bichromatic slowing and collimation to make an intense helium beam

VOLUME 93, NUMBER 21 P H Y S I C A L R E V I E W L E T T E R S week ending19 NOVEMBER 2004

Bichromatic Slowing and Collimation to Make an Intense Helium Beam

M. Partlow, X. Miao, J. Bochmann, M. Cashen, and H. MetcalfPhysics and Astronomy Department, Stony Brook University, Stony Brook, New York 11790-3800, USA

(Received 23 July 2004; published 16 November 2004)

213004-1

The bichromatic force has been used to both slow and collimate a beam of metastable 23S He atoms(He*). The collimation capture range is an extraordinary �85 m=s corresponding to �0:18 radiansfrom our source. Both slowing and collimation were accomplished in the unprecedented short distanceof �5 cm each. The overall brightness increase is �3200, and there is potential for considerably more.

DOI: 10.1103/PhysRevLett.93.213004 PACS numbers: 32.80.Pj, 42.50.Vk

Optical forces on neutral atoms are almost alwaysconsidered in terms of monochromatic light, but theirimplementation with two-frequency light, for examplethe dipole force rectification, has been considered formany years [1,2]. More specifically, the bichromatic force(BF) that arises from two beams of equal intensity andsymmetrical detuning from two-level atomic resonancehas been considered as far back as 1988 [3], observed in1989 [4], demonstrated again in 1997 [5], and morethoroughly investigated since then [6–11].

The BF is most well suited for manipulating atomicbeams, and, in particular, improving their intensity,brightness, and brilliance for a variety of purposes [12].In this Letter we report the active collimation of a beamof metastable 23S1 helium atoms (He*) from a very largecapture angle, as well as slowing and cooling such abeam, both in the very short distances enabled by theBF. We use fiber-amplified light at � � 1:083 �m that iscircularly polarized to drive the transition 23S1 ! 23P2

and optically pump the atoms into the cycling transitionMJ � 1 !2 to make a two-level atom.

The special features of the BF for a two-level atom areits magnitude and velocity capture range that scale withthe detuning from resonance � !‘ �!a. Here !‘ isthe light frequency, !a is the atomic frequency, andtypically jj � 1=�, the natural width of the atomicexcited state. For the � � 1:083 �m transition of He*, � 2�� 1:6 MHz. The force is implemented with twobeams of equal intensity characterized by their Rabifrequency , and detuning �. Whereas the usual radia-tive force F on atoms is limited to F < Frad � �hk =2, theBF is typically Fb � �hk=� Frad (k � 2�=�). More-over, the velocity capture range of the usual radiativeforce is a few times =k, whereas it is �=k for the BF[5]. Finally, the light intensity required for the BF scalesas 2, hence the need for our fiber amplifiers.

There is presently no good theoretical description ofthe BF. The four fields (two in each direction, two fre-quencies) can be paired in different ways. The pair trav-eling in one or the other direction can be considered as anamplitude-modulated carrier that results in the very nice�-pulse model of Refs. [3,5]. Instead, oppositely propa-gating beams at each frequency can be considered as

0031-9007=04=93(21)=213004(4)$22.50

spatially different standing waves, and a dressed atompicture description based on a Floquet Hamiltonian ap-proach is in preparation [13]. We anticipate that this willexplain many of the properties of the BF (see Fig. 1below). Of course, numerical calculations based on directintegration of the optical Bloch equations that simplyconsider the four fields separately have also been studiedin different cases [5–7,13].

Our apparatus has been described in Refs. [8,11]but is briefly reviewed here. Our He* atomic beamsource is modeled after the reverse flow design ofShimizu [14] with modifications originated byMastwijk et al. [15,16]. It consists of a 1 cm diam quartztube with a 1 mm diam tungsten needle along its axis anda 3 cm diam LN2-cooled stainless steel coaxial jacket.The plasma from a dc discharge produces about�1014 He� atoms=sr s with a velocity distribution typicalof �100 K. We have measured this velocity distributionusing a time-of-flight method with a tuning-fork beamchopper, and found the mean longitudinal atomic velocityto be �1000 m=s.

The light for these experiments originated from twoexternal cavity-stabilized SDL-6702-H1 diode laserswhose output was injected into fiber amplifiers [17]. Thediode laser frequencies were locked to atomic resonanceby saturated absorption spectroscopy in a sealed cell witha weak rf discharge. The light frequencies were appropri-ately shifted using AOM’s (acousto-optic modulators).For beam slowing, the counterpropagating bichromaticbeams entered the vacuum system nearly perpendicularto the atomic beam but were reflected to be nearly col-linear by small mirrors placed very close to the atomicbeam. For collimation (force ? to atomic beam), therewere four separate interaction regions, two for each di-mension with spatial phases chosen for each direction (seebelow). The Earth’s field was canceled to �� 1 �T.

For the BF to be effective over the velocity range ofinterest, the optical frequencies must be shifted in thelaboratory frame. For the simplest choice of just twofrequencies, the velocity dependence of the BF is shownby the solid line in Fig. 1. By shifting the frequencies ofthe beams traveling one way upward by =2 and thecounterpropagating ones downward by =2, the center

2004 The American Physical Society 213004-1

velocity (γ/k)

For

ce (

Fra

d)

-20 -10 0 10 20-2

0

2

4

6

8

10

12

30 40

δ/2k

FIG. 1. Calculation of the bichromatic force vs velocity bydirect numerical integration of the optical Bloch equations [5].The dashed line (upshifted by 4Frad for clarity) shows the sameresults offset in velocity by using AOM’s to shift the laserfrequencies in the lab frame (see text). For these plots the Rabifrequency � 22 for each frequency component of eachbeam, � 20 , and the spatial phase difference � � ��=4(this is for the electric fields and the Rabi frequencies—theintensity standing waves have a period �=2 so the measuredshift is �=2). Some of the sharp spikes are multiphoton reso-nances, not numerical artifacts.


velocity of the BF is shifted as shown by the dashed lineof Fig. 1 so the force is strong between v � 0 and vb �=k (raised by 4Frad for clarity).

Atoms subject to the force plotted in Fig. 1 undergo avelocity change as large as vb � =k under the influenceof the approximately constant force Fb � �hk=�. Thusthe relevant time of �b � vb=a � �=k��M=Fb� ��=2!r is the time for the complete velocity change, nota characteristic 1=e time (here !r � �hk2=2M is the recoilfrequency and M is the atomic mass). Note that �b isindependent of : as the velocity range scales up so doesthe force, leaving the characteristic time fixed. For thetransition we use, !r � 2�� 42:5 kHz so �b � 6 �scorresponding to a flight distance of �6 mm for themean atomic velocity in our beam. For collimation, ourlaser beams were Gaussian with waists of�6 mm so their1=e2 intensity width is 12 mm. The useful interactionregions, defined as a 35% decrease of the Rabi frequency,are therefore each about 8 mm long to assure that the BFhas ample time to act on most of the atoms.

To demonstrate bichromatic slowing of He*, we usedAOM’s to produce the requisite laser frequencies in thelaboratory frame (see Fig. 1). We used � 300 MHz, andwe chose to center the BF at vc � 765 m=s to put the peakof slow atoms well outside the unperturbed velocity dis-tribution (see Fig. 8 of Ref. [11]).

The beams from two free-running diode lasers set tothe frequencies !a � � kvc were combined on a polar-izing beam splitter and sent through an AOM operating at50% efficiency to upshift both beams by 2. Thus wemade four frequencies, and these were combined in theproper way on additional polarizing beam splitter cubes.In this way we made two beams containing the frequency

213004-2

pair!‘�kvc� and!‘ � kvc � where!‘ is the laserfrequency.When these beams counterpropagate and!‘ �!a, an atom moving at velocity vc sees the two frequen-cies of each beam Doppler shifted to !a � which areprecisely the frequencies needed to produce the BF.

These beams were injected into independent 1 W fiberamplifiers to produce � the 320 mW needed for atomicbeam slowing with the BF. Mirrors located inside thevacuum system were used to direct the counterpropagat-ing bichromatic laser beams at approximately 1� withrespect to the atomic beam. At this angle the force wasapplied mostly longitudinally with a small transversecomponent. The atomic beam was pulsed using a200 �m slit mounted on a tuning-fork chopper placedin the atomic beam line. We used time-of-flight measure-ments to determine the effect of the bichromatic slowingas shown in Fig. 8 of Ref. [11]. Atoms were slowed by�325 m=s and the distribution was narrowed by�� 3) a temperature reduction by �9.

While short distance deceleration is applicable for He*trapping experiments, acceleration of the He* beam isalso desirable, for example, for atom lithography. Thedirection of the BF is easily reversed by reversing therelative spatial phase of the standing waves. We alsoobserved velocity distributions showing bichromatic ac-celeration. The ability to switch the sign of the BF bycontrolling the relative phase of the counterpropagatingbichromatic fields is a signature effect of the BF.

Active collimation of an atomic beam by transverseapplication of the BF requires some careful consideration.In contrast to the usual optical molasses, Fig. 1 shows thatthe sign of the BF does not reverse with velocity. One wayto achieve collimation with this circumstance is by de-flecting all the atoms to a chosen transverse velocity. Thisscheme has the drawback of geometric dispersion result-ing from the longitudinal velocity distribution of ourbeam (dashed curve of Fig. 8 of Ref. [11]).

Instead, we collimated our atomic beam to the forwarddirection (transverse velocity � 0). Such 1D collimationrequires two interaction regions acting on atoms withpositive or negative initial velocities, respectively. Thiswas done by shifting the center velocities of the forceprofiles by kv � �=2k as shown in Fig. 2. The force wasreversed in the two interaction regions by shifting therelative spatial phase of the standing waves.

Producing the four frequencies needed for collimationwas accomplished quite elegantly using light from a sin-gle diode laser that was locked to !‘ � !a � =2 usingan AOM. The light double passed a different AOM oper-ating at 50% efficiency and at frequency as described inRefs. [6,7]. The resulting four frequencies are !‘ ��3=2� and !‘��1=2� traveling one way and !‘ ��1=2� and !‘ � �3=2� traveling the opposite way.Thus they satisfy the conditions !‘ � in a frame mov-ing at v � =2k. The beams produced this way wereinjected into two fiber amplifiers [17] to produce severalhundred mW of the desired bichromatic light. The output

213004-2

FIG. 3. Three-dimensional visualization of the atomic fluxdensity distribution after 2D BF collimation and optical mo-lasses (see below), measured 22 cm downstream from theatomic beam source. An image with the lasers blocked hasbeen subtracted to remove background contributions. The25 mm diam MCP subtends � 115 mrad and its circularedge corresponds to transverse velocities of � 50 m=s. Thedetuning for BF was � 37 � 2�� 60 MHz and for molas-ses was �10 MHz. The flat surrounding marks the zero-level,negative values indicate atoms have been removed, positivevalues correspond to accumulation of atoms. Quantitative mea-surements are discussed in the text.

velocity (γ/k)

Force (Frad)

4

0

2

6

8

10

12

-12

-10

-8

-6

-4

-2 0 40-20 -10 10 20 30-30

FIG. 2. The bichromatic force vs velocity calculated from theoptical Bloch equations as in Fig. 1 but for the case of two setsof counterpropagating beams having spatial phase and fre-quency shifts of opposite signs. The BF affects atoms ofopposite velocities, and acts in reverse directions. It emulatesoptical molasses but with a very much larger capture range andforce magnitude.


beams were shaped to have elliptical Gaussian profiles,6:3� 1:8 mm 1=e2 radius, with 250 mW cw power. Their�=2 phase shifts were set by appropriate optical delays.

In this way the BF was contrived to emulate opticalmolasses but with a very much larger capture range andforce magnitude. However, it is not a damping force forvelocities of interest, and so its behavior is quite differentfrom that of optical molasses. As discussed above, aninteraction time �b is all that is required to bring aboutthe full velocity change =k. Our one-dimensional ex-periments clearly show atoms are collected from eitherpositive, negative, or both transverse velocity distribu-tions and compressed into the forward direction.

We have also extended these experiments to two di-mensions.We added two more interaction regions orientedto produce collimation perpendicular to that of the firsttwo regions. (The interaction regions must not overlap inorder to keep a fixed phase relation of the counterpropa-gating laser beams.) The atoms encounter these regionssequentially. Each one is only 10 mm long, and so the totallength of the collimation region is about 50 mm.

For imaging the He* beam we used a combination of amicrochannel plate (MCP) and a phosphor screen. Bothatoms and uv light from the discharge eject electronsfrom the front of the MCP with high efficiency (He*atoms carry high internal energy �20 eV), and these elec-trons were amplified and accelerated towards the phos-phor screen. The screen was viewed by a charge-coupleddevice camera whose images are captured by computer.Figure 3 shows a processed view of the MCP-phosphorscreen detector under these conditions. The vertical axisof this contour plot corresponds to the atomic flux densityas a function of position in the x-y detection plane.

For this plot a signal recorded with lasers blocked wassubtracted to remove any background contributions, e.g.,uv light. The full capture range of the BF collimationexceeds 115 mrad as is clearly visible from the negativevalues near the edge. From these measurements we con-

213004-3

clude that our capture range spans the entire 90 mradFWHM divergence of our source output beam, just asexpected for vb � 37 =k � 65 m=s.

We further analyze our atomic beam by transversescanning with stainless steel detectors. These minimizethe effects of the nonlinearities inherent in the MCP/phosphor screen detector. An upstream plate has a 1 mmdiam hole through which He* atoms can pass and releasean electron from the second plate 2 mm downstream with�70% efficiency [18]. We measure the resulting currentfrom the downstream plate vs the detector position. Thesedetectors are mounted on motion feedthroughs so theycan be scanned in one direction across the beam. One islocated 16 cm downstream from the He* source, and theother two (that can scan orthogonally) are 56 cm from thesource. Comparison of our measurements with these threedetectors are completely consistent with each other whichlends confidence to our interpretation of the data.

With the closer detector, the FWHM of the sourceoutput is 15 mm (�90 mrad), suggesting that our sourceis somewhat supersonic. This is corroborated by the ve-locity distribution of Fig. 8 in Ref. [11] that shows a Machnumber of �3. The measured profile with the seconddetector drops to about half of its maximum at its excur-sion extrema of �25 mm, as expected for 90 mrad.

With the BF laser beams, our measurements show thatthe atomic beam spot size is reduced to 3 and 10 mmFWHM at the near and far detectors, respectively. Thedivergence of the BF collimated beam is thus �18 mradand the full capture angle is �180 mrad (twice theFWHM of the beam itself). For the average longitudi-nal velocity of �950 m=s, this corresponds to resid-ual transverse velocities of vt � �9 m=s, a value com-parable to a rough estimate. We choose a damping con-

213004-3

TABLE I. A summary of the various measured quantities.

QuantitySize

fwhm IntensityDivergence

fwhm BrightnessUnits mm �s mm2��1 mrad �s sr m2��1

Raw beam 50 0:3� 109 90 3:7� 1016

BF 10 1:8� 109 18 7:6� 1018

Molasses 4.2 9� 109 7.5 1:2� 1020


stant based on the central region of Fig. 2 to be �b ��2 �hk=��=�12 =k� � �hk2=�6� � and a dipole force dif-fusion constant estimated from Eq. 4.6 of Ref. [19] to beDb � � �hk�2=�2 � (four beams ) !1 � 4). ThenkBTb � Db=�b � 10 �h or �800� the Doppler tempera-ture for � 40 ) vt � �7:6 m=s.

We have also done preliminary experiments with atwo-dimensional, ordinary Doppler molasses stagedownstream of the BF region using intensity Itotal�32 mW=cm2 �Isat � 0:16 mW=cm2� and detuning�10 MHz��6 to achieve capture over this 8–10 m=stransverse velocity spread. This is what is shown in Fig. 3with quantitative results summarized in Table I.

The stainless steel detectors have a known efficiency ofabout 70% [18], and this enables an absolute flux calibra-tion. With the source current at �12 mA, there are 5:6�1014 atoms=s sr in a 10 mm diam spot, corresponding to1:4� 1011 atoms=s at the far detector with the BF only.The various quantities we have measured are summarizedin Table I. It is clear that the collimation using the BFcaptures only � 25% of the atoms, and that the molassescaptures all of these. There are several effects that couldcontribute to this inefficiency discussed below.

The three sublevels of He* exhibit quite different Rabifrequencies for excitation to the 23P2 state with a givenintensity of #�-polarized light. Our intensity is chosen tooptimize the BF for the MJ � 1$ 2 transition, andessentially vanishes for atoms with MJ � �1 and 0 (thez axis is defined by the light polarization). The#�-polarized light optically pumps such atoms to MJ ��1, but with our laser parameters this is sufficiently slowso that atoms starting with MJ � �1 experience no BF,and only about half of those with MJ � 0 are pumped intime. Thus many atoms do not experience the full BF.

Other reasons for this loss arise because about 5% ofthe atoms have such slow longitudinal velocities that theydiverge outside of the beam spot, and another 15% are sofast that they do not have the full �b to be completelyredirected, and there is a significant loss from residuallaser beam imbalance and misalignment.

Recovering these losses and other further improve-ments could produce a flux density high enough to exposea resist for atomic nanolithography in less than 1 min[12,20,21]. Such a short exposure time will enable a newrealm of nanofabrication wherein changes in the opticalmask or target position can be made in real time to pro-duce much more complex structures than have been pre-viously attained.

213004-4

In summary, we have demonstrated the efficacy of theBF to slow He* atoms in a short distance and to collimatethem with an unprecedented capture angle of �180 mradFWHM [22] in only 50 mm interaction length. The colli-mation collects atoms into a divergence angle of 1=10 ofthe capture range and the optical molasses collimatesthem by another factor of 2.5. Further improvementshave the potential to make a beam having >2�1011atoms=mm2 s, which could revolutionize atomicnanofabrication because of its potential for subminuteexposure times.

This work was supported by ONR and NSF.

[1] R. Grimm, Y. Ovchinnikov, A. Sidorov, and V. Letokhov,Phys. Rev. Lett. 65, 1415 (1990).

[2] H. Metcalf and P. van der Straten, Laser Cooling andTrapping (Springer, New York, 1999).

[3] V. Voitsekhovich, M. Danileiko, A. Negriiko, V.Romanenko, and L. Yatsenko, Zh. Tekh. Fiz. 58, 1174(1988) [Sov. Phys. Tech. Phys. 33, 690 (1988)].

[4] V. Voitsekhovich, M. Danileiko, A. Negriiko, V.Romanenko, and L. Yatsenko, Pis’ma Zh. Eksp. Teor.Fiz. 49, 138 (1989) [JETP Lett. 49, 161 (1989)].

[5] J. Soding, R. Grimm, Y. Ovchinnikov, P. Bouyer, andC. Salomon, Phys. Rev. Lett. 78, 1420 (1997).

[6] M. Williams, F. Chi, M. Cashen, and H. Metcalf, Phys.Rev. A 60, 1763(R) (1999).

[7] M. Williams, F. Chi, M. Cashen, and H. Metcalf, Phys.Rev. A 61, 023408 (2000).

[8] M. Cashen and H. Metcalf, Phys. Rev. A 63, 025406(2001).

[9] M. Cashen, O. Rivoire, V. Romanenko, L. Yatsenko, andH. Metcalf, Phys. Rev. A 64, 063411 (2001).

[10] M. Cashen, O. Rivoire, L. Yatsenko, and H. Metcalf,J. Opt. B 4, 75 (2002).

[11] M. Cashen and H. Metcalf, J. Opt. Soc. Am. B 20, 915(2003).

[12] D. Meschede and H. Metcalf, J. Phys. D 36, R17 (2003).[13] L. Yatsenko and H. Metcalf, Phys. Rev. A (to be

published).[14] J. Kawanaka, M. Hagiuda, K. Shimizu, F. Shimizu, and

H. Takuma, Appl. Phys. B 56, 21 (1993).[15] H. Mastwijk, Ph.D. thesis, Utrecht University, 1997.[16] H. Mastwijk, M. van Rijnbach, J. Thomsen, P. van der

Straten, and A. Niehaus, Eur. Phys. J. D 4, 131 (1998).[17] Model # KPS-BT2-YFA-1083-40-COL from Keopsys

Corp., Lannion, France.[18] F. B. Dunning, R. D. Rundel, and R. F. Stebbings, Rev.

Sci. Instrum. 46, 697 (1975).[19] J. Dalibard and C. Cohen-Tannoudji, J. Opt. Soc. Am. B

2, 1707 (1985).[20] S. Petra, L. Feenstra,W. Hogervorst, and W.Vassen, Appl.

Phys. B 78, 133 (2004).[21] S. Petra, K. A. H. van Leeuwen, L. Feenstra,

W. Hogervorst, and W. Vassen, Appl. Phys. B 79, 279(2004).

[22] W. Rooijakkers, W. Hogervorst, and W. Vassen, Opt.Commun. 123, 321 (1996).

213004-4

bichromatic slowing and collimation to make an intense helium beam

Documents