Strong-field coherent backscattering of light inultracold atomic 85Rb

S. BALIKy, P. KULATUNGAy, C. I. SUKENIKy, M. D. HAVEY*y,D. V. KUPRIYANOVz and I. M. SOKOLOVz

yDepartment of Physics, Old Dominion University, Norfolk, VA 23529, USAzDepartment of Theoretical Physics, State Polytechnic University,

195251, St. Petersburg, Russia

(Received 15 February 2005; in final form 29 March 2005)

We report experimental observations of polarization-dependent coherenceloss occurring in strong-field multiple scattering of light in ultracold atomic85Rb. A measure of coherence in multiple light scattering is the degree of contrastof the coherent backscattering enhancement from the vapour. For resonancesaturation parameters up to 9, we see light-polarization-dependent modificationof the backscattering enhancement, suggesting that inelastic atomic lightscattering and dynamic atomic magnetization may play important roles in themultiple scattering process for 85Rb.

1. Introduction

Wave propagation in disordered media has been for many years a subject ofconsiderable and broad scientific interest [1–3]. Experimental and theoretical studiesof ultrasonic waves, electromagnetic radiation, and wave disturbances in thesolid earth, to name a few, have provided deep insights into the physics of thiscomplex subject. Of particular interest has been how wave interference might lead tobreakdown of a classical description of energy transport in a medium. For a stronglyscattering medium of su!cient density that recurrent scattering occurs, interferencecan lead to reduction of, for example, the classical di"usion coe!cient. Modificationof transport properties is a precursor to wave localization, where excitations inthe medium are localized on a characteristic length scale; Anderson localizationof electrons by disorder is a canonical example [4].

Ultracold atomic gases form particularly interesting systems in which tostudy multiple coherent wave scattering. In this case the disorder can be in thespatial distribution of atoms. Among the important atomic characteristics are verynarrow and strong elastic light scattering resonances, well characterized interactionswith external static and electrodynamic fields and, in many cases, quite well knownpairwise atomic interactions. The modification of atomic light scattering in thepresence of stronger electromagnetic fields is also well understood, at least in the case

*Corresponding author. Email: mhavey@physics.odu.edu

Journal of Modern OpticsVol. 52, No. 16, 10 November 2005, 2269–2278

Journal of Modern OpticsISSN 0950–0340 print/ISSN 1362–3044 online # 2005 Taylor & Francis

http://www.tandf.co.uk/journalsDOI: 10.1080/09500340500275934

of scattering from isolated atoms in a single scattering regime [5–7]. However, thesituation where there is multiple scattering of stronger fields is less well understood,and is currently the subject of considerable theoretical and experimental study[8–11]. A major motivation for the research is the association with e"orts to obtainstrong localization of light in an ultracold atomic gas [12–14]. In strong localization,combined electromagnetic-atomic excitations would exist on a length scale on theorder of a light wavelength. Under these conditions, it has been suggested [8–11]that strong field e"ects can become quite important.

To date, studies of multiple light scattering in ultracold atomic gases [15–27]have been done in the so-called weak localization regime, where kl ! 1. Here k isthe wavevector magnitude in the medium, and l is the scattering mean free path.Under this condition scattering may be considered as a sequence of individualscattering and propagation processes. In addition, recurrent scattering, in whicha wave scatters more than once from a single scattering centre, is rare. The coherenceproperties of multiply scattered light are then observable through the so-calledcoherent backscattering (CBS) e"ect [28–30]. In CBS, light scattered in thenearly backward direction from a spatially disordered sample shows an interfero-metric intensity enhancement of up to a factor of two in the light polarizationchannel where single scattering can be suppressed. When CBS is absent, theenhancement so defined is unity. Dephasing due to motion of the scatterers, forexample, can reduce the size of the enhancement. In CBS experiments with ultracoldatoms, the enhancement is also sensitively reduced by the degeneracy of the atomicground levels and inelastic Raman scattering processes. Finally, for atomic samplesthe angular width of the CBS interference fringe is on the order of a milliradian,and is determined by the sample size, optical depth, and inhomogeneous atomdistribution in the sample.

Recent experiments by Chaneliere et al. [8], on the resonance transition in atomicSr have shown a significant reduction in the coherent backscattering enhancementwith increasing excitation strength. Meanwhile, theoretical and model studieshave shown similar qualitative e"ects [9–11] but have not been quantitativelycompared with experiment. In the present paper we report on our observations ofmodification of the coherent backscattering enhancement in ultracold samples of85Rb as the strength of the backscattering light source is varied over a range of about100. Distinctly di"erent modification occurs in two polarization channels under aparticular experimental protocol. In the following sections we first describe thepreparation and characterization of the atomic sample. This is followed by a generaldescription of our experimental protocols used in measurement of atomic coherentbackscattering. Then we present our results and a qualitative discussion of them.

2. Overview of the physical system

2.1 Preparation and description of the ultracold atomic sample

Preparation of the ultracold atomic 85Rb sample used in the measurements has beendescribed in detail elsewhere [21]. Briefly, the samples are formed in a vapour-loaded

2270 S. Balik et al.

magneto-optical trap (MOT) which is operated in a standard six-beam configura-tion. The trapping laser is detuned by "2:7! from resonance, where ! # 5:9 MHz, isthe natural linewidth of the F $ 3 ! F 0$ 4 hyperfine transition. The MOT masterdiode laser (Hitachi HG7851G) is locked to a crossover peak produced in a Doppler-free saturated absorption spectrometer. The master laser is used to injection-locka Sanyo DL7140-201 slave laser, which serves as the main MOT laser. Hyperfinerepumping is achieved by microwave modulation of the slave laser to produce asideband at the wavelength corresponding to the F $ 2 ! F 0 $ 3 hyperfine transi-tion. Optical switching of the MOT is achieved by an acousto-optic modulator(AOM). A single mode fibre optic patchcord is used to improve the laser mode, andto enhance attenuation of the MOT lasers in the ‘o"’ state (#65 dB attenuation ofthe trapping laser light). The average MOT laser power is #19mW.

To characterize the atomic sample, we use absorption and fluorescence imaging,and find that the MOT is not completely spherical [21, 22], but rather is somewhat‘cigar-shaped’ having 1=e2 Gaussian radii of 1.1mm and 1.38m. The radius isdefined according to the density distribution n%r& $ n0 exp%"r2=2r20&, n0 being thepeak density. The peak optical depth (through the centre of the MOT) of about 6,where the optical depth b is defined as resulting in an attenuation of the incidentintensity by a factor e"b. The parameter b is found by direct measurement of thespectral shape of the transmitted CBS light intensity through the centre of the MOT.Probing is made when the MOT lasers are o", for they result in a significantexcited state fraction, decreasing the measured optical depth. For a Gaussian atomdistribution, the optical depth is b $

!!!!!!2"

p#0n0r0, where #0 is the cross-section for

light scattering [31]. With the values given above and an average Gaussian radiusr0 $ 1:2 mm, we find that the MOT contains about 4:3' 108 atoms and has a peakdensity n0 $ 1:6' 1010 atoms-cm"3.

As described in detail elsewhere, the MOT chamber is designed to minimizestray light scattering; because we are observing light which is backscattered fromour sample, it is critical that all other backscattered reflections, including those fromthe viewports, are suppressed. In order to minimize backscattered stray light,windows are wedged and V-type antireflection (AR) coated at 780 nm on theprobe-laser ports. The AR coating results in less than 0.25% reflectivity at780 nm. The entrance port window is also mounted on a ultrahigh vacuum bellows,allowing redirection of unwanted reflections away from the detector.

2.2 Measurement of atomic coherent backscattering

A schematic diagram of the experimental coherent backscattering arrangement isshown in figure 1. There the coherent backscattering light source used in theexperiment is provided by a master–slave arrangement which consists of a lowerpower stabilized external cavity diode laser frequency and a higher power slave laserwhich is injection-locked to the master. The master laser is locked near theF $ 3 ! F 0 $ 4 hyperfine component of the 5s2S1=2 ! 5p2P3=2 transition. Thelaser may be tuned several hundred MHz from nearly any hyperfine resonancein 85Rb by an o"set locking technique using an acousto-optic modulator. Detuningfrom resonance is defined by ! $ !L " !0, where !L is the CBS laser frequency

Coherent backscattering of light in ultracold atomic 85Rb 2271

and !0 is the F $ 3 ! F 0 $ 4 resonance frequency. The laser bandwidth is #1MHz.The typical output power of the master laser is #1mW. The slave laser output ispassed through a rotatable neutral density filter wheel, which allows adjustment ofthe power over a range of approximately 1000. The beam is launched into a singlemode polarization preserving fibre and the output expanded and collimated by atelescope to a 1=e2 diameter of about 8mm. The polarization of the resulting beam isselected and the beam passed through a non-polarizing and wedged 50–50 beamsplitter that passes approximately half of the laser power to the atomic sample. Themaximum power incident on the ultracold atomic sample is approximately 2.5mW.For our beam size, this translates to a maximum intensity of about 25mW/cm2,corresponding to a saturation parameter of about 15.

Backscattered light from the atomic sample is directed by the beamsplittertoward the CCD detector. The remainder of the optics train consists of a 45 cmfocal length field lens, a linear polarizer for polarization analysis, a chopper to blockthe intense MOT fluorescence from the CCD when the MOT lasers are on, and aunity magnification pair of lenses to transfer light from the focus at the chopperblades to the CCD. The angular resolution of the apparatus is about 100 mrad.In the present experiment there are two polarization channels studied. In one,linearly polarized light is incident on the atomic sample, and orthogonal linearlypolarized light is detected. In the other, light of definite helicity is incident on theMOT, and light of the same helicity is detected.

In general, the intensity of backscattered light is measured during a time intervalof length T, which is temporally centred in a 5ms dark interval during which theMOT lasers are turned o". Following this, the MOT lasers are turned on for 20ms,in order to reconstitute the cold atom sample. Typically this procedure is repeatedfor 300 s. A subsequent run of 300 s with the MOT absent allows measurement of thebackground due mainly to hot atom fluorescence excited by the CBS laser. Thisbackground is reduced, during the data-taking phase, by scattering of the CBS beamfrom the MOT atoms. This e"ect is accounted for by direct measurements of theMOT attenuation of the CBS beam intensity.

In the experiments, we are concerned with the intensity and polarizationdependence of the CBS enhancement factor, which is the ratio of the peak intensity

Figure 1. Schematic diagram of the coherent backscattering apparatus used in the ultracoldatom experiments. Shown in the figure is the coherent backscattering (CBS) laser, magneto-optic trap (MOT), linear polarizers (LP), beam splitter (BS) and a charge coupled device(CCD) camera.

2272 S. Balik et al.

of the coherent backscattering cone to the incoherent background intensity.The enhancement [3, 12] is formally defined as

$ $ Is ( Il ( IcIs ( Il

: %1&

In the equation, Is, Il, and Ic represent the respective contributions to the totalintensity from single scattering, ladder terms, and crossed terms in the scatteringdiagrams. In the absence of interference in multiple scattering that survives ensembleaveraging, Ic $ 0, and $ $ 1.

The intensity dependence is parametrized by a saturation parameter [31], s $I=Is, where Is is the on-resonance saturation intensity of about 1.6mW/cm2 forthe electronic 2S1=2 !2P3=2 transition in 85Rb. In general, s depends on thesquared Rabi frequency for the transition of interest, and also on the hyperfinetransition of interest and on the polarization of the incident CBS radiation. Theweak field baseline in the present experiment is defined by an on-resonancesaturation parameter, for the CBS beam, of s $ 0.08; an exposure intervalT$ 0.25ms is short enough in this case that mechanical action on the MOTsample is minimized.

3. Results and discussion

In this section we present experimental results associated with the intensitydependence of coherent backscattering of resonance radiation from ultracold atomic85Rb. In general, we measure the intensity in an angular range of about 15mrad; thecoherent backscattering cone is a sharp enhancement in the intensity on the order of1mrad in full angular width. We obtain two important points. In the first, for opticaldepths larger than unity (as is the case here), we expect that the width of the coneis determined primarily by the spatial distribution of atoms in the MOT. This isbecause the width is roughly determined by the spatial separation between thefirst and last scatterers in a scattering chain. As this average separation is onthe order of the MOT size, we expect that the cone will not be very sensitive tothe saturation parameter. In our measurements, which extended up to a saturationparameter of s$ 9, we in fact did not observe a significant variation of the conewidth with laser intensity, in agreement with this expectation. A similar observationwas made by Chaneliere et al. [8] in measurements in atomic Sr. Second, themaximum enhancement for all measurements is considerably less than the value of$ $ 2 expected in the helicity preserving channel for classical scatterers. The reasonfor this, as first pointed out by Labeyrie et al. [17], is the multiplicity of elasticRaman scattering channels available in the magnetically degenerate ground levelsof 85Rb; not all such channels, even though they are elastic, and preserve the phaseof the scattered radiation, lead to indistinguishable paths required for completeinterference. Typically for ultracold 85Rb samples, $# 1.1–1.2. In weak fields, for thelin ? lin and h kh channels studied here, we obtain peak resonant enhancement

Coherent backscattering of light in ultracold atomic 85Rb 2273

factors in very good agreement with those obtained earlier by us [21, 22], and byLabeyrie et al. [16, 17].

First we present experimental measurements of the CBS laser intensity depen-dence of the coherent backscattering enhancement for the lin ? lin polarizationchannel. CCD camera images of the backscattered light intensity are shown infigure 2. In this data, the total spatially integrated intensity is the same in all fourimages. Further, this data is taken with the protocol that the product sT is constant,where s is the average saturation parameter for the CBS beam and T is the exposuretime of the cold atoms to the CBS beam. As discussed earlier, the baseline saturationparameter and exposure time are selected to minimize mechanical action of theCBS laser on the cold atom sample. For our experimental conditions, this corre-sponds to s $ 0.08, and T $ 0.25ms, so the product sT $ 0.02ms. The data, whichspan a saturation parameter range of more than 100, shows a clear reductionin the contrast of the cone with increasing intensity. This behaviour is shownquantitatively in figure 3, where it is seen that the enhancement $ decreases withincreasing saturation parameter over the data range explored. We point out thatthe measurements are made with a constant incident photon flux, with s and Tvarying. In addition, normalized to the same total measurement time, we observea nearly constant integrated total backscattered intensity under these conditionsand over the range of data taken. This is not surprising for the inhomogeneousand optically deep samples we study. Even though the higher intensity radiationpenetrates further into the sample, nearly all the radiation is ultimately scattered,and the multiply scattered radiation has a nearly isotropic angular distribution.

Figure 2. Dependence on the saturation parameter s, in the lin ? lin polarization channel,of CCD images of the intensity field in the nearly backscattering direction. The spatiallyintegrated intensity is the same in each image.

2274 S. Balik et al.

A similar monotonic decrease in $ has been observed in experiments onthe singlet resonance transition in ultracold Sr [8]. However, the percentagedecrease in $ with increasing s was much larger in that case than in the presentexperiments. In that paper it was suggested that the increasingly inelastic nature oflight scattering in stronger fields is most likely responsible for the observed decreases.This qualitatively makes sense, as the inelastic components of di"erent frequenciesand phases should not completely interfere. However, even though quantitativemodel calculations have been done, a full theoretical simulation of the experiments,including those reported here, is needed. As recent theoretical work on this problemhas shown [8–11], this is an ambitious goal. Any such theoretical model mustexplain, for example the reduced relative sensitivity to increasing saturating fieldsin the present experiment, in comparison with the measurements in Sr.

We have also made measurements under similar conditions, but in the h k hpolarization channel. These data are shown in figure 4 where, in sharp contrast to thedata of figure 3 for the lin ? lin channel, the enhancement remains constant, withinthe experimental uncertainty, with increasing saturation parameter in the range0:04 ) s ) 1:0. We note again that the width of the cone does not significantly varyas s is increased. The approximate constancy of $ is a surprising result. We suggestthe following physical model, which needs to be confirmed by detailed calculation.First, it is known that the enhancement in the h kh channel decreases [22] as thenumber of contributing scattering orders accumulates. At the same time, as theintensity of the CBS laser increases, the cross-section for atomic resonance scatteringdecreases as 1=%1( s&, and the number of contributing scattering orders decreasesroughly as 1=%1( s&2. Qualitatively this mechanism alone should cause the enhance-ment to increase with increasing saturation parameter. On the other hand, theratio of inelastically to elastically scattered radiation increases as the saturationparameter s. Assuming that the inelastically scattered light contributes primarily

s0 2 4 6 8 10

!

1.04

1.06

1.08

1.10

1.12

1.14

sT = 0.02 ms

Figure 3. Dependence of the coherent backscattering enhancement $ on the saturationparameter s in the lin ? lin polarization channel.

Coherent backscattering of light in ultracold atomic 85Rb 2275

to increasing the amount of incoherent background, $ should be decreased. This isin fact what is seen in the lin ? lin channel. These two e"ects, taken together, cancompensate one another for a range of saturation parameters, as we observe inexperiment. However, for large enough s the scattering should be dominated by theinelastic component, and we expect that $ will become small, as in the lin ? linchannel. To test this idea, we made measurements of $ at a quite large saturationparameter s $ 9. In this case we obtained a decrease of $ to 1.01(1), in qualitativesupport of the suggested mechanism.

A second possibility suggests that there may be additional physics in thispolarization channel beyond the dephasing due to nonlinear scattering. Previoustheoretical work by our group [26] has shown that if the atomic sample is oriented,then the CBS enhancement is considerably increased. An e"ect of similar origin wasexperimentally observed by Sigwarth et al. [32]. In that experiment, an increase inthe CBS enhancement was found when an external magnetic field separated theZeeman levels by more than the natural width of the resonance transitions. Thena single, nearly closed Zeeman transition could be spectrally selected. As the intensityof the circularly polarized CBS laser is increased, there are now two potentiallyactive mechanisms which may modify the cone enhancement. In one, the increasedintensity leads to an increased fraction of inelastically scattered light, reducingthe cone enhancement. At the same time, an increasing amount of optical pumpingthroughout the sample leads to an increased magnetization of the atoms in thegas, increasing the enhancement. It is possible that these two mechanisms competewith each other over the saturation range explored in figure 4. To distinguishbetween the two possibilities suggested here, or to identify other possiblemechanisms, will require detailed theoretical simulations, similar to what has alreadybeen done for the weak field case, of realistic experimental situations.

s0.0 0.2 0.4 0.6 0.8 1.0 1.2

!

1.00

1.02

1.04

1.06

1.08

1.10

1.12

sT = 0.02 ms

Figure 4. Dependence of the coherent backscattering enhancement $ on the saturationparameter s in the h k h polarization channel.

2276 S. Balik et al.

4. Summary

An investigation of the influence of strong and saturating incident light on coherentbackscattering from an ultracold atomic Rb atom sample has been reported.Experimental data taken over a range of approximately 100 in the on-resonancesaturation parameter shows that the coherent backscattering enhancement ismodified as the strength of the incident field is increased. This behaviour dependssignificantly on the polarization of the incident radiation, the principal e"ect being adecrease with increasing saturation in the lin ? lin channel. In the h k h channel theenhancement is approximately constant (for s<1) with increasing saturation,suggesting that optical pumping of the Zeeman sublevels in the ground level mayplay an important role in the observed quantitative results. Overall, and similar toprevious results reported in ultracold Sr, the experiments indicate that the increasinginfluence of inelastic atomic light scattering, at larger saturation parameters, reducesthe overall measured enhancement factor.

Acknowledgments

Support for this research was provided by the National Science Foundation(NSF-PHY-0355024) and by the North Atlantic Treaty Organization (PST-CLG-978468).

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