We have observed violet photon emission resulting from energy-pooling collisions between ultracold Rb atoms illuminated by two colors of near-resonant infrared laser light. We have used this emission as a probe of doubly excited state ultracold collision dynamics. We have observed the lowest saturation intensity for light-induced ultracold collisions seen to date which we identify as due to depletion of incoming ground state flux. We have also varied the detuning of the lasers which allows us to clearly identify the effect of spontaneous emission and optical shielding

Bali, S.

Hoffman, D.

Sukenik, C. I.

Walker, T.

English

Old Dominion University

Old Dominion UniversityODU Digital CommonsPhysics Faculty Publications Physics7-1998Low Saturation Intensities in Two-PhotonUltracold CollisionsC. I. SukenikOld Dominion University, csukenik@odu.eduD. HoffmanS. BaliT. WalkerFollow this and additional works at: https://digitalcommons.odu.edu/physics_fac_pubsPart of the Atomic, Molecular and Optical Physics Commons, and the Optics CommonsThis Article is brought to you for free and open access by the Physics at ODU Digital Commons. It has been accepted for inclusion in Physics FacultyPublications by an authorized administrator of ODU Digital Commons. For more information, please contact digitalcommons@odu.edu.Repository CitationSukenik, C. I.; Hoffman, D.; Bali, S.; and Walker, T., "Low Saturation Intensities in Two-Photon Ultracold Collisions" (1998). PhysicsFaculty Publications. 11.https://digitalcommons.odu.edu/physics_fac_pubs/11Original Publication CitationSukenik, C.I., Hoffmann, D., Bali, S., & Walker, T. (1998). Low saturation intensities in two-photon ultracold collisions. PhysicalReview Letters, 81(4), 782-785. doi: 10.1103/PhysRevLett.81.782VOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998Low Saturation Intensities in Two-Photon Ultracold CollisionsC. I. Sukenik,* D. Hoffmann,† S. Bali,‡ and T. WalkerDepartment of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706(Received 12 June 1997; revised manuscript received 20 February 1998)We have observed violet photon emission resulting from energy-pooling collisions between ultracoldRb atoms illuminated by two colors of near-resonant infrared laser light. We have used this emissionas a probe of doubly excited state ultracold collision dynamics. We have observed the lowest saturationintensity for light-induced ultracold collisions seen to date which we identify as due to depletion ofincoming ground state flux. We have also varied the detuning of the lasers which allows us to clearlyidentify the effect of spontaneous emission and optical shielding. [S0031-9007(98)06710-6]PACS numbers: 34.80.Qb, 32.80.Pj, 33.80.–bInteractions between ultracold atoms are of consider-able interest because of the appearance of novel light-induced dynamics at low temperature and the onset ofquantum behavior [1]. Ultracold collisions proved to becrucial in attaining Bose-Einstein condensation, and op-tical control of ultracold collisions appears to provide apromising technique for producing large ensembles of ul-tracold molecules [2]. In this Letter, we report on a studyof light-induced ultracold atomic collisions which, amongother striking observations, display saturation intensitiesfor two-photon processes that are muchlower than ob-served for single-photon processes.Any realistic theoretical treatment of excited state col-lisions must include spontaneous emission as collisiontimes are comparable to excited state lifetimes [3]. Fur-thermore, at ultracold temperatures—unlike thermal col-lisions—the hyperfine interaction plays an important rolein the collision dynamics [4], though the analysis of virtu-ally all experiments to date has ignored hyperfine interac-tions. For the two-photon experiment reported here, weanalyzed the measurements using a semiclassical modelincorporating all hyperfine energy levels. This allows usto elucidate the interplay between the various processesof flux depletion, spontaneous emission, optical shielding,and Franck-Condon overlap. Furthermore, we can quan-titatively explain the striking observation of very low sat-uration intensities in the two-photon collision process.Ultracold collisions begin when two atoms approacheach other in the ground state. The ensuing dynamics de-pend on the number of photons absorbed and emitted bythe colliding atom pair. Absorption of one photon createsa singly excited state (SES). Acceleration on the SES pro-duces trap loss [1]. Collisions involving the absorptionof two photons, producing doubly excited states (DES),allow greater control over the collision dynamics becausethe relative energy of the colliding atoms is set by thedifferenceof the photon frequencies. Here we show thatDES collisions allow insight into some processes whichare masked in SES trap loss measurements. Analysis ofstudies of some of the important dynamical processes ofDES collisions in Na [5] were hampered by the complex-ity of the hyperfine structure in theP3y2 fine-structurelevel, thus emphasizing the importance of exploring asimpler, more tractable system such as theP1y2 mani-fold in Rb [6]. Further simplification results when the ini-tial excitation is to the lowest energy molecular hyperfinemanifold, i.e., from the lowest ground state hyperfine levelto the lowest hyperfine levels of the5S1y2 1 5P1y2 SES.This pathway avoids the complex behavior which resultsfrom entangled attractive and repulsive potential curves.In Rb, the collisional photoassociative ionization chan-nel is closed [7], so we employ a fluorescence detectionmethod which takes advantage of an energy pooling re-action. Energy pooling occurs when the atom pair in theDES reaches small separation and yields a violet photonwith l ­ 421 nm. We have probed the dynamics of thecollision by measuring the relative violet photon produc-tion rateR as a function of laser detuning and intensitywhen two ir laser fields (both withl , 795 nm) are ap-plied. Referring to Fig. 1, one field, of frequencyv1 (in-tensity I1), is tuned below resonance while the other,v2sI2d, is tuned above resonance. We find a strong depen-dence ofR on v2, including the surprising appearanceof deep modulations for87Rb, but not for85Rb. Evenmore striking, we observe saturation at laser intensitiesmuch lower than in any previous ultracold collisions ex-periment. We identify saturation associated withv1 asresulting from a depletion of incoming flux [8], the firstsuch observation of this effect. Depletion results whenxcitation at larger interatomic separation removes groundstate flux available for excitation at shorter distances. Sat-uration of v2 is also observed at small detuning, arisingfrom an optical shielding process [9]. Our model indi-cates that the modulations in thev2 dependence origi-nate from two sources: the onset of new collisionalchannels due to hyperfine structure in the DES, andFranck-Condon (FC) overlap factors. Our data alsodemonstrate the strong influence of spontaneous emissionand optical shielding when the detuning is near the onsetthe two-photon collision.The spectrum of the spontaneously emitted photonsgives important information about the collision process.782 0031-9007y98y81(4)y782(4)$15.00 © 1998 The American Physical SocietyVOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998FIG. 1. (a) Schematic representation of87Rb energy levelsinvolved in the two-photon optical collision; (b) calculated87Rb potential curves showing hyperfine structure of the singlyexcited5S1y2sF ­ 1d 1 5P1y2sF 0 ­ 2d manifold.Because of the depth of the Rb molecular potentials,decay of the DES at close range could result in the emis-sion of photons over a band of many tens of nanometersaround 400 nm. Rather than observing a broad spec-tral distribution, however, we found that our signal wascomprised exclusively of 421 nm photons arising fromenergy pooling:5P 1 5P ! 5S 1 6P, followed by a6P ! 5S decay at 421 nm. The absolute rate coefficientfor violet photon production is observed to be on the or-der of 10214 to 10213 cm3ys for I1 ­ 70 mWycm2 andI2 ­ 200 mWycm2, where I is the average laser inten-sity. We were able to resolve the6P fine structure andfound that transfer to the6P1y2 component is favored overthe 6P3y2 state by a ratio of,2:1. This experiment isone of just two ultracold collision experiments which havesuccessfully detected collisionally produced photons [10].Here we measureR as a probe of the DES collision dy-namics, expecting that any frequency dependence comesfrom light-induced dynamics at large interatomic separa-tion, not from changes in the energy pooling probability.In our experiment,87Rb or 85Rb atoms are confinedin a magneto-optical trap (MOT) similar to that de-scribed previously [11,12]. Five frequencies are derivedfrom three external-cavity diode lasers. One lasersv1dis detunedD1 ­ 290 MHz from the 5S1y2sF ­ 1d !5P1y2sF0 ­ 1d atomic transition (for87Rb), or thesF ­2d ! sF0 ­ 2d transition (for85Rb), and populates attrac-tive 5S1y2 1 5P1y2 curves. Excitation byv1 typicallytakes place at an interatomic separation between 10 and40 nm. The other lasersv2d is detunedD2 ­ 0 2 GHzabove the5S1y2sF ­ 1d ! 5P1y2sF0 ­ 2d atomic tran-sition (for 87Rb), or thesF ­ 2d ! sF0 ­ 3d transition(for 85Rb). All lasers can be switched on and off usingacousto-optic modulators. The MOT lasers are switchedoff when v1 andv2 are present to reduce the number ofcollisional pathways [11]. For a typical sequence the traplaser is turned on for80 ms, followed by2 ms of opti-cally pumping nearly all the atoms to the lowest groundstate level, and, finally,15 ms of v1 andv2. Violet pho-tons impinged on the detector at a very modest rate ofonly tens of photons per second, so we carefully filteredout all scattered near-ir light using a series of filters [13].In order to obtain a violet photon spectrum, a liquid N2cooled charge-coupled device camera was used in con-junction with a 0.275 meter monochromator with a reso-lution of , 0.3 nm.Our data consist of measurements ofR as I1, I2, andD2 are varied. In Fig. 2(a) we showR as a function ofI1 at fixed v2. The curve is typical, independent ofv2.Notice that the saturation occurs atI1 , 30 mWycm2,much lower than previously observed in ultracold colli-sions. When saturation has been observed in trap-lossmeasurements [14] and photoassociative ionization stud-ies [5], the saturation intensity has always been on theorder of several hundred mWycm2. We have identifiedthe saturation here as arising from a population deple-tion mechanism similar to that suggested by Gallagherin Ref. [8]. This is the first observation of this collisionmechanism. Although transitions from the ground stateto a given SES state may not be saturated, after traversingseveral resonances the incoming ground state flux can be-come substantially depleted. To see this, we plot in Fig. 3the remaining ground state flux as a function of atom-pairseparation. The transition amplitudes are calculated basedon the collision model discussed below.Our data also show thatv2 photons affect the collisionsin several ways. Depending on the detuning,v2 caneither induce excitations from the SES to one of threehyperfine levels of the5P1y2 1 5P1y2 state or causeexcitations from the ground state to repulsive curves ofthe SES. The latter excitation initiates an optical shieldingprocess; after excitation to a repulsive curve byv2 theatom pair is prevented from coming close enough tobe excited byv1. This can occur even ifjD2j . jD1jbecause, as can be seen from Fig. 3, at a given detuningmany repulsive curves have Condon points at largerRthan do the attractive curves. Because only one SES isinvolved, depletion byv2 in the excitation to the DES isunimportant. The importance of shielding is demonstratedby Fig. 2(b), which shows violet photon production asa function of I2 for two values ofv2 in 87Rb. At adetuning of 150 MHz, saturation is observed, whereas at783VOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998FIG. 2. Intensity dependences of violet photon productionrates as a function of average intensity of (a)v1 for 85Rb;(b) v2 with D2 ­ 150 and 300 MHz for 87Rb. Populationdepletion is responsible for the low saturation intensity in (a),while the saturation in the 150 MHz data of (b) results fromoptical shielding. Solid lines are results of the model describedin the text.300 MHz the rate is essentially linear with intensity. Thesaturation in the 150 MHz data is due to enhanced opticalshielding at higher intensity. At 300 MHz, less flux isdiverted byv2 to the repulsive SES curves resulting inlittle saturation of violet photon production. The shape ofboth curves is explained by our model and displayed withthe data in Fig. 2. Thus, the saturation effects ofv1 andv2 arise from very distinct physical mechanisms. Forv1,flux depletion produces the low saturation, while forv2,optical shielding is the dominant effect.We have also measured the violet photon productionrate as a function of detuning. In Fig. 4 we show theviolet photon count rate as a function ofv2 for 85Rb and87Rb. Qualitatively the two curves share many features,but in 87Rb pronounced modulations of the signal areobserved. We will explain these features with referenceto our model which we now describe.Our calculations begin by determining all the long-range hyperfine states [15]. We calculate the excitationprobability to each SES hyperfine curve using the familiartwo-level Landau-Zener (LZ) curve crossing formula,explicitly including the FC wave function overlap factor[16]. We use semiclassical WKB wave functions forFIG. 3. Ground state flux as a function of interatomic separa-tion for two colliding 85Rb sF ­ 2d atoms. Population deple-tion and shielding occur as the colliding atoms traverse Condonpoints. A qualitatively similar curve is obtained for87Rb.the SES and ans-wave ground state wave function withpublished scattering lengths [17]. The Rabi frequencyused in the LZ formula is calculated using a magnetic-sublevel averaged matrix element. For all excitations,we average over the intensity of the standing waves ofv1 and v2. Optical shielding byv2 and flux depletionFIG. 4. Violet photon production rate as a function ofD2 for(a) 87Rb and (b)85Rb. The solid line shows results from acalculation described in the text.784VOLUME 81, NUMBER 4 P H Y S I C A L R E V I E W L E T T E R S 27 JULY 1998of the ground state arise naturally in the model as fluxis removed from the ground state at each Condon point.Once excited byv1, we allow the atoms to approach eachother classically. Along their trajectory they may becomeresonant withv2 before decaying and be excited to oneof the three hyperfine levels of the DES. The excitationprobability to the DES is calculated according to the LZformula. The wave functions for the three DES hyperfinelevels are taken to be sinusoidal with an adjustable phasetreated as a free parameter. Last, we calculate the survivalprobability in the DES to reach small separation (,1 nm),where we assume a violet photon is produced with aprobability independent ofv2. We have used a singleinitial relative velocity of 20 cmys.This semiclassical model, while much more compre-hensive than any others used to date in excited-state ul-tracold collisions, is clearly not complete. Whiles wavesare certainly very important, higher order partial wavesshould also contribute to the signal. We expect that inclu-sion of higher partial waves in the model would result inbetter reproduction of the detuning dependence, whereasthe effects on the intensity dependence would be minimal.By averaging over magnetic sublevels, we have neglectedpossible effects due to magnetic orientation. Since theexcitation probability at a given Condon point is small,using a magnetically averaged oscillator strength is likelya good approximation. For similar reasons, our treatmentof the Condon points as independent is probably fairlyaccurate. These approximations are necessitated by bothtractability and an incomplete knowledge of all relevantwave functions.Using the model, we now interpret the detuning de-pendence. In Fig. 4(a), the first peak, whose onset isat 90 MHz, results from excitation to the10 1 20 DES[18]. Similarly, the third peak originates predominantlyfrom excitation to the20 1 20 state. The frequency dif-ference in the onset of the peaks corresponds to the812.5 MHz hyperfine splitting of the excited state. Other“peaks” in the data are actually modulations introducedby the FC overlap factors for excitation byv2. No-tice that although there is a nonvanishing oscillatorstrength to the lower of the three DES hyperfine levelsbelow anv2 detuning of 90 MHz, violet photon produc-tion there is very strongly suppressed by optical shielding.The rather different structure for the two isotopes comesfrom several effects. In the case of85Rb, the smallerhyperfine splitting, the increased number of contributinghyperfine levels, and the different FC factors result in adetuning spectrum with less pronounced features than for87Rb. No single factor seems to exclusively determine thelevel of modulation in the data. We also note that whenthe v2 detuning is small and thus the relative momentumin the DES is low, the impact of spontaneous emission onthe collision dynamics is most pronounced. The effect ismanifested as a suppression of the first and third peaks inFig. 4(a).In conclusion, we have observed violet photon produc-ion in collisions of ultracold Rb atoms. The violet pho-tons, which result from excitation to the5P1y2 1 5P1y2state followed by an energy pooling to the5S 1 6P state,are used to probe the doubly excited state dynamics. Wehave observed the lowest saturation intensity measured todate in an ultracold light-induced collision process. Weidentify this low saturation intensity as resulting from apopulation depletion of incoming flux. We have devel-oped a hyperfine structure inclusive model to simulate thecollision dynamics. Measurement of both the frequencyand intensity dependence in conjunction with our modelreveal for the first time the interplay between dynamicsassociated with spontaneous emission, optical shielding,oscillations in Franck-Condon overlap factors, and popu-lation depletion. Careful choice of states and laser fre-quencies allowed the effects of hyperfine structure to berevealed without undue complexity, thus facilitating inter-pretation of the experimental results.We acknowledge support from the NSF and thePackard Foundation.*Present address: Old Dominion University, Departmentof Physics, Norfolk, VA 23529.†Present address: Harvard-Smithsonian Center forAstrophysics, 60 Garden Street, Cambridge, MA 02138.‡Present address: Duke University, Department of Physics,Durham, NC 27708.[1] See T. Walker and P. Feng, Adv. At. Mol. Opt. Phys.34,125 (1994); J. Weiner, Adv. At. Mol. Opt. Phys.35, 45(1995).[2] Y. B. Band and P. S. Julienne, Phys. Rev. A51, R4317(1995).[3] See K.-A. Suominen, J. Phys. B29, 5981 (1996).[4] P. Fenget al., Phys. Rev. A47, R3495 (1993).[5] P. A. Molenaaret al., Phys. Rev. Lett.77, 1460 (1996);V. Bagnatoet al., Phys. Rev. Lett.70, 3225 (1993); M. E.Wagshulet al., Phys. Rev. Lett.70, 2074 (1993).[6] M. G. Peterset al., Phys. Rev. A50, R906 (1994).[7] D. Leonhardt and J. Weiner, Phys. Rev. A52, R4332(1995).[8] A. Gallagher, Phys. Rev. A44, 4249 (1991).[9] R. Napolitanoet al., Phys. Rev. A55, 1191 (1997), andreferences therein.[10] A. Fioretti et al., Phys. Rev. A55, R3999 (1997).[11] D. Hoffmannet al., J. Opt. Soc. Am. B11, 712 (1994).[12] P. Feng and T. Walker, Am. J. Phys.63, 905 (1995).[13] Schott BG39 and Melles Griot 03 FIV 026.[14] L. Marcassaet al., Phys. Rev. A47, R4563 (1993).[15] T. Walker and D. Pritchard, Laser Phys.4, 1085 (1994).[16] N. F. Mott and H. S. W. Massey,The Theory ofAtomic Collisions (Oxford University Press, London,1965), 3rd ed.[17] N. R. Newburyet al., Phys. Rev. A51, R2680 (1995);J. R. Gardneret al., Phys. Rev. Lett.74, 3764 (1995).[18] As we measureD2 from the5S1y2sF ­ 1d ! 5P1y2sF 0 ­2d atomic transition (for87Rb), the 10 1 10 peak wouldoccur at negativeD2.785

Low Saturation Intensities in Two-Photon Ultracold Collisions

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Low Saturation Intensities in Two-Photon Ultracold Collisions

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