A compact, laser cooling apparatus for simultaneous cooling of

lithium and rubidium

Keith Ladouceur, Bruce G. Klappauf, Janelle Van Dongen, Nina Rauhut, Bastian Schuster,

Arthur K. Mills, David J. Jones, and Kirk W. Madison

Department of Physics & Astronomy, University of British Columbia,6224 Agricultural Road, Vancouver, BC, V6T 1Z1, Canada

We report on a dual species laser cooling apparatus capable of collecting over 108 87Rbor 85Rb atoms from an atomic vapor or up to (8 ± 2) × 107 6Li atoms directly into amagneto-optic trap (MOT) from an effusive oven without the need for a Zeeman slower. Theuse of a miniature atomic oven placed close to the trapping region yields a compact vacuumsystem while still producing adequate lithium ensembles and a high quality vacuum in the10−10 Torr range. The atomic sources, laser system, and vacuum system are described.In addition, we use this system to study atom loss from the MOT due to interspeciescollisions between 6Li and 85Rb or 87Rb. We report for the first time the heteronuclear losscoefficients for 6Li–85Rb mixtures. c© 2008 Optical Society of America

OCIS codes: (020.3320) Laser cooling. (020.7010) Laser trapping. (140.2020) Diodes lasers.(140.3280) Laser amplifiers. (020.2070) Effects of collisions.

References

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10. U. Schloder, C. Silber, T. Deuschle, and C. Zimmermann, “Saturation in heteronuclear photoassociationof 6Li7Li,” Physical Review A 66, 061403 (2002).

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13. M. Pichler, H. Chen, and W. C. Stwalley, “Photoassociation spectroscopy of ultracold Cs below the6P3/2 limit,” The Journal of Chemical Physics 121, 6779–6784 (2004).

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15. E. Wille, F. M. Spiegelhalder, G. Kerner, D. Naik, A. Trenkwalder, G. Hendl, F. Schreck, R. Grimm,T. G. Tiecke, J. T. M. Walraven, S. J. J. M. F. Kokkelmans, E. Tiesinga, and P. S. Julienne, “Exploringan ultracold fermi-fermi mixture: Interspecies feshbach resonances and scattering properties of 6Li and40K,” Physical Review Letters 100, 053201 (2008).

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18. E. R. Hudson, N. B. Gilfoy, S. Kotochigova, J. M. Sage, and D. DeMille, “Inelastic collisions of ultracoldheteronuclear molecules in an optical trap,” Physical Review Letters 100, 203201 (2008).

19. W. Salzmann, U. Poschinger, R. Wester, M. Weidemuller, A. Merli, S. M. Weber, F. Sauer, M. Plewicki,F. Weise, A. M. Esparza, L. Woste, and A. Lindinger, “Coherent control with shaped femtosecond laserpulses applied to ultracold molecules,” Physical Review A 73, 023414 (2006).

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1. Introduction

The simultaneous laser cooling of multiple species in magneto-optic traps (MOTs) has become increasinglycommon in recent years as the motivations for studying the physics of mixed species ultra-cold gases havebecome more apparent. Trapping of different isotopes in the same apparatus has been useful for precisemeasurements of isotopic differences of trapping performance (revealing the precise role of hyperfine changingcollisions in a MOT) and mixed-isotope light-assisted collisions in a MOT [1, 2]. In addition, multi-isotopeensembles provide near equal mass mixtures of fermionic and bosonic components [3–5] and are well suited tosympathetic cooling to lower temperatures because the collision partners have almost equal mass [6,7]. Dueto Pauli exclusion, the evaporative cooling of magnetically trapped (i.e. spin polarized) fermionic species isseverely limited at low temperatures where only s-wave collisions occur. Sympathetic cooling of a fermionicspecies by thermal contact with a cold bosonic atomic ensemble, even in the case of different masses, is aviable scheme and further motivates the creation of dual species MOTs [4,8,9]. The simultaneous laser coolingof different atomic species also offers the possibility to perform precise measurements of the heteronuclearmolecular potentials through photoassociation spectroscopy [10–13] and through the study of heteronuclearFeshbach resonances [14–16]. Ultra-cold ensembles of heteronuclear molecules [17–20] have been proposed fora wide variety of new applications in ultra-cold chemistry, quantum computation and quantum simulation[21–23].

In this paper, we describe the features of a dual species trapping apparatus capable of collecting over 108

87Rb or 85Rb atoms from an atomic vapor or (8± 2)× 107 6Li atoms directly from an miniature oven placedclose to the trapping region without the need for a Zeeman slower. The advantage of this configuration isthat it does not require additional slowing optics or solenoids and is therefore very compact in comparison toa Zeeman slowed atomic source and yet yields a captured flux of more than 4×106 lithium atoms per secondwith a high quality vacuum in the 10−10 Torr range. In the following sections, we present the important andunique features of our experimental system, we describe the optimization and characterization of the dualMOT, and we use this system to measure the MOT trap loss due to interspecies collisions between 6Li and85Rb or 87Rb. We report for the first time all of the heteronuclear loss coefficients for 6Li–87Rb and 6Li–85Rbmixtures as well as the homonuclear loss coefficients for 6Li, 85Rb, and 87Rb.

2. Experimental setup

The MOT trapping region is centered within an optically polished Borosilicate cell (Pyrex box manufacturedby Starna Scientific Ltd, formerly Optiglass Ltd). This cell is bonded (by Technical Glass, Inc.) on both endsto glass to metal transitions with the atomic sources introduced on one end and supported inside the cellby a 2.75 inch conflat electrical feedthrough. The other end of the cell is connected through a stainless steelbellows and 6 inch conflat cross to a 20 L s−1 Varian StarCell ion pump and a SAES CapaciTorr NEG pump.

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Fig. 1. Front view of rubidium dispensers and lithium oven.

The outer dimensions of the glass cell are 30 mm × 30 mm × 100 mm with a 5 mm wall thickness.The rubidium vapour dispensers, as well as the effusive lithium oven, are located 10 cm from the trapping

region in order to maximize the capturable atom flux from the lithium oven. A small circular beam block3 mm in diameter is situated between the oven and the trapping region in order to shield the MOT centerfrom the direct output of the effusive oven. This configuration is similar to that reported in [24], with theexception that in this work the trapping light for lithium is single frequency and is not broadened in anyway to enhance the loading of the MOT. The lithium MOT loads directly from the effusive oven without anyadditional slowing stages to compensate for the high average velocity of the lithium atoms from the oven,such as a Zeeman slower [25]. The result is a compact vacuum system with a high quality vacuum and a LiMOT with almost 108 atoms in steady state.

Key to achieving a good vacuum with an atomic oven less than 10 cm from the MOT was the carefulpreparation of the enriched (95% 6Li) sample and systematic degassing of the oven. Lithium is highly reactivewith both organic and inorganic reactants, including nitrogen and hydrogen. The initial sample of lithiumwas cleaned with petroleum ether to remove residual oil from the surface in an argon filled glove-box. A cleanrazor blade was used to remove the black exterior from all sides of the lithium sample. On a clean surface,and with a new blade, the piece was reduced in size so that it fit easily within the oven reservoir.

The lithium oven, made of a non-magnetic alloy of nickel and chromium (80% nickel and 20% chromium),consists of a cylindrical reservoir 7.6 mm long, 4 mm in diameter with an internal volume of 81 mm3. Theresevoir is enclosed by a cap, connected by two spiral arms at the top which lock to the cap with a twistingmotion. As shown in Fig. 1, the cap is 5.2 mm long, 5 mm in diameter, and has a 0.8 mm hole through thecenter. The two thin extensions of the cap serve as mechanical support and electrical contacts, and are themajor source of heating due to their small thickness (0.6 mm) and length (1.25 cm). At a current of 9 A,the oven heats to approximately 250 ◦C in 3 minutes. The atomic beam profile from the oven was measuredby fluorescence imaging and by observing the coating produced on a glass flat 10 cm away. The atomic fluxwas primarily contained within an emission cone with an angular divergence of 15 degrees, corresponding to

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the aspect ratio of the exit hole in the cap.The lithium oven was degassed by heating it to increasing temperatures within an auxillary preparation

chamber such that the total pressure from outgassing never exceeded 10−5 Torr. This was also done sothat the melted lithium could incorporate into the nickel mesh that lined the reservoir while removing themajority of the trapped nitrogen, oxygen, and hydrogen. The outgassed contaminants were identified andmonitored by a residual gas analyser (RGA). The oven was heated until the outgassed pressure at a currentof 10 A fell below the base pressure of the preparation chamber (5 × 10−8 Torr; 10 l s−1 pumping speed).The mesh was critical for proper operation of the oven as it prevented the lithium from wicking out of the hotoven. After degassing, the preparation chamber was flushed with argon (the use of dry nitrogen was avoidedsince it was found to contaminate the lithium) and the oven was quickly moved to the experimental vacuumchamber where a 6-day bakeout at 200 ◦C was performed. We estimate that the usable lithium occupies 1/4of the oven volume and therefore that a total of 11 mg is available. The performance of the lithium MOTlocated 10 cm from the oven is shown in Fig. 3.

Rubidium is selectively released using a commercial SAES Getters dispenser. Passing a current throughthe dispenser results in the emission of atomic 85Rb and 87Rb vapour at their natural abundances of 72.17%and 27.83%.

3.036 GHz

121 MHz

29 MHz

63 MHz

F’=4

780 nm

52S1/2

52P3/2

F’=3

F’=2F’=1

F=3

F=2

85Rb

87Rb

6.835 GHz

267 MHz

72 MHz

157 MHz

F’=3

780 nm

52S1/2

52P3/2

F’=2

F’=1F’=0

F=2

F=1

22S1/2

22P3/2

6Li

228 MHz

1.7 MHz

2.8 MHz

F’=1/2

pu

mp

rep

um

p

671 nm

F’=3/2

F’=5/2

F=3/2

F=1/2

pu

mp

rep

um

p

pu

mp

rep

um

p

!Rb = 2! ! 6.07 MHz!Li = 2! ! 5.87 MHz

Fig. 2. Atomic energy levels (not to scale) and transitions used for magneto-optic trappingof lithium and rubidium atoms. A major difference between rubidium and lithium is thatthe hyperfine level spacings in the excited state are very large compared to the naturallinewidth for rubidium (ΓRb = 2π × 6.07 MHz) while they are actually smaller than thenatural linewidth for lithium (ΓLi = 2π × 5.87 MHz).

The laser systems for lithium and rubidium are composed of grating-stabilized and injection-seeded diodelasers (master and slave lasers). In total, five master lasers are required for the experiment. Each isotopeof Rb requires a separate master laser to generate the pump light, also referred to as the “cooling” light,(F = 3 → F ′ = 4 for 85Rb and F = 2 → F ′ = 3 for 87Rb) and repump light (F = 2 → F ′ = 3 for85Rb and F = 1 → F ′ = 2 for 87Rb) on the 52S1/2 → 52P3/2 transition for Rb trapping. The pump(F = 3/2→ F ′ = 5/2) and repump (F = 1/2→ F ′ = 3/2) light tuned to the 22S1/2 → 22P3/2 transition forlithium is generated from a single master laser. Fig. 2 shows a diagram of the atomic energy levels and thepump and repump light tuned below their respective resonances by ∆νp and ∆νr. A major difference betweenrubidium and lithium is that the hyperfine level spacings in the excited state are very large compared tothe natural linewidth for rubidium while they are actually smaller than the natural linewidth for lithium.This has dramatic consequences on the operation of the MOTs. In the case of rubidium, the radiation

5

pressure exerted on the atoms in the MOT is primarily due to the pump or cooling light which is tunedto an almost “closed transition” and only rarely excites off-resonantly a lower hyperfine level in the excitedstate resulting in hyperfine pumping in the ground state. The atoms need only rarely scatter repump lightto counteract this optical pumping, and the repump beam therefore exerts an almost negligible force on theatoms. Consequently, only a small intensity is required for the repump light and it can be introduced intothe MOT without concern for its polarization or direction. In stark contrast, the excited state spacing inlithium is so small that the pump (cooling) light, which is typically tuned to the red of the transition byseveral linewidths, excites with similar rates all three excited states, and the upper, F = 3/2, ground stateis rapidly depleted. In this case, the repump light has a similar scattering rate as the pump light of the sameintensity. It therefore contributes to cooling and exerts a force on atoms in the MOT comparable to thatexerted by the pump light. Consequently, both the pump and repump light must be introduced into the trapalong all three directions with similar intensities for the proper operation of the lithium MOT.

The master lasers are frequency stabilized using modulation-transfer saturated absorption spectroscopy ina reference cell containing either rubidium or lithium atomic vapor. The stabilized linewidth of the masterlasers is estimated to be 1.5 MHz and was determined from a heterodyne beatnote measurement betweentwo master lasers locked to two different atomic transitions. The partial pressure of rubidium at roomtemperature is 10−7 Torr providing an adequate optical depth in a 10 cm glass cell; however, the partialpressure of lithium is exceedingly low (below 10−20 Torr) at room temperature and necessitates the use of aheat pipe to perform absorption spectroscopy. Our heat pipe is a hollow nickel cylinder 10 cm long and witha 1 cm inner diameter. The cylinder is enclosed by end caps with a 3 mm hole to allow the passage of light.The heat pipe is filled with 1 g of lithium and lies inside a stainless steel tube 40 cm long and filled with1 Torr of argon to limit the mean free path of the hot lithium so that the windows on the outer stainlessvacuum envelope are not coated. The heat pipe is heated to 410 ◦C from the outside by thermal contactwith the stainless tube which is embedded in an insulated heating element. The vacuum windows reside farfrom the insulated region and are at room temperature.

Acousto-optic modulators in double pass configuration (to minimize beam steering) are used to fine tunethe frequency of the trapping light before the final stage of amplification. Our amplifiers are injection lockedsingle-mode diode lasers comprised of either the MLD780-100S5P from Intelite Inc. with 90 mW output at780 nm or the HL6535M from Hitachi with 90 mW at 658 nm. We operate the MLD780-100S5P at 18 ◦C and125 mA which produces approximately 60 mW when injected. We use HL6535MG98 lasers from Opnext,Inc. for the 671 nm amplifiers. These diodes are nominally 658 nm devices and were wavelength selected tooperate at or above 661 nm at a temperature of 25 ◦C. By heating these lasers to 69 ◦C, their free runningwavelength is between 667 and 668 nm. At this temperature, the output power is significantly reduced andwe observe an output of 30 mW at 164 mA. In contrast to the 780 nm amplifiers where the spectrum is verypure (more than 99% of the output power of the diode is at the seed frequency), the output spectrum ofthe 671 nm amplifiers, when injected with 1 mW of seed light, is observed to include a broad backgroundcentered at the free running wavelength. Injection locking of laser diodes is a frequency pulling effect andrequires that one of the diode laser’s intrinsic cavity modes be in near resonance with the seed. The injectionbehavior of laser diodes which do not have an anti-reflection coated front facet and which therefore have amoderately high finesse is very sensitive to the diode current and temperature. At a fixed temperature, weobserve a discrete set of current ranges (a few mA wide) within which the amplifiers will lock and which areseparated by current ranges for which no amplification of the seed is observed. For the very highest currentranges, we observe that as the current is varied across the range where amplification of the seed occurs,the fraction of the output power contained at the seed frequency varies between 66 and 33%. Unfortunatelythis performance could not be improved upon by varying the seed injection power. Other than reducing the

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overall power of the injected seed, the broad background does not appear to have a deleterious effect onthe operation of the lithium MOT. However, this broad, non-resonant background is observed to limit theapparent optical density of the MOT in absorption images.

Mechanical shutters and electro-optical modulators are used to control the overall power of the Rb andLi MOT light after amplification. The light for trapping is combined into a single beam by way of severalpolarization beam splitter cubes and a dichroic mirror. This combined beam is then expanded to a 1/e2

diameter of 8 mm, divided, and prepared with the correct polarization using dual wavelength optics andintroduced into the MOT cell along the three mutually orthogonal axes in a retro-reflection configuration.This configuration was chosen over a 6 independent beam configuration in order to maximize the opticalpower available for trapping. In addition, we observed that spatial filtering of the beams was unnecessaryand in fact detrimental since even a 20% loss in optical power resulted in more than a 30% reduction of thelithium MOT number. The total optical power delivered to the dual species MOT is approximately 38 mWand 4 mW at the Rb pump and repump frequencies and 11 mW and 6.5 mW at the Li pump and repumpfrequencies respectively, assuming half the power of the lithium amplifiers is at the seed frequencies.

The atom numbers in the MOT are monitored by means of fluorescence detection. The fluorescence fromthe Rb and Li MOTs are separated by a dichroic mirror and are detected independently on two ThorlabsSMIPD2B photodiodes. Interference filters with a 10 nm transmission bandwidth centered at 671 nm and780 nm are used to suppress cross-talk and spurious signals from room lights. The fluorescence measurementsfrom the photodiodes are used as the basis for calculating the atom number within the MOTs. In addition,images of the dual MOT fluorescence are recorded by two charge-coupled device (CCD) cameras alongorthogonal directions. These images are used to characterize the spatial overlap of the clouds. We emphasizehere that the atom numbers reported in this manuscript represent lower bounds since it is difficult toaccount for all imperfections and possible misalignments in the detection system (which necessarily occludefluorescence collection) and to account for the effect of non-uniform illumination due to the optical thicknessof the atomic clouds. Also, the scattering rate is computed assuming the atoms are located in the region ofhighest intensity for all 6 MOT beams; however, slight misalignments of these trapping beams can reducethe total illumination intensity and yet are observed to produce a stable MOT. All of these effects reducethe total amount of fluorescence collected and therefore leads to a systematic underestimate of the numberof atoms present in the MOT.

3. Results

3.A. Single Species Optimization

In a single species configuration, lithium and rubidium MOT numbers were first optimized independentlyby carrying out an exhaustive search in the pump (∆νp) and repump (∆νr) detunings for a range of axialmagnetic field gradients between 10 to 50 G cm−1. Although the lithium MOT showed improved performanceat high field gradients (above 30 G cm−1), the rubidium atom number was dramatically suppressed above28 G cm−1. A compromise of 23 G cm−1 was chosen as the operational magnetic field gradient. The optimumMOT parameters at this magnetic field gradient are summarized in table 1.

The highest atom number we were able to trap for 6Li was (8 ± 2) × 107 atoms using a detuning fromresonance of ∆νp = −5.8ΓLi and ∆νr = −4.4ΓLi for the pump and repump light, respectively. Note thatthe saturation intensities given in table 1 are calculated for the case of an an isotropic pump field withequal components in all three possible polarizations [26]. In addition, the lithium interaction was assumedto include all of the allowed 22P3/2 excited state levels due to our large detuning relative to the excited statehyperfine splittings.

Fig. 3 shows the behavior of this oven loaded lithium MOT at a field gradient of 23 G cm−1. The atomic

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Table 1. Optimal parameter settings for each MOT in a single species configuration withan axial field gradient of 23 G cm−1: Wavelength and width of the D2 line, saturationintensities (assuming isotropic light polarization), pump and repump intensities along allthree principle axes, relative detunings of the pump and repump light ( ∆νp and ∆νr), andthe steady state atom number. The steady state Rb atom number depends on the amountof Rb background vapor in the cell which in turn introduces additional loss in the lithiumMOT due to an increased background collision rate. This steady state Rb atom number wastaken at a Rb pressure which suppressed the Li MOT number by a factor of 20 from themaximum (8± 2)× 107.

6Li 85Rb/87RbλD2,vac (nm) 670.977 780.241Γ/2π (MHz) 5.87 6.07Isat (mW cm−2) 3.8 3.58 [26]Ip/Isat 25 72Ir/Isat 14 3.0∆νp (Γ) -5.8 -1.8∆νr (Γ) -4.4 -0.7N∞ (8± 2)× 107 ≥ (7± 2)× 107

loading rate (R), the inverse loss rate (Γ−1), and steady state atom number (N ∞Li ) of the 6Li MOT are shown

as a function of the current supplied to the oven. These parameters were determined by fitting the loadingcurve of the 6Li MOT to the solution, N(t) = N ∞

Li (1− e−Γt) of the differential equation N = R− ΓN . Thesteady state number is then the product of the loading and inverse loss rates, N ∞

Li = RΓ . In this model we

neglect any loss due to homonuclear light assisted collisions and therefore the loss term due to collisions withthe residual background vapor, Γ, is overestimated. The corresponding inverse loss rate of the MOT (Γ−1) isunderestimated slightly but gives a good indication of the background pressure of the vacuum system limitedby outgassing from the oven. The longest inverse loss rates measured for lithium were on the order of 50 scorresponding to a background vapor pressure of approximately 2× 10−10 Torr [27]. As the temperature ofthe oven increases so does the captured flux and the loss rate. At a current of Ioven = 9.5 A, the steady stateatom number is maximized. There exists a clear tradeoff between the inverse loss rate of the lithium MOTand the steady state atom number, and by running the oven at 8 A instead of 9.5 A the inverse loss rate canbe increased by more than a factor of two with only a factor of two reduction in the trapped number.

The steady state Rb atom number depends on the amount of Rb background vapor in the cell which inturn introduces additional loss in the lithium MOT due to an increased background collision rate. Thereforethe steady state rubidium and lithium atom numbers vary inversely as the Rb background vapor pressure isincreased. In the absence of homonuclear light assisted collision losses, the lithium MOT number in steadystate is N ∞

Li = RLiγLi

where the loss rate of lithium γLi = ΓLi,bg + ΓLi,Rb has contributions from collisionswith residual background gas (ΓLi,bg) and with rubidium atoms (ΓLi,Rb) introduced by the dispenser. Boththe rubidium load rate, RRb, and the loss term ΓLi,Rb are proportional to the rubidium vapor pressurein the cell so they are proportional to each other, RRb ∝ ΓLi,Rb. Furthermore, if we neglect homonuclearlight assisted collisions in rubidium, the steady state rubidium MOT number is simply proportional to the

8

Fig. 3. A comparison of the loading rate (R), inverse loss rate (Γ−1), and steady state atomnumber (N ∞

Li ) for a single species Li MOT in the absence of background Rb vapour as afunction of the current supplied to the effusive oven with parameter values as defined intable 1. The trend lines are only a guide to the eye.

rubidium load rate and we have then ΓLi,Rb ∝ N ∞Rb. We can therefore express the lithium MOT number in

terms of the rubidium MOT number as N ∞Li (N ∞

Rb) = N ∞Li (0)/(1+ εN ∞

Rb) where N ∞Li (0) is the lithium MOT

atom number in the absence of any residual rubidium vapor and ε is a system dependent constant. For ourtrapping parameters, ε is 2.5×10−7. When the rubidium pressure is chosen to equalize the number of trappedrubidium and lithium, 107 atoms of each species are present in the dual MOT. This atom number suppressiondue to residual vapor is the primary limitation to the atom number in all multi-species MOTs where one ormore species is loaded from an atomic vapor. As was shown in the work of Taglieber et. al, the addition of aZeeman slower can produce a much larger lithium loading rate (by two orders of magnitude) allowing the Rbvapor pressure to be run at a correspondingly higher pressure creating a larger Rb MOT while maintainingthe same size lithium MOT as that reported here [28]. Clearly the drawback of this approach to achievinglarge vapor loaded MOTs is that the inverse loss rate due to background collisions in such a system is severelylimited.

3.B. Dual Species Operation

In order to simultaneously trap Li and Rb, as discussed above, the axial field gradient was above the optimalvalue for Rb and below that for Li. In addition, the Rb background pressure was chosen so that the RbMOT was comparable in number to the Li MOT. We observe, under these conditions, on the order of 107

atoms of each species are present in the dual MOT.Because we use a retro-reflection configuration, the return beams are less intense and the radiation pressure

imbalance forces the MOT to reside a few mm away from the magnetic field zero. In addition, we observedthat, when optimized individually, the two MOT clouds do not overlap completely. In order to study traploss due to interspecies collisions between 6Li and 85Rb, 87Rb, we carefully adjusted the alignment and powerbalance of the rubidium and lithium trapping light as well as the external magnetic bias field so that the

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Fig. 4. Experimental loading sequence of two spatially overlapping 6Li and 87Rb MOTs. 1)Li is allowed to load in the absence of cold Rb in the MOT at an oven current of 9.5 A.2) After 100 s the Rb repump light is turned on and the Rb MOT loads. The additionalatom loss induced by the Rb MOT suppresses the Li MOT and results in a new steadystate atom number. 3) Both MOTs are emptied by turning off the magnetic field gradient,and after a short wait time the Rb MOT is allowed to load in absence of Li. 4) After 100 sthe Li repump light is turned on and the Li MOT loads. A drop in the Rb MOT number isobserved and the steady state numbers approach a new equilibrium. The reduction in the87Rb MOT number is 10%, a factor of 5 less than the 50% reduction observed in the 6LiMOT number. This illustrates the non-reciprocal nature of the heteronuclear loss terms.

clouds were well overlapped. We observed that this configuration was not optimal for the loading of eitherspecies in single species operation; however, it was necessary to achieve the best possible spatial overlap ofthe clouds to measure the interspecies collisions in the dual MOT. The atom number loading dynamics forthe atomic species A in the presence of the atomic species B is modelled by the following rate equation

dNA

dt= RA − ΓANA − βA,A

∫n2

A dV − βA,B

∫nA nB dV (1)

where RA is the loading rate, ΓA the loss rate due to collisions between the trapped atoms of species A androom-temperature residual gas, βA,A the loss rate due to homonuclear collisions between trapped atoms ofspecies A, βA,B the loss rate of atoms of species A due to heteronuclear collisions with trapped atoms ofspecies B, NA is the trapped atom number of species A, nA and nB are the density distributions of speciesA and B, respectively.

It is important to note that the order of the subindices in the heteronuclear loss term βA,B is crucial,as βA,B and βB,A are not reciprocal quantities due to the different MOT recapture probabilities for speciesA and B [29]. The recapture probabilities differ because of differences in the MOT capture velocities andthe mass differences of the atoms which results in different final velocities after an inelastic heteronuclear

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collision. The trap loss parameters βA,A and βA,B are determined by fitting the loading dynamics and steadystate MOT numbers to the above model in the case of single and double species loading.

Fig. 4 shows the time evolution of the atom numbers during a typical experimental loading sequence.The decrease of the steady state atom number in the dual MOT configuration as compared to the singleMOT configuration is attributable to losses incurred from collisions between trapped lithium and rubidiumatoms. The loading dynamics of the single species MOT is used to determine the parameters RA, ΓA, thehomonuclear βA,A term, and the steady state atom number. Once the steady state is achieved, each MOTis imaged (in single species operation) using two independent and orthogonally positioned CCD cameras.These images allow for the determination of the overlap of the atomic density distributions.

We compute the overlap integrals using the 2D images of the atomic clouds. These images are taken insingle species operation along two orthogonal imaging axes and it is assumed that the shape and position ofthe clouds (i.e. the shape of the normalized density distribution) is constant throughout the measurementsequence and in the presence of the other species. This assumption of constant geometry is justified since thedensity in our MOTs never exceeds 2.5× 1010 cm−3. Previous work has shown that MOTs grow in numberwith constant volume up to densities larger than 3 × 1010 cm−3 where the outward pressure on the cloudfrom multiple scattering becomes significant [30].

We define the normalized density distribution as ρA ≡ nAN∞A

, where N ∞A is the steady state atom number

of species A in the presence of species B. In this case, the heteronuclear term can be computed by solvingEq. 1 in steady state to give

βA,B =RA − ΓAN ∞

A − βA,A(N ∞A )2

∫ρ2AdV

N ∞A N ∞

B

∫ρAρBdV

. (2)

We compute the overlap and self-overlap integrals for the normalized distributions from the cloud imagesand assume these geometric factors do not change during the loading of the MOTs. Our evaluation of theintegrals from 2D images relies on the assumption that the density distribution can be written as a productof three independent functions along the x, y, and z axes (i.e. that ρA(x, y, z) = f(x)g(y)h(z)). This latterassumption will always overestimate the overlap and therefore provide a lower bound on βLi,Rb as it excludespathological distributions which would conspire to reside in the same volume of space but with no overlap.We observe that the overlap integrals for the normalized distributions vary by less than 20% for the twoimages taken along orthogonal axes and we estimate the overlap from the average of the two.

Table 2 shows the results of our measurements for both the homonuclear and heteronuclear collision losscoefficients compared with previously published results where available. The primary uncertainty arises fromour uncertainty in the absolute atom numbers in the MOT.

In agreement with previous studies on Rb MOTs, we observe that β85Rb,85Rb is significantly larger thanβ87Rb,87Rb; however, our absolute values are more than a factor of 10 larger than those of Ref. [31]. In thatwork of Gensemer et al., the β85Rb,85Rb and β87Rb,87Rb values were observed to vary with intensity and thevalues quoted in table 2 were obtained at a total trap intensity 6 times lower and a magnetic field gradient5 times lower than in this experiment. No previously published data exists for β6Li,6Li, and our value issignificantly larger than β7Li,7Li for similar MOT parameters. We also report for the first time heteronuclearloss coefficients for 6Li–85Rb mixtures and find similar results to that for 6Li–87Rb mixtures. We note herethat although β6Li,6Li enters into the determination of β6Li,85Rb and β6Li,87Rb, because it is so small incomparison its influence on the heteronuclear term is almost negligible. In particular, the heteronuclear termchanges by less than 10% if we artificially set β6Li,6Li = 0.

It is interesting to compare the heteronuclear terms β6Li,85Rb and β6Li,87Rb with β85Rb,6Li and β87Rb,6Li.Cold collisions in the presence of light produce atom loss from the MOT by two generic mechanisms: inelasticcollisions and ground state molecule formation. In the former case, a pair of atoms collide in an excited

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Table 2. Homonuclear and heteronuclear collision loss coefficients for rubidium and lithiummixtures. The ellipsis indicate values for which no data is available.

Term This work [cm3s−1] Published Value [cm3s−1]β85Rb,85Rb (1.0± 0.7)× 10−10 > 7× 10−12 [31]β87Rb,87Rb (2.0± 1.0)× 10−11 > 2× 10−12 [31]β6Li,6Li (5.0± 3.0)× 10−11 . . .β7Li,7Li . . . 3× 10−12 [32]

β6Li,85Rb (4.0± 2.0)× 10−10 . . .β6Li,87Rb (2.5± 1.0)× 10−10 (1.5± 0.5)× 10−10 [33], 8× 10−12 [28]

β85Rb,6Li (5.0± 2.5)× 10−11 . . .β87Rb,6Li (1.7± 0.7)× 10−11 . . .

electronic state and relax to a lower state during the collision converting the difference of internal energiesinto relative kinetic energy. If the resulting velocities are large enough, the atoms will escape from the MOTdespite the dissipative radiation pressure forces. In the latter case, the colliding pair undergoes a spontaneousRaman scattering event to form a ground state dimer which is essentially transparent to the trapping lightand both atoms are lost from the MOT. If all of the Li-Rb light assisted collisions formed ground state dimers,one would expect the heteronuclear terms to be reciprocal, β6Li,85Rb = β85Rb,6Li and β6Li,87Rb = β87Rb,6Li.On the other hand, conservation of energy and momentum implies that the kinetic energy evolved in aninelastic collision is not distributed equally among partners with unequal mass and therefore, because ofrecapture in the MOT, the heteronuclear loss coefficients are not expected to be reciprocal. For an inelasticcollision between atoms initially at rest, the velocity away from the center of mass will be different by themass ratio, which is a factor of more than 14 for lithium and rubidium. Certain collisions can thereforeproduce free lithium atoms with velocities well above and free rubidium atoms with velocities well belowthe MOT capture velocity. Consider, for example, an inelastic collision between a ground state 87Rb andan excited state 6Li atom which induces fine structure relaxation in the lithium atom. This would evolvean energy of h × 10 GHz (the 6Li fine structure splitting) accelerating the 87Rb to 2.5 m/s and the 6Li to35.3 m/s. Given a typical MOT capture velocity of 20 m/s, this could produce lithium loss with little or norubidium atom loss. Ground state hyperfine relaxation of rubidium (evolving 6.8 and 3.0 GHz for 87Rb and85Rb, respectively) would produce similar results and also contributes to the heteronuclear loss terms. Inthis work, we find the β6Li,85Rb and β6Li,87Rb terms are a factor of 10 larger than the β85Rb,6Li and β87Rb,6Li

terms implying most of the collisions result in unbound atoms and not ground state molecules.In summary, we have presented an apparatus for simultaneously trapping either 85Rb or 87Rb and 6Li from

an effusive lithium oven without the use of a Zeeman slower. This dual MOT is capable of collecting over(7±2)×107 87Rb or 85Rb atoms and (8±2)×107 6Li atoms. The use of a miniature atomic oven placed closeto the trapping region yields a compact vacuum system while still producing adequate lithium ensemblesfor this and other work. We have presented the features of our apparatus, described the optimization andcharacterization of the dual MOT, and presented measurements of interspecies collisions in Li-Rb mixtures.

B.G.K. acknowledges support from the Canadian Institute for Advanced Research. This research wassupported by the Canadian Foundation for Innovation, and the Natural Sciences and Engineering Research

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Council of Canada.

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