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PHYSICAL REVIEW A, VOLUME 62, 030701~R!

Light-induced ultracold spin-exchange collisions

Renee C. Nesnidal and Thad G. WalkerDepartment of Physics, University of Wisconsin–Madison, Madison, Wisconsin 53706

~Received 5 October 1999; published 18 August 2000!

We study collisional loss rates due to spin-exchange collisions in very-low-intensity87Rb magneto-opticaltraps. The loss rate exhibits an unpredicted intensity dependence for low intensities, accounting for a largedisparity between loss rates observed in light-force traps and magnetically confined Bose condensates. Possiblecollision mechanisms considered include light-altered collision phase shifts, flux enhancement, and excited-state hyperfine changing collisions.

PACS number~s!: 34.50.Rk, 32.80.Pj, 34.80.Nz

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The development of magneto-optical trapping techniqhas provided a unique environment for observing very-loenergy atomic collisions. The ability to reach submillikelvtemperatures means that collisions occur on time scalelong as microseconds and that long-range potentials plaimportant role in the collision process. Additionally, with thdevelopment of Bose-Einstein condensation techniquebetter understanding of these low-energy collisions is imptant. In particular, recent work has shown that it is possito dramatically manipulate low-energy scattering proceswith judicious application of external fields@1#.

Collisional losses from light-force traps such as tmagneto-optical trap~MOT! place important constraints otrap operation, in particular limiting the number of trappatoms. For common vapor cell alkali-metal MOTs, whiuse light tuned within a few linewidths of an atomic resnance, excited-state collisions dominate trap loss whentrap laser intensity exceeds a few mW/cm2. Extensive stud-ies of excited-state collisions have produced a fairly deand quantitative understanding of trap loss for light tunsubstantially off resonance, but the near resonant casimportant to the MOT remains poorly understood@2,3#. Forlow-intensity MOTs, studies@4–6# of Cs and Rb reportedextremely large loss-rate coefficients~in excess of 10211

cm3/s) below an abrupt intensity threshold at 1–2 mW/cm2.The threshold behavior is naturally explained as a turn-onthe ground-state spin-exchange collision channel:

~F52!1~F52!→H ~F51!1~F51!

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for 87Rb. Loss from this collision channel turns on when ttrap depth becomes comparable to the ground-state hypesplitting. For such a purely ground-state process, the extation is that once the trap depth becomes smaller thanhyperfine splitting the loss rate should be independenintensity.

Inelastic spin-exchange collisions also constrain the pformance of magnetic traps and the production of BoEinstein condensates~BECs! in mixed spin states, especiallif the rate coefficients are comparable to those observeMOTs. Thus one of the biggest recent surprises in the fiof ultracold collisions was the discovery by the JILA BE

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group of a87Rb Bose condensate consisting of atoms in tdifferent spin states@7#. The double condensate was formeusing evaporative cooling ofuF,mF&5u1,21& atoms, andsympathetic cooling ofu2,2& atoms via elastic collisions withthe u1,21& atoms. The sympathetic cooling worked withodisastrous spin-exchange induced trap loss only becausspin-exchange rate coefficient was not the theoreticallypected 10211 cm3/s consistent with MOT data@8#, but nearlythree orders of magnitude smaller—2.2(9)310214 cm3/s.The surprisingly low spin exchange rate was quickly eplained theoretically as a serendipitous matching of theglet and triplet scattering lengths for87Rb @9#. Under thoseconditions the phase shifts associated with the singlettriplet potentials are nearly identical. The cross sectionspin exchange is proportional to sin2(fs2ft), and thus thecoincidence in scattering lengths results in a destructiveterference, suppressing the spin-exchange rate. This sexchange suppression appears to be unique to87Rb.

In this paper we demonstrate that the MOT spin-excharates are intensity dependent, indicating that light playsessential role in spin-exchange collisions. This result agillustrates that low-energy-scattering processes are sensto externally applied fields@1#.

It is not entirely surprising that the rate measured forBEC is smaller than the rate measured for the traditioMOT. An obvious difference between the two experimentsthe temperature. The temperature of the BEC was below500-nK transition temperature, while the MOT temperatuare typically on the order of 100mK. Using the best poten-tials available, Williams@10# calculated the expected temperature dependence of spin-exchange collisions. At Mtemperatures, the maximum predicted rate is only on theder of 6310213 cm3/s, a factor of 30 lower than the measured MOT rate. Further recent refinements increase thisdiction by about a factor of 2 to 5, still substantially belothe MOT measurements@12#. Of course, the second principadifference between the MOT and BEC experiments ispresence of the near-resonant trap laser used to producMOT. It is the trap laser effects on the spin-exchange rathat we report in this paper.

Our experiments were performed in a low-pressuvapor-loaded87Rb MOT. The rubidium pressure was keptthe low 10211 Torr range, so that losses due to collisiowith hot rubidium atoms were small compared to the ult

©2000 The American Physical Society01-1

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RENEE C. NESNIDAL AND THAD G. WALKER PHYSICAL REVIEW A 62 030701~R!

cold collisions. The vacuum chamber was carefully prepaprior to assembly in order to allow for base pressures asas 10211 Torr, with resulting trap lifetimes as long as 1000

The basic experiment was performed by first loadingtrap from the background at high intensity, using bothtrap laser and an additional high-power laser. After loadia shutter blocked the additional laser, and the trap lasetensity was switched, using a liquid-crystal retarder andlarizer to an intensity between 0.25 and 5 mW/cm2. ~Thetrap laser beams had a 1/e2 diameter of 1.0 cm.! The trapfluorescence was recorded as a function of time whiletrap was allowed to decay for 10–15 min. A fluorescenimage of the trapped atoms was taken with a liqunitrogen–cooled charge-coupled-device camera to determthe trap density. The density as a function of time was thfit to the analytic solution of the rate equation for trap los

dN

dt5L2GN2bE n2~r !d3r , ~2!

wheren(r ) is the position-dependent atom density,L is theloading rate,G is the loss rate due to collisions with hobackground gas, andb is the loss rate due to cold collision

The measured ultracold collision loss rates as a funcof intensity for a laser detuning of one linewidth and twdifferent magnetic field gradients are shown in Fig. 1. Staing from high intensity we find the usual linear dependenon intensity~not shown! for intensities above 4 mW/cm2, inagreement with previous experiments. As the intensity iscreased further, Fig. 1 shows the previously reported shincrease in trap loss rate@5#. We then note, however, that avery low intensities the trap loss rate does not level offexpected, but instead decreases roughly linearly withcreasing intensity. As the temperature of the atoms doesvary strongly at the intensities and detunings of our MO@13#, we cannot attribute the observations to a temperadependence.

The simplest interpretation of Fig. 1 is that the collisiomechanism is intensity dependent, releasing a fixed quaof energy per collision. At low intensity the trap depthsmaller than the energy release, causing the observed in

FIG. 1. Loss rates due to ultracold collisions as a functiontotal trap laser intensity with a detuning ofD521G. The circlesand squares indicate data taken with a magnetic-field gradient oand 18 G/cm, respectively. The solid lines have been includeguide the eye.

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sity dependence of the rate coefficient to reflect the inheintensity dependence of the collision process. When thedepth becomes comparable to the energy release, thecoefficient decreases, as the atoms no longer leave the

Figure 1 shows that the slope of the data at low intensis the same for both magnetic-field gradients. As the intsity is increased, the data taken with the lower gradient tuover, while the higher gradient data continue to increaseearly. Thus the peak rate coefficient is larger for the higgradient data. The trap depth is weaker at a given intenfor the higher-magnetic-field gradient that allows atomsescape the trap at higher intensities, increasing the peakshifting it to higher intensity. This interpretation is consistewith the predictions of trap depth models@6,11# for low-intensity traps with high field gradients. The intensity depedence for laser detunings ofD521.5G and22G is shownin Fig. 2. As in the previous data, there is a decrease inloss rate at lower intensities. Clearly the collision proceresponsible for the low-intensity data shown in Figs. 1 anis intensity dependent and releases a fixed amount of eneA recent experiment has confirmed that spin-exchange rdecrease when near-resonant MOT light is removed@12#.

An important figure of merit for these measurementsthe quantity 2bno /G that compares the loss from ultracocollisions to background loss. To reliably distinguish the twloss mechanisms, it is important for this ratio to be largthan 1. In theD521G measurements at 10 G/cm, the tracould be operated at lower intensities than the data indichowever, the figure of merit became prohibitively sm(;1) at the lowest intensities, due to a rapid decreasedensity. For the larger detuning data, the initial density wquite large. Unfortunately the density became large enothat radiation trapping effects were observed. To eliminthe radiation trapping, many fewer atoms were loaded ithe trap. The reduced number of atoms caused a reductiothe trap fluorescence signal, which degraded our ovesignal-to-noise ratio. In all cases, however, there is clearlyintensity dependence of the trap loss rates at low intensNo intensity dependence of the background rateG was ob-served. At the lowest intensities, where the volume ofatom cloud is greatest, the limited depth of field of our ca

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FIG. 2. Loss rates as a function of total trap laser intensitylarger laser detunings. The1’s and circles indicate data taken aD521.5G and22G, respectively.

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LIGHT-INDUCED ULTRACOLD SPIN-EXCHANGE COLLISIONS PHYSICAL REVIEW A62 030701~R!

era system produced a tendency to blur our trap images.effect could produce systematically low measured trap dsities, and hence overestimates ofb. We took care to mini-mize this effect, but we note that any additional correctwould tend to increase the slope ofb at low intensity, furtheraccentuating the strong observed intensity dependence.transients taken near the peak and below the peak at nidentical trap densities, shown in Fig. 3, show clearly tsubstantial reduction in the trap-loss rate at very low laintensity.

The existence of a rapid onset strongly implies thatcollision process releases a fixed quantity of energy. Tfact makes it almost certain that the collision process ihyperfine changing or spin-exchange mechanism.

The most straightforward explanation of the data is tthe spin-exchange occurs in an excited-state hyperfichanging process, namely,

5S~F52!15P3/2→5S~F51!15P3/2,

with the release of 6.8/2 GHz of energy to each of the toutgoing atoms. This process is somewhat analogouexcited-state fine-structure changing collisions that occuhigher trapping intensities@2#. Such a process would begiwith excitation of the colliding atoms at long range;1000 Åto radiatively stable attractive excited-state potentials. Tatoms are accelerated to the region around 150 Å wherehyperfine interaction is decoupled by the dipole-dipole intaction. The decoupling would then result in transfer of tatoms to a potential curve that dissociates to the 5S(F51)15P3/2 asymptote.

Assuming excited-state hyperfine changing collisionsresponsible for our observations, it is difficult to understawhy the rate coefficient is;103 larger than for the high-intensity excited-state loss mechanism. For the high-intenloss mechanism, strong arguments@14# favor radiative es-cape as its source. In this case radiative escape beginsexcitation at long range to long-lifetimeS1P3/2 states—analogous to the radiatively stable 2u state when hyperfineinteractions are ignored—followed by transfer to strong

FIG. 3. Loss transients taken at intensities near the peak~1.1mW/cm2) and well below the peak~0.2 mW/cm2). The moregradual decay at 0.2 mW/cm2 clearly shows that the cold collisionloss rate at the same density is greatly reduced as compared t1.1-mW/cm2 rate.

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radiating states in the hyperfine decoupling region. Becathe transfer from radiatively stable to unstable states occin the hyperfine decoupling region, the collision dynamicsradiative escape and excited-state hyperfine changing csions are nearly identical. The two loss processes differ oin the states to which the atoms are transferred. In the casradiative escape the atoms are transferred from a radiatistable state to an unstable state. On the other hand, excstate hyperfine changing collisions involve transfer to stacorrelated with a specific ground-state hyperfine asymptIf anything, this argument favors a smaller rate coefficiefor excited-state hyperfine changing collisions as compato radiative escape collisions.

Given that the excited-state hyperfine changing procesan unlikely explanation for the data, we turn to ground-stspin-exchange collisions that involve light. The key to texplanations for the low spin-exchange rates for magncally trapped87Rb was the near identity of the singlet antriplet scattering phase shifts. Thus a possible explanationthe observed light intensity dependence is that the preseof the near-resonant light upsets the delicate balance betwthe singlet and triplet phase shifts that suppressed theexchange in the double BEC experiment. The presence otrap laser couples the 1/R3 excited potentials to the groundstate 1/R6 potential. This coupling may alter the singletriplet phase balance in at least two ways. First, the excitstate coupling most certainly occurs at long range but malso be important at small interatomic separations whground-state spin exchange occurs. We note, for examthat the Movre-Pichler fine-structure potentials@15# for Rbpredict that the trap laser can resonantly excite the repul0g

1 P1/2 potential at roughly 11–12 Å, precisely the regionwhich ground-state spin exchange occurs. Whethernearly diabatic crossing or coupling to other states canrupt the phase balance is an open question. The excited-couplings can also affect spin exchange at long range. Ein the absence of significant ground-state singlet/triplet spting, we note that at long range different hyperfine levels wcouple with different strengths to the various singlet and trlet excited-state potentials. This difference in coupling pduces an effective spin-exchange potential at long rangemight be sufficient to disrupt the singlet-triplet phase bance.

Another possible explanation is flux enhancement duethe presence of the trap laser, which has been previoobserved for excited-state collisions@16#. In this case, a col-liding pair of atoms absorbs a photon and is acceleratedthe excited-state potential. The atoms therefore return toground state via spontaneous emission with increased veity. The effective collision energy is therefore increased, ain particular additional partial waves not normally preseunder MOT conditions can then overcome the centrifubarrier and participate in spin exchange. In particular,estimate that thed-wave contribution to the collision procesmay be significantly enhanced.

Spin-exchange collisions of S1/2 atoms are important in awide variety of physical phenomena, a partial list being t21-cm line in radioastronomy@17#, masers @18#, spin-polarized H and D targets@19#, spin-exchange optical pump

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RENEE C. NESNIDAL AND THAD G. WALKER PHYSICAL REVIEW A 62 030701~R!

ing @20,21#, atomic clocks @22#, BECs @23#, and spin-polarized hydrogen@24#. The spin-exchange collisions thaoccur in low-intensity MOTs are unique in that they are sesitive to the energy transfer properties of spin exchange.

In conclusion, we find a pronounced intensity dependeof ultracold spin-exchange collisions in low-intensimagneto-optical traps. It is clear that weak resonant lifields qualitatively and quantitatively change the behavior

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low-temperature spin-exchange collisions. As the expmental signatures of the above possible explanations arsimilar, further theoretical work is needed to distinguithem.

Support for this work came from the National ScienFoundation and the Packard Foundation. We appreciate fful discussions with S. Gensemer, P. Gould, P. Julienne,C. Williams.

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