MOT which has a typical cap-ture velocity lt 60 m sminus1 As discussed in Section II C 2a near effusive buffer gas cooled beam can be producedby adding one slowing cell to the typical buffer gas cellAlthough this type of beam has been found to have atypically lower extraction efficiency(sim 1) than a hydro-dynamically extracted beam without a slowing cell the

23

low forward velocity of the beam makes direct loading ofexotic atomic beams into MOTs feasible Additionallythe very high fluxes possible with ablation of certain met-als can lead to a superior beam system

The longitudinal and transverse temperatures of CaHmolecules in a beam produced with a slowing cell weremeasured to be sim 5 K and sim 25 K respectively [10]Since the cooling mechanism only relies on elastic col-lisions with the He buffer gas we expect atomic beamsproduced from such a slowing cell to have properties simi-lar to the beam of CaH (except of course for any possiblemass-related differences) For example the forward ve-locity of a slow Yb beam with a longitudinal temperatureof 5 K is sim 30 m sminus1 which is consistent with the forwardvelocity of a Yb beam demonstrated by Patterson [102]using a similar cell design Employing a one-dimensionallaser cooling model the capture velocity of a MOT isgiven by vc = (|∆|+ Γ)k [97] where ∆ is the detuningof the cooling laser and Γ is the natural linewidth ForYb assuming |∆| = Γ = 2πtimes28 MHz the capture veloc-ity is 22 m sminus1 implying a large fraction of a buffer gascooled Yb beam can be loaded without any longitudinallaser slowing (see Table IV)

Collisional heating from the buffer gas streamingthrough the MOT region could be a concern Typicallythe buffer density inside the slowing cell is on the orderof 1014 cmminus3 Although it is difficult to measure the Hebeam profile a good approximation is to assume thatthe He beam attains the same temperatures as the CaHmolecular beam Therefore the collisional heating fromthe buffer gas is negligible compared to the cooling powerfrom the scattered photons starting from a distance of10 cm away from the aperture where the He density islt 1012 cmminus3 Any potential loss due to the divergenceof the beam can be mitigated by employing transverselaser cooling to collimate the atomic beam between thecell aperture and MOT Assuming the transverse capturevelocity is given by vct = Γk we can estimate the load-ing efficiency of a buffer gas cooled beam into MOTs byconsidering the velocity distributions that are within vcttransversely and vc longitudinally

Table IV shows some exotic atoms that have beenloaded into MOTs from effusive oven sources and havealso been buffer gas cooled Of these species only Ybhas been realized as a buffer gas beam so far[5] Giventhe generality of the buffer gas beam technique we be-lieve that producing cold and slow exotic atomic beamswith beam properties similar to the CaH beam[10] isvery likely We can therefore estimate the loading effi-ciency of these atoms into MOTs from buffer gas beamsfload by assuming that these proposed atomic beamswould have the same longitudinal and transverse tem-peratures of the CaH beam 5 K and 25 K respectivelyBased on the ablation yields inside the buffer gas cellNablation reported in the past[4] and a typical extrac-tion efficiency of the slowing cell of fext sim 5 times 10minus3 wecan estimate potential loaded numbers per ablation pulseNload sim Nablationtimesfexttimesfload shown as the last column

Atom Ntrappedexp fload [] Nload [pulseminus1]

Yb [97] 107 21 2 times 1010

Ag [98] 3 times 106 17 3 times 109

Dy [100] 25 times 108 33 3 times 109

Er [99] 106 39 4 times 108

Tm [101] 7 times 104 03 3 times 106

TABLE IV Some exotic atoms which have been loaded into aMOT from an effusive oven source and also buffer gas cooledNtrappedexp is the number of atoms that were loaded into theMOT in the respective experiments fload is the projectedloading efficiency from a buffer gas beam source and Nload

is the projected number of atoms which could be trapped inthe MOT with a single pulse from a buffer gas source Adescription of these estimates may be found in the text

in Table IV The estimated numbers of atoms loaded perpulse are high compared to the reported trapped num-bers By loading 1minus 10 pulses the expected atom num-bers (or densities) accumulated in MOTs could approacha regime where the radiation pressure and collisions be-tween ground and excited state atoms would limit theatomic density[103] Co-loading multiple species with-out using high temperature ovens and Zeeman slowersinto a MOT is feasible by simply ablating several speciessimultaneously

B Precision measurements

Another application of molecular beams is the preci-sion determination of molecular properties This is madepossible by the lack of collisions in the beam regionand enhanced by the large volume of advanced molec-ular beam production manipulation and spectroscopytechniques[1 2] Precision spectroscopy with supersonicbeams is a workhorse in chemistry and physics As thereader can surely surmise by now many precision mea-surements can benefit from the high flux and low for-ward velocity afforded by buffer gas cooled beams Inthis section we will review some molecular beam preci-sion measurements and discuss how they could benefitfrom buffer gas cooled beam technology

1 Electric dipole moments

In 1950 Purcell and Ramsey[104] were the first to se-riously consider the possibility of a fundamental parti-cle (ie an electron or nucleon) possessing a permanentelectric dipole moment (EDM) Before this time it waswidely (though not universally[105]) believed that a fun-damental particle could not possess such a moment be-cause it would violate parity (P) and time-reversal (T)invariance in the following manner Since a dipole mo-ment is a vector quantity it must be aligned with the spinof the particle which is the only intrinsic vector associ-

24

ated with a fundamental particle However an electricdipole moment is a polar vector while spin is an axial(or pseudo-) vector so these two quantities must behaveoppositely under inversion of coordinate systems or rever-sal of time yet the previous argument requires them touniquely determine each other Although no permanentEDM of a fundamental particle has ever been measured(despite over 50 years of experimental searches[106])such a discovery would have a profound impact on ourunderstanding of particle physics and cosmology For anaccessible discussion about EDMs of fundamental par-ticles and their implications see the article by FortsonSandars and Barr[107] for more details see the book byKhriplovich and Lamoreaux[28]

The essential idea of nearly every EDM search isto look for a small shift in precession frequency of aspin in an electric field as the electric field direction is

reversed[28] For a particle with spin ~S magnetic dipolemoment micro and electric dipole moment d in a parallel

magnetic field ~B and electric field ~E the spin of the par-ticle (which is parallel to both the magnetic and electricdipole moment) will precess about the fields with angularfrequency

ω =d~E + micro~B

~middot~S

|~S| (57)

Consider an experiment where ~S and ~B are kept fixed

but the direction of ~E is reversed and then the frequency

ωplusmn is measured for the two different orientations plusmn~E The value of the electric dipole moment d can then beextracted by comparing these two measured values

d =~(ω+ minus ωminus)

2~E middot ~S|~S| (58)

The determination of d then reduces to a precision mea-surement of the frequencies ωplusmn Precise frequency mea-surements are best accomplished by the separated oscilla-tory field (or Ramsey) method[2] in which the spins areallowed to precess for a time (the ldquocoherence timerdquo) τbefore the accumulated phase angle is measured therebydetermining ω If such an experiment is repeated witha total of N spins the uncertainty in the EDM is givenby[28]

δd =~τ

|~E|radicN|~S|

(59)

From this equation we can see that an EDM ex-periment should have large electric fields long coher-ence times and large count rates Neutral objects suchas neutrons or atoms can simply be placed in largeelectric fields however charged particles like electronsor protons would simply accelerate out of the electricfield Sandars[108] realized that not only could an elec-tric dipole moment of a charged object be inferred bystudying a composite neutral object such as an atom or

molecule but the electric dipole moment could actuallybe enhanced For example Sandars calculated[109] thatan electric dipole moment of the electron de could in-duce an electric dipole moment of an atom dA with arelativistic ldquoenhancement factorrdquo dAde that can be over100 for Cs atoms The basic idea[110] is that the electroncan sample the atomic electric field which is typically oforder

Eatomic asympe2

4πε0a20

asymp 5 GV cmminus1 (60)

where a0 is the Bohr radius This is considerably largerthan a typical macroscopic lab field of 100 kV cmminus1Atoms cannot take full advantage of this enhancementbecause they cannot be fully polarized in laboratory elec-tric fields[111] however polar molecules can be polarizedin lab fields and for this reason most current electronEDM experiments use polar molecules[111]

The molecules which have the highest enhancementfactor have high-Z atoms with partially filled electronshells and tend to be chemically reactive have high melt-ing points and are often free radicals[111] For this rea-son effusive beam sources of these molecules are typ-ically not feasible the Boltzmann distribution of rota-tional states at temperatures where the species have ap-preciable vapor pressure put only a tiny fraction in anysingle rotational state (however performing an electronEDM experiment with molecules in a hot vapor cell is apossibility[112]) A molecular beam for an EDM searchshould therefore have low temperature and in light ofEq (59) a low forward velocity to allow the moleculesto interact with the fields for a long time giving largeτ For the types of molecules under consideration buffergas cooled beams[3 7 9] have considerable advantagesover the standard supersonic beam[11] As discussed ear-lier the brightness for refractory or chemically reactivespecies can be very high with buffer gas beams and theyhave considerably slower forward velocities In Table Iwe can see that a buffer gas cooled ThO beam has aslower forward velocity and over 100 times the bright-ness compared to a demonstrated state-of-the-art YbFsupersonic beam both of which are currently being usedfor an electron EDM search These reasons make buffergas cooled beams an attractive option for electron EDMsearches with some existing supersonic experiments con-sidering switching to buffer gas cooling[70]

Searches for the electron EDM are currently underwayin molecular beams of YbF[27] ThO[59] and WC[113]as well as several other atomic molecular and solid statesystems[111]

2 Parity violation and anapole moments

The exchange of weak neutral currents between theconstituent particles of an atom or molecule can lead toobservable parity violating effects in their spectra Pre-cision examinations of these effects known as atomic

25

parity violation (APV) allow the study of nuclear andelectroweak physics using atomic systems[29] An ex-perimentally feasible approach to using APV to probeelectroweak physics was first proposed in 1974[114] andsince then APV has been observed in a number ofatoms[29 115ndash117] Here we will briefly discuss howbuffer gas beams may improve experimental studies ofAPV detailed discussions of APV theory and experi-ments may be found elsewhere[29 30 115 118]

Weak neutral currents The exchange of a neutralZ0 boson between the nucleus and the electrons in anatom can give rise a parity-violating electronic contactpotential[114] This potential can mix atomic states ofopposite parity such as a valence electron in S12 andP12 atomic orbitals This mixing can either be mea-sured by searching for parity violating optical rotationin atomic emissionabsorption[114 117] or by lookingfor interference between the APV induced state mixingand the mixing provided by an external electric field (theStark-interference method[119]) APV has been mea-sured in a number of atoms[29 116] and comparison totheory gives tests of the standard model at low energies

Nuclear anapole moments Another parity violatingeffect in an atom is the anapole moment[29 118 120]which arises from an exchange of a Z0 or Wplusmn boson be-tween nucleons in a nucleus Like the parity-violatingpotential above the interaction is a contact potential be-tween the electrons and nuclear anapole moment Theobservable effect is very similar to that of the weak neu-tral currents discussed above with the important ex-ception that the size of the effect will vary dependingon the nuclear spin An experimental signature of ananapole moment is then a difference in parity violat-ing amplitudes between different hyperfine levels Sofar only a single anapole moment has been measuredin the 133Cs nucleus[121] though other experiments areunderway[30]

Enhancement of parity violation in diatomic moleculesParity-violating effects have thus far been observed onlyin atoms though the search has been extended to di-atomic molecules for very compelling reasons Moleculeshave states of opposite parity (rotational states and insome cases ΛΩ-doublets[85]) which are typically muchsmaller than the spacing between opposite parity elec-tronic states in atoms so the effects of nuclear-spin-dependent parity-violating violation (such as anapolemoments) can be greatly enhanced[122ndash125] This mix-ing can be increased even further by applying exter-nal magnetic fields to push rotational states to near-degeneracy DeMille et al[124] proposed (and are work-ing on) an experiment to use a supersonic beam of BaFfree radicals in a 2Σ electronic state to measure parity-violating amplitudes with high precision

Similar to the case with an EDM measurement theshot-noise limited uncertainty (Eq (59)) in the parity vi-olating amplitude scales as prop Nminus12Tminus1 where N is thetotal number of interrogated molecules and T is the timethat the molecules spend interacting with the electro-

magnetic fields Also similar to the EDM measurementsis the choice of molecules including[30] BiO BiS HgFLaO LaS LuO LuS PbF and YbF These are all freeradicals with heavy nuclei and are therefore prime candi-dates for production in a buffer gas cooled beam Thereare even some molecules which have already been dis-cussed such as YbF and BaF (Table I) for which usinga buffer gas beam can deliver over 100 times the bright-ness of a supersonic beam with a slower forward velocity(allowing for the same time T with a shorter apparatuseasing technical requirements) It is for this reason thata BaF anapole moment experiment (at Yale[124]) is pur-suing a buffer gas cooled beam source[12]

3 Time-variation of fundamental constants

There has been much recent interest in the ques-tion of whether or not fundamental constants are trulyldquoconstantrdquo or whether their values have changed overtime In particular the dimensionless fine structureconstant α = e24πε0~c and electron-proton mass ra-tio micro = memp have attracted special attention due tothe possibility of measuring their variation from mul-tiple independent sources Detailed discussions of thetheory and experiments discussed here may be found inreviews[38 126]

Searches for time-variation of fundamental constantstypically take one of two approaches One is to lookat data which may give information about α or micro froma very long time ago for example by examining astro-nomical spectra at large redshifts[38 127] but with lim-ited accuracy (though the search may be coupled with alaboratory precision spectroscopy experiment) Anothertechnique is to use measurements with high precision butover a comparatively short timescale for example by us-ing an atomic clock[128 129] The current limits on microand α are

micro

micro= (1plusmn 3)times 10minus16 yrminus1

from the inversion spectrum of ammonia measured insources with high redshift[127] and

α

α= (minus16plusmn 23)times 10minus17 yrminus1

from comparing optical clocks[128]As with EDMs and parity violation molecules can have

large enhancement factors which could allow for moresensitive measurements In particular the α and micro de-pendence of fine structure splitting ωf prop α2 rotational

splitting ωr prop micro and vibrational splitting ωv prop micro12 aredifferent[38] and if two levels with different hyperfinerotational or vibrational character are nearly degener-ate there can be significant sensitivity enhancement[130]in changes to both micro and α This enhancement can beseveral orders of magnitude (compared to atoms) and

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

23

low forward velocity of the beam makes direct loading ofexotic atomic beams into MOTs feasible Additionallythe very high fluxes possible with ablation of certain met-als can lead to a superior beam system

The longitudinal and transverse temperatures of CaHmolecules in a beam produced with a slowing cell weremeasured to be sim 5 K and sim 25 K respectively [10]Since the cooling mechanism only relies on elastic col-lisions with the He buffer gas we expect atomic beamsproduced from such a slowing cell to have properties simi-lar to the beam of CaH (except of course for any possiblemass-related differences) For example the forward ve-locity of a slow Yb beam with a longitudinal temperatureof 5 K is sim 30 m sminus1 which is consistent with the forwardvelocity of a Yb beam demonstrated by Patterson [102]using a similar cell design Employing a one-dimensionallaser cooling model the capture velocity of a MOT isgiven by vc = (|∆|+ Γ)k [97] where ∆ is the detuningof the cooling laser and Γ is the natural linewidth ForYb assuming |∆| = Γ = 2πtimes28 MHz the capture veloc-ity is 22 m sminus1 implying a large fraction of a buffer gascooled Yb beam can be loaded without any longitudinallaser slowing (see Table IV)

Collisional heating from the buffer gas streamingthrough the MOT region could be a concern Typicallythe buffer density inside the slowing cell is on the orderof 1014 cmminus3 Although it is difficult to measure the Hebeam profile a good approximation is to assume thatthe He beam attains the same temperatures as the CaHmolecular beam Therefore the collisional heating fromthe buffer gas is negligible compared to the cooling powerfrom the scattered photons starting from a distance of10 cm away from the aperture where the He density islt 1012 cmminus3 Any potential loss due to the divergenceof the beam can be mitigated by employing transverselaser cooling to collimate the atomic beam between thecell aperture and MOT Assuming the transverse capturevelocity is given by vct = Γk we can estimate the load-ing efficiency of a buffer gas cooled beam into MOTs byconsidering the velocity distributions that are within vcttransversely and vc longitudinally

Table IV shows some exotic atoms that have beenloaded into MOTs from effusive oven sources and havealso been buffer gas cooled Of these species only Ybhas been realized as a buffer gas beam so far[5] Giventhe generality of the buffer gas beam technique we be-lieve that producing cold and slow exotic atomic beamswith beam properties similar to the CaH beam[10] isvery likely We can therefore estimate the loading effi-ciency of these atoms into MOTs from buffer gas beamsfload by assuming that these proposed atomic beamswould have the same longitudinal and transverse tem-peratures of the CaH beam 5 K and 25 K respectivelyBased on the ablation yields inside the buffer gas cellNablation reported in the past[4] and a typical extrac-tion efficiency of the slowing cell of fext sim 5 times 10minus3 wecan estimate potential loaded numbers per ablation pulseNload sim Nablationtimesfexttimesfload shown as the last column

Atom Ntrappedexp fload [] Nload [pulseminus1]

Yb [97] 107 21 2 times 1010

Ag [98] 3 times 106 17 3 times 109

Dy [100] 25 times 108 33 3 times 109

Er [99] 106 39 4 times 108

Tm [101] 7 times 104 03 3 times 106

TABLE IV Some exotic atoms which have been loaded into aMOT from an effusive oven source and also buffer gas cooledNtrappedexp is the number of atoms that were loaded into theMOT in the respective experiments fload is the projectedloading efficiency from a buffer gas beam source and Nload

is the projected number of atoms which could be trapped inthe MOT with a single pulse from a buffer gas source Adescription of these estimates may be found in the text

in Table IV The estimated numbers of atoms loaded perpulse are high compared to the reported trapped num-bers By loading 1minus 10 pulses the expected atom num-bers (or densities) accumulated in MOTs could approacha regime where the radiation pressure and collisions be-tween ground and excited state atoms would limit theatomic density[103] Co-loading multiple species with-out using high temperature ovens and Zeeman slowersinto a MOT is feasible by simply ablating several speciessimultaneously

B Precision measurements

Another application of molecular beams is the preci-sion determination of molecular properties This is madepossible by the lack of collisions in the beam regionand enhanced by the large volume of advanced molec-ular beam production manipulation and spectroscopytechniques[1 2] Precision spectroscopy with supersonicbeams is a workhorse in chemistry and physics As thereader can surely surmise by now many precision mea-surements can benefit from the high flux and low for-ward velocity afforded by buffer gas cooled beams Inthis section we will review some molecular beam preci-sion measurements and discuss how they could benefitfrom buffer gas cooled beam technology

1 Electric dipole moments

In 1950 Purcell and Ramsey[104] were the first to se-riously consider the possibility of a fundamental parti-cle (ie an electron or nucleon) possessing a permanentelectric dipole moment (EDM) Before this time it waswidely (though not universally[105]) believed that a fun-damental particle could not possess such a moment be-cause it would violate parity (P) and time-reversal (T)invariance in the following manner Since a dipole mo-ment is a vector quantity it must be aligned with the spinof the particle which is the only intrinsic vector associ-

24

ated with a fundamental particle However an electricdipole moment is a polar vector while spin is an axial(or pseudo-) vector so these two quantities must behaveoppositely under inversion of coordinate systems or rever-sal of time yet the previous argument requires them touniquely determine each other Although no permanentEDM of a fundamental particle has ever been measured(despite over 50 years of experimental searches[106])such a discovery would have a profound impact on ourunderstanding of particle physics and cosmology For anaccessible discussion about EDMs of fundamental par-ticles and their implications see the article by FortsonSandars and Barr[107] for more details see the book byKhriplovich and Lamoreaux[28]

The essential idea of nearly every EDM search isto look for a small shift in precession frequency of aspin in an electric field as the electric field direction is

reversed[28] For a particle with spin ~S magnetic dipolemoment micro and electric dipole moment d in a parallel

magnetic field ~B and electric field ~E the spin of the par-ticle (which is parallel to both the magnetic and electricdipole moment) will precess about the fields with angularfrequency

ω =d~E + micro~B

~middot~S

|~S| (57)

Consider an experiment where ~S and ~B are kept fixed

but the direction of ~E is reversed and then the frequency

ωplusmn is measured for the two different orientations plusmn~E The value of the electric dipole moment d can then beextracted by comparing these two measured values

d =~(ω+ minus ωminus)

2~E middot ~S|~S| (58)

The determination of d then reduces to a precision mea-surement of the frequencies ωplusmn Precise frequency mea-surements are best accomplished by the separated oscilla-tory field (or Ramsey) method[2] in which the spins areallowed to precess for a time (the ldquocoherence timerdquo) τbefore the accumulated phase angle is measured therebydetermining ω If such an experiment is repeated witha total of N spins the uncertainty in the EDM is givenby[28]

δd =~τ

|~E|radicN|~S|

(59)

From this equation we can see that an EDM ex-periment should have large electric fields long coher-ence times and large count rates Neutral objects suchas neutrons or atoms can simply be placed in largeelectric fields however charged particles like electronsor protons would simply accelerate out of the electricfield Sandars[108] realized that not only could an elec-tric dipole moment of a charged object be inferred bystudying a composite neutral object such as an atom or

molecule but the electric dipole moment could actuallybe enhanced For example Sandars calculated[109] thatan electric dipole moment of the electron de could in-duce an electric dipole moment of an atom dA with arelativistic ldquoenhancement factorrdquo dAde that can be over100 for Cs atoms The basic idea[110] is that the electroncan sample the atomic electric field which is typically oforder

Eatomic asympe2

4πε0a20

asymp 5 GV cmminus1 (60)

where a0 is the Bohr radius This is considerably largerthan a typical macroscopic lab field of 100 kV cmminus1Atoms cannot take full advantage of this enhancementbecause they cannot be fully polarized in laboratory elec-tric fields[111] however polar molecules can be polarizedin lab fields and for this reason most current electronEDM experiments use polar molecules[111]

The molecules which have the highest enhancementfactor have high-Z atoms with partially filled electronshells and tend to be chemically reactive have high melt-ing points and are often free radicals[111] For this rea-son effusive beam sources of these molecules are typ-ically not feasible the Boltzmann distribution of rota-tional states at temperatures where the species have ap-preciable vapor pressure put only a tiny fraction in anysingle rotational state (however performing an electronEDM experiment with molecules in a hot vapor cell is apossibility[112]) A molecular beam for an EDM searchshould therefore have low temperature and in light ofEq (59) a low forward velocity to allow the moleculesto interact with the fields for a long time giving largeτ For the types of molecules under consideration buffergas cooled beams[3 7 9] have considerable advantagesover the standard supersonic beam[11] As discussed ear-lier the brightness for refractory or chemically reactivespecies can be very high with buffer gas beams and theyhave considerably slower forward velocities In Table Iwe can see that a buffer gas cooled ThO beam has aslower forward velocity and over 100 times the bright-ness compared to a demonstrated state-of-the-art YbFsupersonic beam both of which are currently being usedfor an electron EDM search These reasons make buffergas cooled beams an attractive option for electron EDMsearches with some existing supersonic experiments con-sidering switching to buffer gas cooling[70]

Searches for the electron EDM are currently underwayin molecular beams of YbF[27] ThO[59] and WC[113]as well as several other atomic molecular and solid statesystems[111]

2 Parity violation and anapole moments

The exchange of weak neutral currents between theconstituent particles of an atom or molecule can lead toobservable parity violating effects in their spectra Pre-cision examinations of these effects known as atomic

25

parity violation (APV) allow the study of nuclear andelectroweak physics using atomic systems[29] An ex-perimentally feasible approach to using APV to probeelectroweak physics was first proposed in 1974[114] andsince then APV has been observed in a number ofatoms[29 115ndash117] Here we will briefly discuss howbuffer gas beams may improve experimental studies ofAPV detailed discussions of APV theory and experi-ments may be found elsewhere[29 30 115 118]

Weak neutral currents The exchange of a neutralZ0 boson between the nucleus and the electrons in anatom can give rise a parity-violating electronic contactpotential[114] This potential can mix atomic states ofopposite parity such as a valence electron in S12 andP12 atomic orbitals This mixing can either be mea-sured by searching for parity violating optical rotationin atomic emissionabsorption[114 117] or by lookingfor interference between the APV induced state mixingand the mixing provided by an external electric field (theStark-interference method[119]) APV has been mea-sured in a number of atoms[29 116] and comparison totheory gives tests of the standard model at low energies

Nuclear anapole moments Another parity violatingeffect in an atom is the anapole moment[29 118 120]which arises from an exchange of a Z0 or Wplusmn boson be-tween nucleons in a nucleus Like the parity-violatingpotential above the interaction is a contact potential be-tween the electrons and nuclear anapole moment Theobservable effect is very similar to that of the weak neu-tral currents discussed above with the important ex-ception that the size of the effect will vary dependingon the nuclear spin An experimental signature of ananapole moment is then a difference in parity violat-ing amplitudes between different hyperfine levels Sofar only a single anapole moment has been measuredin the 133Cs nucleus[121] though other experiments areunderway[30]

Enhancement of parity violation in diatomic moleculesParity-violating effects have thus far been observed onlyin atoms though the search has been extended to di-atomic molecules for very compelling reasons Moleculeshave states of opposite parity (rotational states and insome cases ΛΩ-doublets[85]) which are typically muchsmaller than the spacing between opposite parity elec-tronic states in atoms so the effects of nuclear-spin-dependent parity-violating violation (such as anapolemoments) can be greatly enhanced[122ndash125] This mix-ing can be increased even further by applying exter-nal magnetic fields to push rotational states to near-degeneracy DeMille et al[124] proposed (and are work-ing on) an experiment to use a supersonic beam of BaFfree radicals in a 2Σ electronic state to measure parity-violating amplitudes with high precision

Similar to the case with an EDM measurement theshot-noise limited uncertainty (Eq (59)) in the parity vi-olating amplitude scales as prop Nminus12Tminus1 where N is thetotal number of interrogated molecules and T is the timethat the molecules spend interacting with the electro-

magnetic fields Also similar to the EDM measurementsis the choice of molecules including[30] BiO BiS HgFLaO LaS LuO LuS PbF and YbF These are all freeradicals with heavy nuclei and are therefore prime candi-dates for production in a buffer gas cooled beam Thereare even some molecules which have already been dis-cussed such as YbF and BaF (Table I) for which usinga buffer gas beam can deliver over 100 times the bright-ness of a supersonic beam with a slower forward velocity(allowing for the same time T with a shorter apparatuseasing technical requirements) It is for this reason thata BaF anapole moment experiment (at Yale[124]) is pur-suing a buffer gas cooled beam source[12]

3 Time-variation of fundamental constants

There has been much recent interest in the ques-tion of whether or not fundamental constants are trulyldquoconstantrdquo or whether their values have changed overtime In particular the dimensionless fine structureconstant α = e24πε0~c and electron-proton mass ra-tio micro = memp have attracted special attention due tothe possibility of measuring their variation from mul-tiple independent sources Detailed discussions of thetheory and experiments discussed here may be found inreviews[38 126]

Searches for time-variation of fundamental constantstypically take one of two approaches One is to lookat data which may give information about α or micro froma very long time ago for example by examining astro-nomical spectra at large redshifts[38 127] but with lim-ited accuracy (though the search may be coupled with alaboratory precision spectroscopy experiment) Anothertechnique is to use measurements with high precision butover a comparatively short timescale for example by us-ing an atomic clock[128 129] The current limits on microand α are

micro

micro= (1plusmn 3)times 10minus16 yrminus1

from the inversion spectrum of ammonia measured insources with high redshift[127] and

α

α= (minus16plusmn 23)times 10minus17 yrminus1

from comparing optical clocks[128]As with EDMs and parity violation molecules can have

large enhancement factors which could allow for moresensitive measurements In particular the α and micro de-pendence of fine structure splitting ωf prop α2 rotational

splitting ωr prop micro and vibrational splitting ωv prop micro12 aredifferent[38] and if two levels with different hyperfinerotational or vibrational character are nearly degener-ate there can be significant sensitivity enhancement[130]in changes to both micro and α This enhancement can beseveral orders of magnitude (compared to atoms) and

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

24

ated with a fundamental particle However an electricdipole moment is a polar vector while spin is an axial(or pseudo-) vector so these two quantities must behaveoppositely under inversion of coordinate systems or rever-sal of time yet the previous argument requires them touniquely determine each other Although no permanentEDM of a fundamental particle has ever been measured(despite over 50 years of experimental searches[106])such a discovery would have a profound impact on ourunderstanding of particle physics and cosmology For anaccessible discussion about EDMs of fundamental par-ticles and their implications see the article by FortsonSandars and Barr[107] for more details see the book byKhriplovich and Lamoreaux[28]

The essential idea of nearly every EDM search isto look for a small shift in precession frequency of aspin in an electric field as the electric field direction is

reversed[28] For a particle with spin ~S magnetic dipolemoment micro and electric dipole moment d in a parallel

magnetic field ~B and electric field ~E the spin of the par-ticle (which is parallel to both the magnetic and electricdipole moment) will precess about the fields with angularfrequency

ω =d~E + micro~B

~middot~S

|~S| (57)

Consider an experiment where ~S and ~B are kept fixed

but the direction of ~E is reversed and then the frequency

ωplusmn is measured for the two different orientations plusmn~E The value of the electric dipole moment d can then beextracted by comparing these two measured values

d =~(ω+ minus ωminus)

2~E middot ~S|~S| (58)

The determination of d then reduces to a precision mea-surement of the frequencies ωplusmn Precise frequency mea-surements are best accomplished by the separated oscilla-tory field (or Ramsey) method[2] in which the spins areallowed to precess for a time (the ldquocoherence timerdquo) τbefore the accumulated phase angle is measured therebydetermining ω If such an experiment is repeated witha total of N spins the uncertainty in the EDM is givenby[28]

δd =~τ

|~E|radicN|~S|

(59)

From this equation we can see that an EDM ex-periment should have large electric fields long coher-ence times and large count rates Neutral objects suchas neutrons or atoms can simply be placed in largeelectric fields however charged particles like electronsor protons would simply accelerate out of the electricfield Sandars[108] realized that not only could an elec-tric dipole moment of a charged object be inferred bystudying a composite neutral object such as an atom or

molecule but the electric dipole moment could actuallybe enhanced For example Sandars calculated[109] thatan electric dipole moment of the electron de could in-duce an electric dipole moment of an atom dA with arelativistic ldquoenhancement factorrdquo dAde that can be over100 for Cs atoms The basic idea[110] is that the electroncan sample the atomic electric field which is typically oforder

Eatomic asympe2

4πε0a20

asymp 5 GV cmminus1 (60)

where a0 is the Bohr radius This is considerably largerthan a typical macroscopic lab field of 100 kV cmminus1Atoms cannot take full advantage of this enhancementbecause they cannot be fully polarized in laboratory elec-tric fields[111] however polar molecules can be polarizedin lab fields and for this reason most current electronEDM experiments use polar molecules[111]

The molecules which have the highest enhancementfactor have high-Z atoms with partially filled electronshells and tend to be chemically reactive have high melt-ing points and are often free radicals[111] For this rea-son effusive beam sources of these molecules are typ-ically not feasible the Boltzmann distribution of rota-tional states at temperatures where the species have ap-preciable vapor pressure put only a tiny fraction in anysingle rotational state (however performing an electronEDM experiment with molecules in a hot vapor cell is apossibility[112]) A molecular beam for an EDM searchshould therefore have low temperature and in light ofEq (59) a low forward velocity to allow the moleculesto interact with the fields for a long time giving largeτ For the types of molecules under consideration buffergas cooled beams[3 7 9] have considerable advantagesover the standard supersonic beam[11] As discussed ear-lier the brightness for refractory or chemically reactivespecies can be very high with buffer gas beams and theyhave considerably slower forward velocities In Table Iwe can see that a buffer gas cooled ThO beam has aslower forward velocity and over 100 times the bright-ness compared to a demonstrated state-of-the-art YbFsupersonic beam both of which are currently being usedfor an electron EDM search These reasons make buffergas cooled beams an attractive option for electron EDMsearches with some existing supersonic experiments con-sidering switching to buffer gas cooling[70]

Searches for the electron EDM are currently underwayin molecular beams of YbF[27] ThO[59] and WC[113]as well as several other atomic molecular and solid statesystems[111]

2 Parity violation and anapole moments

The exchange of weak neutral currents between theconstituent particles of an atom or molecule can lead toobservable parity violating effects in their spectra Pre-cision examinations of these effects known as atomic

25

parity violation (APV) allow the study of nuclear andelectroweak physics using atomic systems[29] An ex-perimentally feasible approach to using APV to probeelectroweak physics was first proposed in 1974[114] andsince then APV has been observed in a number ofatoms[29 115ndash117] Here we will briefly discuss howbuffer gas beams may improve experimental studies ofAPV detailed discussions of APV theory and experi-ments may be found elsewhere[29 30 115 118]

Weak neutral currents The exchange of a neutralZ0 boson between the nucleus and the electrons in anatom can give rise a parity-violating electronic contactpotential[114] This potential can mix atomic states ofopposite parity such as a valence electron in S12 andP12 atomic orbitals This mixing can either be mea-sured by searching for parity violating optical rotationin atomic emissionabsorption[114 117] or by lookingfor interference between the APV induced state mixingand the mixing provided by an external electric field (theStark-interference method[119]) APV has been mea-sured in a number of atoms[29 116] and comparison totheory gives tests of the standard model at low energies

Nuclear anapole moments Another parity violatingeffect in an atom is the anapole moment[29 118 120]which arises from an exchange of a Z0 or Wplusmn boson be-tween nucleons in a nucleus Like the parity-violatingpotential above the interaction is a contact potential be-tween the electrons and nuclear anapole moment Theobservable effect is very similar to that of the weak neu-tral currents discussed above with the important ex-ception that the size of the effect will vary dependingon the nuclear spin An experimental signature of ananapole moment is then a difference in parity violat-ing amplitudes between different hyperfine levels Sofar only a single anapole moment has been measuredin the 133Cs nucleus[121] though other experiments areunderway[30]

Enhancement of parity violation in diatomic moleculesParity-violating effects have thus far been observed onlyin atoms though the search has been extended to di-atomic molecules for very compelling reasons Moleculeshave states of opposite parity (rotational states and insome cases ΛΩ-doublets[85]) which are typically muchsmaller than the spacing between opposite parity elec-tronic states in atoms so the effects of nuclear-spin-dependent parity-violating violation (such as anapolemoments) can be greatly enhanced[122ndash125] This mix-ing can be increased even further by applying exter-nal magnetic fields to push rotational states to near-degeneracy DeMille et al[124] proposed (and are work-ing on) an experiment to use a supersonic beam of BaFfree radicals in a 2Σ electronic state to measure parity-violating amplitudes with high precision

Similar to the case with an EDM measurement theshot-noise limited uncertainty (Eq (59)) in the parity vi-olating amplitude scales as prop Nminus12Tminus1 where N is thetotal number of interrogated molecules and T is the timethat the molecules spend interacting with the electro-

magnetic fields Also similar to the EDM measurementsis the choice of molecules including[30] BiO BiS HgFLaO LaS LuO LuS PbF and YbF These are all freeradicals with heavy nuclei and are therefore prime candi-dates for production in a buffer gas cooled beam Thereare even some molecules which have already been dis-cussed such as YbF and BaF (Table I) for which usinga buffer gas beam can deliver over 100 times the bright-ness of a supersonic beam with a slower forward velocity(allowing for the same time T with a shorter apparatuseasing technical requirements) It is for this reason thata BaF anapole moment experiment (at Yale[124]) is pur-suing a buffer gas cooled beam source[12]

3 Time-variation of fundamental constants

There has been much recent interest in the ques-tion of whether or not fundamental constants are trulyldquoconstantrdquo or whether their values have changed overtime In particular the dimensionless fine structureconstant α = e24πε0~c and electron-proton mass ra-tio micro = memp have attracted special attention due tothe possibility of measuring their variation from mul-tiple independent sources Detailed discussions of thetheory and experiments discussed here may be found inreviews[38 126]

Searches for time-variation of fundamental constantstypically take one of two approaches One is to lookat data which may give information about α or micro froma very long time ago for example by examining astro-nomical spectra at large redshifts[38 127] but with lim-ited accuracy (though the search may be coupled with alaboratory precision spectroscopy experiment) Anothertechnique is to use measurements with high precision butover a comparatively short timescale for example by us-ing an atomic clock[128 129] The current limits on microand α are

micro

micro= (1plusmn 3)times 10minus16 yrminus1

from the inversion spectrum of ammonia measured insources with high redshift[127] and

α

α= (minus16plusmn 23)times 10minus17 yrminus1

from comparing optical clocks[128]As with EDMs and parity violation molecules can have

large enhancement factors which could allow for moresensitive measurements In particular the α and micro de-pendence of fine structure splitting ωf prop α2 rotational

splitting ωr prop micro and vibrational splitting ωv prop micro12 aredifferent[38] and if two levels with different hyperfinerotational or vibrational character are nearly degener-ate there can be significant sensitivity enhancement[130]in changes to both micro and α This enhancement can beseveral orders of magnitude (compared to atoms) and

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

25

parity violation (APV) allow the study of nuclear andelectroweak physics using atomic systems[29] An ex-perimentally feasible approach to using APV to probeelectroweak physics was first proposed in 1974[114] andsince then APV has been observed in a number ofatoms[29 115ndash117] Here we will briefly discuss howbuffer gas beams may improve experimental studies ofAPV detailed discussions of APV theory and experi-ments may be found elsewhere[29 30 115 118]

Weak neutral currents The exchange of a neutralZ0 boson between the nucleus and the electrons in anatom can give rise a parity-violating electronic contactpotential[114] This potential can mix atomic states ofopposite parity such as a valence electron in S12 andP12 atomic orbitals This mixing can either be mea-sured by searching for parity violating optical rotationin atomic emissionabsorption[114 117] or by lookingfor interference between the APV induced state mixingand the mixing provided by an external electric field (theStark-interference method[119]) APV has been mea-sured in a number of atoms[29 116] and comparison totheory gives tests of the standard model at low energies

Nuclear anapole moments Another parity violatingeffect in an atom is the anapole moment[29 118 120]which arises from an exchange of a Z0 or Wplusmn boson be-tween nucleons in a nucleus Like the parity-violatingpotential above the interaction is a contact potential be-tween the electrons and nuclear anapole moment Theobservable effect is very similar to that of the weak neu-tral currents discussed above with the important ex-ception that the size of the effect will vary dependingon the nuclear spin An experimental signature of ananapole moment is then a difference in parity violat-ing amplitudes between different hyperfine levels Sofar only a single anapole moment has been measuredin the 133Cs nucleus[121] though other experiments areunderway[30]

Enhancement of parity violation in diatomic moleculesParity-violating effects have thus far been observed onlyin atoms though the search has been extended to di-atomic molecules for very compelling reasons Moleculeshave states of opposite parity (rotational states and insome cases ΛΩ-doublets[85]) which are typically muchsmaller than the spacing between opposite parity elec-tronic states in atoms so the effects of nuclear-spin-dependent parity-violating violation (such as anapolemoments) can be greatly enhanced[122ndash125] This mix-ing can be increased even further by applying exter-nal magnetic fields to push rotational states to near-degeneracy DeMille et al[124] proposed (and are work-ing on) an experiment to use a supersonic beam of BaFfree radicals in a 2Σ electronic state to measure parity-violating amplitudes with high precision

Similar to the case with an EDM measurement theshot-noise limited uncertainty (Eq (59)) in the parity vi-olating amplitude scales as prop Nminus12Tminus1 where N is thetotal number of interrogated molecules and T is the timethat the molecules spend interacting with the electro-

magnetic fields Also similar to the EDM measurementsis the choice of molecules including[30] BiO BiS HgFLaO LaS LuO LuS PbF and YbF These are all freeradicals with heavy nuclei and are therefore prime candi-dates for production in a buffer gas cooled beam Thereare even some molecules which have already been dis-cussed such as YbF and BaF (Table I) for which usinga buffer gas beam can deliver over 100 times the bright-ness of a supersonic beam with a slower forward velocity(allowing for the same time T with a shorter apparatuseasing technical requirements) It is for this reason thata BaF anapole moment experiment (at Yale[124]) is pur-suing a buffer gas cooled beam source[12]

3 Time-variation of fundamental constants

There has been much recent interest in the ques-tion of whether or not fundamental constants are trulyldquoconstantrdquo or whether their values have changed overtime In particular the dimensionless fine structureconstant α = e24πε0~c and electron-proton mass ra-tio micro = memp have attracted special attention due tothe possibility of measuring their variation from mul-tiple independent sources Detailed discussions of thetheory and experiments discussed here may be found inreviews[38 126]

Searches for time-variation of fundamental constantstypically take one of two approaches One is to lookat data which may give information about α or micro froma very long time ago for example by examining astro-nomical spectra at large redshifts[38 127] but with lim-ited accuracy (though the search may be coupled with alaboratory precision spectroscopy experiment) Anothertechnique is to use measurements with high precision butover a comparatively short timescale for example by us-ing an atomic clock[128 129] The current limits on microand α are

micro

micro= (1plusmn 3)times 10minus16 yrminus1

from the inversion spectrum of ammonia measured insources with high redshift[127] and

α

α= (minus16plusmn 23)times 10minus17 yrminus1

from comparing optical clocks[128]As with EDMs and parity violation molecules can have

large enhancement factors which could allow for moresensitive measurements In particular the α and micro de-pendence of fine structure splitting ωf prop α2 rotational

splitting ωr prop micro and vibrational splitting ωv prop micro12 aredifferent[38] and if two levels with different hyperfinerotational or vibrational character are nearly degener-ate there can be significant sensitivity enhancement[130]in changes to both micro and α This enhancement can beseveral orders of magnitude (compared to atoms) and

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

26

there are several promising species[38] including CuSIrC LaS LaO LuO SiBr YbF Cs2 and Sr2 Several ofthese molecules may be difficult to produce through nor-mal beam methods but are prime candidates for buffergas beam production

C Cold collisions and trap loading

The study of cold molecular collisions may impact ar-eas of fundamental physics astrophysics and chemistryFor example several cold neutral-neutral reactions arecalculated to proceed with a large rate [131ndash133] andhence may play crucial roles in cold chemistry of inter-stellar clouds where low mass stars may be formed[134]The number of direct measurements of reaction rates in-volving cold molecules is small compared to the numberof theoretical calculations but new measurements couldbe used in detailed astrophysical modeling and can assistfurther theoretical calculations[40 131 132]

Collision studies at high temperatures may involvemany internal states and scattering channels which cancomplicate both theory and measurements cooling thesample to a few K can reduce the involved states andchannels making the problem more tractable In addi-tion the potential energy provided by electromagneticfields on magnetic or polar molecules (typically a fewTesla or kV cmminus1 respectively) can be comparable tothe thermal energy of the cold molecule which makesthe experimental control of collisions and chemical reac-tions an achievable goal[26 46]

Understanding cold molecular collisions is an impor-tant step for producing ultra-cold molecules via directcooling methods Cold molecules produced from directmethods (buffer gas cooling supersonic expansion withStark deceleration etc) so far possess a thermal en-ergy gt kB times 1 mK There are a few possible paths toapproach ultra-cold temperatures including evaporativecooling and sympathetic cooling of molecules The for-mer (latter) relies on removing molecules (atoms) fromthe high energy tail in a thermal distribution followedby subsequent elastic molecule-molecule (atom-molecule)collisions which rethermalize molecules to a lower tem-perature Therefore good molecule-molecule or atom-molecule collision properties are required for bringingcold molecules into ultra-cold temperatures

Buffer gas cooling can provide a large molecular sam-ple in a single quantum state with a kinetic energy onthe order of sim kBtimes K Several cold atom-molecule andmolecule-molecule systems have been investigated usingbuffer gas cooling including collisions of He atoms with2Σ and 3Σ molecules[56 135] N + NH[136] and ND3 +OH[60]

The He + molecule and N + NH collision systems in-volved magnetic trapping of molecules and resulted indeeper understanding of atom-molecule interactions Forexample the He + 2Σ and 3Σ molecule collision systemsrevealed the spin relaxation mechanisms of 2Σ and 3Σ

molecules in magnetic traps[4] Cold N + NH collisionsindicated not only that N might be a good candidate forsympathetic cooling of NH but that a cold chemical re-action N + NH rarr N2 + H may be suppressed in themagnetic field[136]

1 ND3 + OH collisions

Trapping molecules provides an ideal environment forstudying cold molecular collisions by providing a long in-teraction time Using trapped molecules as the scatteringtarget and monitoring the molecular trap loss allows ab-solute measurements of the collision cross sections [137]Although several chemically interesting molecules havebeen cooled via direct methods and trapped inelasticmolecular collisions or reactions have not been observedin the trap because of a low molecular density and a lowcollisional energy (sim 100 mK) Assuming a typical elasticcross section of 10minus14cm2 an elastic NH + NH collisionoccurs in hundreds of seconds with a molecular densityof 108 cmminus3 at 05 K which is much longer than the traplifetime of sim1 s in the buffer gas loading experiment[135]

Absolute atom-molecule cross section measurementswere obtained for the OH+D2 and OH+He systems byscattering supersonic D2 and He beams off of magneti-cally trapped OH molecules[137] The lowest collisionalenergies (84 K for He and 200 K for D2) achieved witha cooled supersonic nozzle were two order of magnitudeshigher than the trapping potential of the molecules Insuch a situation it is difficult to differentiate the contri-butions of elastic and inelastic collisions to the total crosssection and control the collisions with an external fieldSince buffer gas cooled beams of molecules can be coldslow and bright they are an attractive choice for thestudy of molecular collisions In addition several buffergas beams can provide continuous output (see Table II)which could allow molecular interaction times compara-ble to the lifetime of the trapped species

Such an experiment was performed by Sawyer et al[60] by combining a buffer gas cooled beam of ND3 withtrapped OH molecules Collisions were studied on thesim1 s timescale and led to the first observation of cold(5 K) heteromolecular dipolar collisions The continu-ous ND3 beam was guided to suppress the backgroundbuffer gas giving a typical molecular density of 108 cmminus3

and a mean velocity of 100 m sminus1 before colliding withOH A supersonic OH beam was Stark-decelerated andloaded to a magnetic trap with a density of sim 106 cmminus3

at a temperature of 70 mK To study the ND3 + OHcollisions the trap lifetime of OH in the presence of anND3 beam was compared to the lifetime solely limited bycollisions with the background gas yielding a trap losscross section of σlossexp = 027 times 10minus12 cm2 At a collisionenergy of few K only tens of partial waves participatein the collision and hence external fields can affect thecollisional properties After applying a large electric fieldto polarize both OH and ND3 σlossexp increased by a factor

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

27

of 14Sawyer et al also performed both quantum scatter-

ing and semi-classical calculations to compute the elasticand inelastic OH + ND3 cross sections The calculatedcross sections were orders of magnitude larger than typi-cal gas-kinetic values possibly resulting from the dipolarinteraction To calculate the cross sections in the fieldSawyer et al included a long range and anisotropic dipo-lar interaction term C3r

3 in addition to an isotropicvan der Waals interaction for the zero field case Theydiscovered that the elastic cross section increased by afactor of 27 in the presence of a field compared to arelatively constant inelastic cross section After consid-ering the probability of an elastic scattering leaving OHun-trapped Sawyer et al found the value of σlossexp andits increase in the field were consistent the theoreticalmodel indicating the elastic OH + ND3 collisions notonly dominate the trap loss but can be controlled by theexternal electric field

Compared to other beam technologies buffer gascooled beams are well suited for these types of colli-sion experiments Stark-deceleration of a supersonic ND3

source can yield a beam with a forward velocity of sim 90 msminus1 and a peak density of sim 108 cmminus3 but with pulsedoperation lt 1 ms pulse duration and repetition fre-quency of few Hz[18] The fractional loss of trappedmolecules due to colliding with another beam is givenby

∆NN = minuskloss∆t = minusnbeamσlossvrel∆t (61)

where nbeam is the density of the beam and vrel is themean relative velocity Using a continuous buffer gascooled ND3 beam increases the average interaction timeby a factor of sim100 compared to a Stark-decelerated ND3

beam leading to a higher sensitivity in observing coldcollisions

2 Direct trap loading of molecules

Cold and slow beams of CaH with a kinetic energyof few kbtimesK can be created by using a slowing cell (seeSection II C 2) which should allow direct loading of themolecules into a magnetic trap A magnetic lens or guidecan be used to ensure that the buffer gas atoms do notinterfere with the trapped molecules similar to the ex-periment of Sawyer et al[60] discussed earlier Here wewill explore one possible loading scheme which combinesmagnetic slowing and optical pumping to achieve traploading of slow CaH molecules By using a buffer gascooled beam the proposed method benefits from largemolecular fluxes chemical versatility and high vacuumin the trapping area A similar scheme had been em-ployed to continuously load an atomic Cr beam into anoptical dipole trap[138]

Figure 16 illustrates the scheme to continuously loadCaH molecules into a quadrupole trap When a low-fieldseeking molecule (mprimeprimej = 12) enters the trap it travels up

the potential hill and slows down Near the saddle pointa laser can optically pump the molecules to the high-field seeking state (mprimeprimej = minus12) Molecules continue tobe decelerated while approaching the center of the trapwhen another laser pumps the molecule into the trappedmprimeprimej = 12 state In this loading scheme molecules witha kinetic energy large enough to overcome two potentialhills can reach the trap center Molecules with a kineticenergy lower than the trap depth after deceleration willremain trapped For a magnetic quadrupole trap witha depth of 4 T the capture energy for CaH is 5ndash7 Ksuggesting that a large fraction of the slow CaH beamcan be captured

To reduce the background buffer gas density in traparea a magnetic lens can be used to collimate themolecular beam while the buffer gas is pumped awaywith charcoal cryopumps (see Section II E) We per-formed a semi-classical Monte Carlo simulation to cal-culate the efficiency of loading the CaH beam into the 4T deep quadrupole trap indicating a typical efficiency ofsim 5times10minus3 or about 3times106 trapped molecules per pulseThe background gas density in the trapping region canbe kept low such that molecules can be accumulated inthe trap via continuously loading leading to a total num-ber of 107 minus 108 over time This compares favorably tothe typical values of 104minus5 molecules loaded into a trapfrom a Stark-decelerated supersonic source[17 139ndash142]

We would like to point out that this scheme is gen-eral and applicable to other magnetic species includingatoms More importantly it only requires scattering afew photons to achieve loading and therefore does notrequire a highly closed cycling transition This opensup the possibility of trapping a large class of magneticmolecules

E=-microB

2Σ+ (jrdquo=12)

2Π12 (jrsquo=12 mjrsquo=plusmn12)

mjrdquo=+12

mjrdquo=minus12

FIG 16 Loading scheme of a slow buffer gas beam into amagnetic trap Pink and black curves indicate the poten-tial energy of the low-field and high-field seeking states in amagnetic trap respectively Red and blue arrows show theoptical pumping processes to achieve irreversible loading dueto spontaneous emissions

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

28

IV ACKNOWLEDGMENTS

Thanks to John Barry Sid Cahn Dave DeMilleRichard Hedricks Emil Kirilov Dave Patterson Dave

Rahmlow Julia Rasmussen and Joe Smallman for help-ing us gather information for this paper and to ColinConnolly and Elizabeth Petrik for feedback on themanuscript

[1] G Scoles Atomic and molecular beam methods (OxfordUniversity Press 1988)

[2] N Ramsey Molecular beams (Oxford University Press1985)

[3] S E Maxwell N Brahms R DeCarvalho D R GlennJ S Helton S V Nguyen D Patterson J PetrickaD DeMille and J M Doyle Phys Rev Lett 95173201 (2005)

[4] W C Campbell and J M Doyle Cold moleculesTheory experiment applications (CRC Press 2009)chap 13 pp 473ndash508

[5] D Patterson and J M Doyle J Chem Phys 126154307 (2007)

[6] J B Anderson AIChE Journal 13 1188 (1967)[7] N R Hutzler M F Parsons Y V Gurevich P W

Hess S B Petrik E A C Vutha D DeMilleG Gabrielse and J M Doyle Phys Chem ChemPhys 13 18976 (2011)

[8] Magnetically guided flux While Patterson et al[5] didnot explicitly measure the total output flux numericalsimulations and experience with similar magnetic guidesshows that guide transmission is typically around 10

[9] J F Barry E S Shuman and D DeMille Phys ChemChem Phys 13 18936 (2011)

[10] H Lu J Rasmussen M J Wright D Pattersonand J M Doyle Phys Chem Chem Phys 13 18986(2011)

[11] M R Tarbutt J J Hudson B E Sauer E A HindsV A Ryzhov V L Ryabov and V F Ezhov J PhysB 35 5013 (2002)

[12] D Rahmlow PhD thesis Yale University (2010)[13] M-F Tu J-J Ho C-C Hsieh and Y-C Chen The

Review of Scientific Instruments 80 113111 (2009)[14] R J Ackermann and E G Rauh High Temperature

Science 5 463 (1973)[15] L D van Buuren C Sommer M Motsch S Pohle

M Schenk J Bayerl P W H Pinkse and G RempePhys Rev Lett 102 033001 (2009)

[16] C Sommer L D van Buuren M Motsch S PohleJ Bayerl P W H Pinkse and G Rempe FaradayDiscuss 142 203 (2009)

[17] H L Bethlem B G F M H Crompvoets J R TvanRoij A J A and G Meijer Nature 406 491 (2000)

[18] H L Bethlem F M H Crompvoets R T JongmaS Y T van de Meerakker and G Meijer Phys RevA 65 053416 (2002)

[19] T Junglen T Rieger S A Rangwala P W H Pinskeand G Rempe Eur Phys J D 31 365 (2004)

[20] M H Anderson J R Ensher M R Matthews C EWieman and E A Cornell Science 269 198 (1995)

[21] K B Davis M-O Mewes M R Andrews N J vanDruten D S Durfee D M Kurn and W KetterlePhys Rev Lett 75 3969 (1995)

[22] C Chin M Bartenstein A Altmeyer S RiedlS Jochim J H Denschlag and R Grimm Science 305

1128 (2004)[23] M W Zwierlein J R Abo-Shaeer A Schirotzek C H

Schunck and W Ketterle Nature 435 1047 (2005)[24] J Simon W S Bakr R Ma M E Tai P M Preiss

and M Greiner Nature 472 307 (2011)[25] M Greiner O Mandel T Esslinger T Hansch and

I Bloch Nature 415 39 (2002)[26] L D Carr D DeMille R V Krems and J Ye New

Journal of Physics 11 055049 (2009)[27] J J Hudson D M Kara I J Smallman M R Sauer

B E end Tarbutt and E A Hinds Nature 473 493(2011)

[28] I B Khriplovich and S K Lamoreaux CP-violationwithout strangeness electric dipole moments of parti-cles atoms and molecules (Springer-Verlag 1997)

[29] J Ginges and V Flambaum Physics Reports 397 63(2004)

[30] V A Dzuba and V V Flambaum (2010)arXiv10094960v2

[31] D DeMille Phys Rev Lett 88 067901 (2002)[32] P Rabl D DeMille J M Doyle M D Lukin R J

Schoelkopf and P Zoller Phys Rev Lett 97 033003(2006)

[33] A Andre D DeMille J M Doyle M D Lukin S EMaxwell P Rabl R J Schoelkopf and P Zoller Na-ture Physics 2 636 (2006)

[34] A Micheli G K Brennen and P Zoller NaturePhysics 2 341 (2006)

[35] T Lahaye C Menotti L Santos M Lewenstein andT Pfau Reports on Progress in Physics 72 126401(2009)

[36] D DeMille S Sainis J Sage T Bergeman S Ko-tochigova and E Tiesinga Phys Rev Lett 100043202 (2008)

[37] E R Hudson H J Lewandowski B C Sawyer andJ Ye Phys Rev Lett 96 143004 (2006)

[38] V V Flambaum and M G Kozlov in Cold moleculestheory experiment applications (Taylor and Francis2009) pp 597ndash625

[39] M Schnell and G Meijer Angew Chem Int Ed 486010 (2009)

[40] M Hummon W Campbell H-I Lu E TsikataY Wang and J Doyle Phys Rev A 78 050702 (2008)

[41] W Klemperer Proc Nat Acad Sci 103 12232 (2006)[42] S Ospelkaus K-K Ni D Wang M H G de Miranda

B Neyenhuis G Quemener P S Julienne J L BohnD S Jin and J Ye Science 327 853 (2010)

[43] K-K Ni S Ospelkaus D Wang G QuemenerB Neyenhuis M H G de Miranda J L Bohn J Yeand D S Jin Nature 464 1324 (2010)

[44] W C Campbell T V Tscherbul H-I Lu E TsikataR V Krems and J M Doyle Phys Rev Lett 102013003 (2009)

[45] J J Gilijamse S Hoekstra S Y T van de MeerakkerG C Groenenboom and G Meijer Science 313 1617

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

29

(2006)[46] R V Krems Phys Chem Chem Phys 10 4079

(2008)[47] For example Doret et al[143] created a Bose-Einstein

condensate without laser cooling by loading a magnetictrap with buffer gas cooled Helowast atoms at a temperatureof sim1 K and then evaporatively cooling to quantumdegeneracy

[48] H J Metcalf and P van der Straten Laser Cooling andTrapping (Springer-Verlag 1999)

[49] E S Shuman J F Barry D R Glenn and D DeMillePhys Rev Lett 103 223001 (2009)

[50] E S Shuman J F Barry and D Demille Nature 467820 (2010)

[51] J Doyle B Friedrich R V Krems and F Masnou-Seeuws The European Physical Journal D 31 149(2004)

[52] B Friedrich and J M Doyle ChemPhysChem 10 604(2009)

[53] H L Bethlem and G Meijer International Reviews inPhysical Chemistry 22 73 (2003)

[54] K Bergmann H Theuer and B W Shore Review ofModern Physics 70 1003 (1998)

[55] K-K Ni S Ospelkaus M H G de Miranda A PersquoerB Neyenhuis J J Zirbel S Kotochigova P S Juli-enne D S Jin and J Ye Science 322 231 (2008)

[56] J D Weinstein R deCarvalho T Guillet B Friedrichand J M Doyle Nature 395 148 (1998)

[57] D Patterson E Tsikita and J Doyle Phys ChemChem Phys 12 9736 (2010)

[58] Frank Pobell Matter and Methods at Low Temperatures(Springer-Verlag 1996)

[59] A C Vutha W C Campbell Y V Gurevich N RHutzler M Parsons D Patterson E Petrik B SpaunJ M Doyle G Gabrielse et al Journal of PhysicsB Atomic Molecular and Optical Physics 43 074007(2010)

[60] B C Sawyer B K Stuhl M Yeo T V TscherbulM T Hummon Y Xia J Klos D Patterson J MDoyle and J Ye Phys Chem Chem Phys 13 19059(2011)

[61] H Pauly Atom Molecule and Cluster Beams I(Springer-Verlag 2000)

[62] B N Chichkov C Momma S Nolte F von Al-vensleben and A Tunnermann Appl Phys A 63 109(1996)

[63] D R Olander Pure and Applied Chemistry 62 123(1990)

[64] R M Gilgenbach C H Ching J S Lash and R ALindley Phys Plasmas 1 1619 (1994)

[65] G M Davis M C Gower C Fotakis T Efthimiopou-los and P Argyrakis Applied Physics A 36 27 (1985)

[66] J K Messer and F C De Lucia Phys Rev Lett 532555 (1984)

[67] D Patterson J Rasmussen and J M Doyle New JPhys 11 55018 (2009)

[68] R deCarvalho J Doyle B Friedrich T GuilletJ Kim D Patterson and J Weinstein The EuropeanPhysical Journal D 7 289 (1999)

[69] J Kim PhD thesis Harvard University (1997)[70] S M Skoff R J Hendricks C D J Sinclair J J

Hudson D M Segal B E Sauer E A Hinds andM R Tarbutt Phys Rev A 83 023418 (2011)

[71] J B Hasted Physics of Atomic Collisions (Elsevier1972)

[72] W Campbell G Groenenboom H-I Lu E Tsikataand J Doyle Phys Rev Lett 100 083003 (2008)

[73] R K Pathria Statistical Mechanics (Butterworth-Heinemann 1996)

[74] A Sushkov and D Budker Phys Rev A 77 042707(2008)

[75] M-J Lu K Hardman J Weinstein and B ZygelmanPhys Rev A 77 60701 (2008)

[76] M-J Lu and J D Weinstein New Journal of Physics11 055015 (2009)

[77] J Petricka PhD thesis Yale University (2007)[78] R J Hendricks (2011) private Communication[79] M Hummon (2011) private Communication[80] H Lu J Rasmussen and J M Doyle (2009) laser

Cooling of Buffer Gas Beams presented at DAMOP2009

[81] Y Sone Molecular gas dynamics (Birkhauser Boston2007)

[82] R Fox and A McDonald Introduction to Fluid Me-chanics (John Wiley and Sons 1998)

[83] T Von Karman From Low-Speed Aerodynamics to As-tronautics (Pergamon Press 1963)

[84] C Sommer M Motsch S Chervenkov L D van Bu-uren M Zeppenfeld P W H Pinkse and G RempePhys Rev A 82 013410 (2010)

[85] G Herzberg Molecular Spectra and Molecular Struc-ture Spectra of Diatomic Molecules 2nd ed (Krieger1989)

[86] C Szewc J D Collier and H Ulbricht Rev Sci In-strum 81 106107 (2010)

[87] S Rangwala T Junglen T Rieger P Pinkse andG Rempe Phys Rev A 67 043406 (2003)

[88] J B Hopkins J Chem Phys 78 1627 (1983)[89] D A Fletcher K Y Jung C T Scurlock and T C

Steimle J Chem Phys 98 1837 (1993)[90] T G Dietz M A Duncan D E Powers and R E

Smalley J Chem Phys 74 6511 (1981)[91] R Campargue J Phys Chem 88 4466 (1984)[92] H Ashkenas and F S Sherman (Academic Press 1966)

p 84[93] M D Di Rosa Eur Phys J D 31 395 (2004)[94] B K Stuhl B C Sawyer D Wang and J Ye Phys

Rev Lett 101 243002 (2008)[95] E L Raab M Prentiss A Cable S Chu and D E

Pritchard Phys Rev Lett 59 2631 (1987)[96] Y Takahashi Y Takasu K Maki K Komori

T Takano K Honda A Yamaguchi Y Kato M Mi-zoguchi M Kumakura et al Laser Physics 14 621(2004)

[97] K Pandey K D Rathod A K Singh and V Natara-jan Phys Rev A 82 043429 (2010)

[98] G Uhlenberg J Dirscherl and H Walther Phys RevA 62 063404 (2000)

[99] J J McClelland and J L Hanssen Phys Rev Lett96 143005 (2006)

[100] S H Youn M Lu U Ray and B L Lev Phys RevA 82 043425 (2010)

[101] D Sukachev A Sokolov K Chebakov A AkimovS Kanorsky N Kolachevsky and V Sorokin PhysRev A 82 011405 (2010)

[102] D Patterson PhD thesis Harvard University (2010)

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References

30

[103] W Ketterle K B Davis M A Joffe A Martin andD E Pritchard Phys Rev Lett 70 2253 (1993)

[104] E M Purcell and N F Ramsey Phys Rev 78 807(1950)

[105] P A M Dirac Rev Mod Phys 21 392 (1949)[106] J H Smith E M Purcell and N F Ramsey Phys

Rev 108 120 (1957)[107] N Fortson P Sandars and S Barr Phys Today 56

33 (2003)[108] P G H Sandars Physics Letters 14 194 (1965)[109] P G H Sandars Physics Letters 22 290 (1966)[110] E D Commins J D Jackson and D P DeMille

American Journal of Physics 75 532 (2007)[111] E D Commins and D DeMille in Lepton Dipole Mo-

ments edited by B L Roberts and W J Marciano(World Scientific 2010) chap 14 pp 519ndash581

[112] S Bickman P Hamilton Y Jiang and D DeMillePhys Rev A 80 1 (2009)

[113] J Lee E Meyer R Paudel J Bohn and A LeanhardtJournal of Modern Optics 56 2005 (2009)

[114] M A Bouchiat and C C Bouchiat Physics Letters B48B 111 (1974)

[115] J Guena M Lintz and M A Bouchiat ModernPhysics Letters A 20 375 (2005)

[116] K Tsigutkin D Dounas-Frazer a Family J StalnakerV Yashchuk and D Budker Phys Rev Lett 103071601 (2009)

[117] L M Barkov and M Zolotorev Pisrsquoma v ZhurnalEksperimentalnoi i Teoreticheskoi Fiziki 27 379 (1978)

[118] D Budker D Kimball and D DeMille Atomic physicsAn exploration through problems and solutions (OxfordUniversity Press USA 2008)

[119] R Conti P Bucksbaum S Chu E Commins and LHunter Phys Rev Lett 42 343 (1979)

[120] Y B Zelrsquodovich Sov Phys JETP 33 1531 (1957)[121] C S Wood S C Bennett D Cho B P Masterson

J L Roberts C E Tanner and C E Wieman Science275 1759 (1997)

[122] L Labzovskii Sov Phys JETP 48 434 (1978)[123] O P Sushkov and V V Flarnbaurn Sov Phys JETP

48 608 (1978)[124] D DeMille S B Cahn D Murphree D a Rahmlow

and M G Kozlov Phys Rev Lett 100 023003 (2008)[125] V V Flambaum and I B Khriplovich Physics Letters

110A 121 (1985)

[126] C Chin V V Flambaum and M G Kozlov New Jour-nal of Physics 11 055048 (2009)

[127] V Flambaum and M Kozlov Phys Rev Lett 98240801 (2007)

[128] T Rosenband D B Hume P O Schmidt C W ChouA Brusch L Lorini W H Oskay R E DrullingerT M Fortier J E Stalnaker et al Science 319 1808(2008)

[129] S Blatt A Ludlow G Campbell J ThomsenT Zelevinsky M Boyd J Ye X Baillard M FoucheR Le Targat et al Phys Rev Lett 100 140801(2008)

[130] V Flambaum and M Kozlov Phys Rev Lett 99150801 (2007)

[131] H Sabbah L Biennier I R Sims Y GeorgievskiiS J Klippenstein and I W M Smith Science 317102 (2007)

[132] T J Frankcombe and G Nyman Journal of PhysicalChemistry A 111 13163 (2007)

[133] D Edvardsson C F Williams and D C Clary Chem-ical Physics Letters 431 261 (2006)

[134] H J Fraser M R S McCoustra and D A WilliamsAstronomy amp Geophysics 43 210 (2002)

[135] W Campbell E Tsikata H-I Lu L van Buuren andJ Doyle Phys Rev Lett 98 213001 (2007)

[136] M Hummon T Tscherbul J K los H-I LuE Tsikata W Campbell A Dalgarno and J DoylePhys Rev Lett 106 053201 (2011)

[137] B C Sawyer B K Stuhl D Wang M Yeo and J YePhys Rev Lett 101 203203 (2008)

[138] M Falkenau V V Volchkov J Ruhrig A Griesmaierand T Pfau Phys Rev Lett 106 163002 (2011)

[139] S Y T van de Meerakker P H M Smeets N Van-haecke R T Jongma and G Meijer Phys Rev Lett94 023004 (2005)

[140] S Y T van de Meerakker N Vanhaecke M P Jvan der Loo G C Groenenboom and G Meijer PhysRev Lett 95 013003 (2005)

[141] J J Gilijamse S Hoekstra S A Meek M MetsalaS Y T van de Meerakker and G Meijer J ChemPhys 127 221102 (2007)

[142] S Hoekstra M Metsala P C Zieger L ScharfenbergJ J Gilijamse G Meijer and S Y T van de Meer-akker Phys Rev A 76 063408 (2007)

[143] S C Doret C B Connolly W Ketterle and J MDoyle Phys Rev Lett 103 103005 (2009)

• The Buffer Gas Beam An Intense Cold and Slow Source for Atoms and Molecules
• • Contents
  • I Introduction
  • • A Cold atoms and molecules
    • B Buffer gas cooling and beam production
    • • II Buffer Gas Cooled Beams
      • • A Species production thermalization diffusion and extraction
        • B Properties of buffer gas cooled beams
        • C Additional cooling and slowing
        • D Effusive and supersonic beam properties
        • E Technical details of source construction
        • • III Applications
          • • A Laser cooling of buffer gas beams
            • B Precision measurements
            • C Cold collisions and trap loading
            • • IV Acknowledgments
              • References