An Adaptable Dual Species Effusive Source and Zeeman Slower Design Demonstrated with Rb and Li
William Bowden, Will Gunton, Mariusz Semczuk, Kahan Dare, Kirk W. Madison
AAn Adaptable Dual Species Effusive Source and Zeeman Slower Design Demonstratedwith Rb and Li
William Bowden, ∗ Will Gunton, Mariusz Semczuk, Kahan Dare, and Kirk W. Madison
The Department of Physics and Astronomy, University of British Columbia, Vancouver, Canada (Dated: November 12, 2018)We present a dual-species effusive source and Zeeman slower designed to produce slow atomicbeams of two elements with a large mass difference and with very different oven temperature re-quirements. We demonstrate this design for the case of Li and Rb and achieve magneto-opticaltrap (MOT) loading rates equivalent to that reported in prior work on dual species (Rb+Li) Zee-man slowers operating at the same oven temperatures. Key design choices, including thermallyseparating the effusive sources and using a segmented coil design to enable computer control of themagnetic field profile, ensure that the apparatus can be easily modified to slow other atomic species.By performing the final slowing using the quadrupole magnetic field of the MOT, we are able toshorten our Zeeman slower length making for a more compact system without compromising per-formance. We outline the construction and analyze the emission properties of our effusive sources.We also verify the performance of the source and slower, and we observe sequential loading rates of8 × atoms/s for a Rb oven temperature of 120 ◦ C and 1 . × atoms/s for a Li reservoir at450 ◦ C, corresponding to reservoir lifetimes for continuous operation of 10 and 4 years respectively.
The ability to trap and cool multiple atomic specieshas garnered much interest within the cold atom commu-nity because the complex interactions within these sys-tems give rise to a diverse range of physical phenomena.Quantum degenerate Fermi-Fermi [1, 2], Fermi-Bose [3–6], and Bose-Bose [7–9] gases allow for the study of novelstates of matter which cannot be investigated in singlespecies experiments. In particular, mixtures with largemass ratios, like those species presented here, are of inter-est for many body physics in the study of superfluidity[10], spin impurities, and Effimov physics [11]. Unfor-tunately, large mass differences also results in practicalchallenges when trying to slow multiple species.Abundant samples of cold atoms are also a prerequisitefor the formation of ultracold hetero-nuclear molecules[12–14] whose long range dipole-dipole interactions leadto exotic phases of matter and possible quantum infor-mation applications [15–17]. LiRb is an excellent candi-date for such studies as it is predicted to have the sec-ond largest electric inherent dipole moment of the alkalidimers and when in the triplet state has the added ad-vantage of a magnetic dipole moment [18]. Furthermore,for certain experiments, there are practical advantages tohaving the ability to trap multiple species. For example,one species with poor collisional properties (which limitthe efficacy of evaporative cooling) can be cooled sympa-thetically via interactions with the other species [19–22].In other cases, one species can serve as an atomic de-tector to measure properties of the system, as has beendemonstrated for thermodynamic measurements [23, 24].Creating large samples of cold atoms while still main-taining a good vacuum in the trapping region can beachieved by creating an atomic beam with an effusiveoven separated from the trapping region by a differen-tial pumping tube and by decelerating the beam before ∗ [email protected] capture in a MOT using a Zeeman slower. Because theslowing of different species, especially those with very dif-ferent masses, requires different magnetic field profiles,some multi-species experiments rely on a separate effu-sive source and Zeeman slower for each species. How-ever, to achieve a more compact setup, several realiza-tions of multi-species Zeeman slowers have been devel-oped (both dual [25, 26] and triple species [27, 28]).These approaches have dealt with the complications ofdual species sources and Zeeman slowers in various ways.In this work, we present and demonstrate a designthat combines several key elements from previous work toachieve a compact, simple to fabricate dual–species effu-sive source and Zeeman slower adaptable to and effectivefor a wide variety of species combinations. We exper-imentally demonstrate with Rb and Li that our designis well suited even for species combinations with largemass differences and with effusive sources requiring verydifferent operating temperatures. In particular, we ob-serve loading rates of 8 × Rb atoms/s for a reservoirtemperature of 120 ◦ C and 1 . × Li atoms/s with areservoir temperature of 450 ◦ C, corresponding to reser-voir lifetimes of four and 10 years respectively. These Rband Li loading rates are equivalent to those reported inprior work on multi-species Zeeman slowers operating atthe same oven temperatures.While our design achieves versatility and optimal per-formance for the sequential loading of the two species,in part, by including electronic switching between differ-ent magnetic field profiles as previously demonstrated byParis-Mandoki et al. [29], our design differs substantiallyfrom that work in two key respects that make ours easierto build and more generally applicable to multi-speciesslowers.The elements of our design include the following threekey features. (1) We create our atomic beam using acompact source composed of two thermally and physicallyseparated effusive ovens with microtube array output noz- a r X i v : . [ phy s i c s . a t o m - ph ] N ov zles for extended operational lifetimes. The separationof the beam output nozzles avoids the complications as-sociated with a common mixing chamber such as backflow contamination of the reservoirs and chemical reac-tions within the mixing chamber [25, 26] and allows forthe independent and optimal temperature operation foreach source. Our design was inspired by the three speciesatomic beam created by Wille et al. ; however, unlike theirdesign which required highly specialized machining, oursources are made almost exclusively from standard vac-uum parts [27, 28]. (2) We generate our Zeeman slowing magnetic fieldprofile with a segmented coil design that enables com-puter control of the field profile thus allowing switch-ing between the optimal operation of the slower for eachspecies. This feature also permits the adaptation of theslower to a new and different species without physicalchanges to the slower section. Our slower coil consists ofa set of eight independent solenoids and is very similarto the design shown to be very effective for a Cs+Li dualspecies slower created by Paris-Mandoki et al. [29]. (3) We mitigate the problem of beam blooming by dis-engaging the atoms from the Zeeman slowing light at theend of the slower using a magnetic field profile with asharp drop created by a final disengagement coil and al-lowing the final stage of slowing to occur inside the MOTtrapping region.
Beam blooming occurs when the trans-verse velocity spread of the atomic beam (continually in-creasing because of transverse heating) becomes signifi-cant compared to the longitudinal velocity of the beam(which is decreasing during slowing). If this occurs in-side the slower or just beyond it, the atomic beam maydiverge so much that a significant fraction of the atomswill not reach the MOT. The growth of the transversevelocity spread because of the reemission of absorbedphotons during slowing is proportional to the geomet-ric mean of the recoil velocity and the velocity differencefrom slowing [26]. For this reason, beam blooming isa much more severe problem in light species (here thegrowth of the transverse velocity spread in Li is a factorof 8 larger than for Rb after slowing), and mitigating thiseffect has been approached in a variety of ways includingadding transverse cooling inside the Zeeman slower [ ? ],minimizing the distance (to 15 cm) between the end ofthe slower and the MOT [26], and matching the MOTquadrupole field to the Zeeman slowing field to achievethe final slowing stage inside the MOT region [29]. Inorder to avoid the additional expense and complicationsof a transverse cooling stage and to relax the constraintthat the MOT be close to the end of the slower (requiredfor the field matching slowing design of Paris-Mandoki etal. [29]), we chose to simply disengage our atomic beamfrom the slower at a high velocity allowing the atoms tomove a relatively long distance to the MOT region with-out loss from beam divergence and then to complete thefinal stage of slowing inside the MOT trapping regionby using the MOT quadrupole field. This feature wasparticularly important for our realization which involved the use of standard UHV parts including a long quartzto stainless transition connecting our quartz cell to ourvacuum system.Section 1 of this paper describes the design and con-struction of the Zeeman slower and effusive sources whilehighlighting some important considerations when design-ing multi-species cold atom experiments. Section 2 val-idates the performance of the system by loading MOTsof both species and discusses the results and their impli-cations for slowing other atomic species. I. DESIGN AND CONSTRUCTIONA. Effusive Sources
Effusive sources are a common starting point for mostlaser cooling experiments and accurately predicting theiremission properties is critical to ensuring proper perfor-mance. Reloading the source after its depletion is a non-trivial task as it can potentially compromise the vacuumand often requires baking all or part of the system toachieve the desired base pressure. For this reason, it isdesirable to maximize the lifetime of the effusive sourcewithout reducing the center line intensity of the atomicbeam. One common approach is to use a recirculatingor candlestick source where thermal gradients wick backand recollect atoms which are emitted off-axis [30]. Thedownside of such sources is their complexity in designand operation. An alternative is the use of arrays of largeaspect ratio microtubes. The microtubes collect the ma-jority of atoms exiting off-axis and emit some fractionback into the reservoir without compromising the cen-ter line intensity of the atomic beam. This increases thelongevity of the source without reducing loading rates.In the regime where the mean free path of atoms ismuch longer than the length of the tube, the rate at whichatoms are emitted from the effusive source through anopening of area A containing an atomic vapor of density n with mean velocity ¯ v is N = nAκ ¯ v , (1)where the parameter κ is the Clausing factor and is de-rived from the geometry of the exit channel [31, 32]. Thedesign of such effusive sources for multi-species Zeemanslowers is complicated since they require collinear atomicbeams. One approach is to connect multiple reservoirs toa common mixing chamber where the atoms exit via thesame opening [25]. The steady state flux of the variousspecies out of the effusive source is controlled by the ratethey enter the mixing chamber. Care needs to be taken toprevent back flow between reservoirs and possible chem-ical reactions within the mixing chamber. Furthermore,the temperature of the mixing chamber must be keptwarmer than the hottest reservoir to prevent condensa-tion, which results in a higher mean velocity for atomsleaving the source than could otherwise be achieved withseparate sources. This is especially problematic when theelements have vastly different vapor pressures at a giventemperature, as it is the case when working with mostalkali and alkali-earth mixtures. We elected to follow analternative approach demonstrated by Wille et al. [27]of having separate sources with no mixing chamber toavoid such complications while still producing paralleland overlapping atomic beams by offsetting slightly theiroutput ports. This ensures our design is easily adaptedto accommodate different atomic species.To simplify the design over that presented by Wille etal. , the entire Li source and the majority of the Rb sourcewas made from off-the-shelf vacuum components. The Lisource was made from a 1.33 (cid:48)(cid:48) ConFlat nipple sealed onboth sides with a ConFlat blank. A 4 mm × µ m. Unlike othermicrotube designs which require a retaining plug or bar[33], we found that press fitting the tubes held them suf-ficiently secure and well aligned. All gaskets within theLi oven are made from annealed nickel because coppercannot maintain a UHV seal as it is quickly corroded bythe hot Li. During initial testing, copper gaskets wereused and failed within a few hours to days dependingon the operational temperature. Prior to loading thesource, the Li (which was stored in a petroleum ether)was cleaned inside an argon filled glove bag by rinsing itin acetone and then cleaving off the outer oxidized layers.Approximately 3 g of Li was loaded into the oven, whichgives an estimate source lifetime of four years at a contin-ual operational temperature of 450 ◦ C. Common to mostmircotube sources, the outlet is kept warmest to preventclogging. However, the resulting temperature gradientleads to thermal wiking of the molten Li towards thehottest region (the outlet) as in the operation of a stan-dard heat pipe. During testing, we observed molten Libeing pulled through the microtube opening by capillaryaction which completely depleted the source. To preventthis, we lined the oven with a nichrome mesh to which Lipreferentially adheres and helps to ensure it remains inthe source. The mesh ensures that even with large tem-perature gradients, the liquid Li remains confined to theinside of the source and does not contact the microtubes.The Rb source is slightly more complex in design asthe sample, which has a very high vapour pressure at el-evated temperatures, must remain sealed in a glass am-pule which is broken in-situ after the bakeout process.The ampule’s base and top are held by two modified CF-blanks connected by a flexible bellows which is used tocrack the ampule [34]. In order for the Rb and Li atomicbeams to be parallel and only slightly offset, the bellowsis connected to a hollow stainless cylinder which extendsinto the vacuum system and ends directly below the Liexit channel. A 4 mm × FIG. 1. Key components of the effusive sources: (A) Rboven with microtube array, (B) Li oven cap with microtubearray, (C) close up of Rb microtube array. top of the cylinder prior to being press fitted with micro-tubes. The key components of both sources are shown inFigure 1.
B. Dual Species Zeeman Slower
Zeeman slowers have been used extensively in ultra-cold atom experiments to produce beams of slow atomsas they are simple to construct, require relatively lowpower in the slowing lasers, and are robust against de-viation in magnetic field or misalignment. Alternativeapproaches for loading MOTs include transferring atomsfrom a 2D MOT [35, 36], loading atoms directly from abackground pressure produced by a dispenser [37], andcapturing the unslowed atomic beam emitted by an oven[38]. The 2D MOT approach has been successfully im-plemented for loading multiple species [39, 40], but issignificantly more complex and expensive than alterna-tive designs (such as a Zeeman slower) primarily due thehigh power requirements for cooling. The dispenser ap-proach is the simplest to implement, but only works forspecies with appreciable vapor pressure at room temper-ature such as Rb. For elements such as Li where the va-por pressure is exceedingly low at room temperature, anoven producing an atomic beam with direct line of sightto the MOT is required. Having dispensers or atomicovens close to the trapping region can result in higherbackground pressures that limit the trap lifetime andthus the achievable atom number in the MOT[41, 42].However, such an approach has proven successful in theproduction of degenerate gases of Li [43].By placing the atomic oven further away from the trap-ping region, differential pumping techniques can be usedto reduce the contribution of the background pressure inthe trapping region due to the hot atomic sources. Tooffset the reduction in the trappable atom flux resultingfrom moving the oven away from the MOT, a Zeemanslowing stage is used to slow fast moving atoms to a ve-locity which can be captured by the trap.Zeeman slowers are classified as one of three types de-pending on the polarization of the slowing light and mag-netic field which in turn determines the atomic transitionthat is used for slowing. The classifications are σ + (de-creasing magnetic field), σ − (increasing magnetic field),and spin-flip (magnetic field has zero crossing at somepoint in the slower) [44]. The magnetic field profile forthe σ + slower, which is presented in this work, is givenby B ( z ) = (cid:126) kv c µ (cid:115) − zamv c − (cid:126) δµ (2)where k is the wavevector of the slowing beam, v c is thecapture velocity of the slower (i.e. the largest velocityclass it can slow), µ is the magnetic moment of the tran-sition, a is the deceleration, and δ is the laser detuning.We note that because of power broadening, the slowingof a particular velocity class can and may occur before itreaches the magnetic field at which it is exactly on res-onance with the slowing light. In addition, if the atomstemporarily fall out of the cycling transition and are re-pumped back into it (see discussion below), the slowingmay occur just after the location in space where they areexactly on resonance with the slowing light. The upperlimit on deceleration, a max , imposed by the finite scatter-ing rate constrains the maximum magnetic field gradientwhich can be used for slowing to (cid:12)(cid:12)(cid:12)(cid:12) dB ( z ) dz (cid:12)(cid:12)(cid:12)(cid:12) (cid:28) (cid:126) ka max µv ( z ) , (3)commonly referred to as the adiabatic slowing condition[45]. In practice, the magnetic field is stretched spatiallyby a factor η which relates the deceleration experiencedby the atoms to a max via a = ηa max . If this gradientis exceeded, atoms will fall out of resonance with theslowing beam and will stop decelerating. In this work,we actually use this phenomenon to disengage the atomsfrom the slower to mitigate beam blooming and to ensurethey are not stopped or turned around before reachingthe MOT. The unintended stopping and reversing of theatomic trajectories in the Zeeman slower is a primaryconsideration when optimizing its performance.The maximum gradient is typically different for variousatomic species which limits the feasibility of simultaneousslowing. In general, the ratio η η = m µ k Γ m µ k Γ , (4)must be close to unity for efficient simultaneous slowing.For Li and Rb this ratio is 0.04 (predomintly due to thelarge mass difference). This greatly reduces the effective-ness of simultaneous slowing by using a fixed current or FIG. 2. Experimental apparatus showing the two effusivesources (Li, Rb), cold finger (CF), beam shutter (BS), differ-ential pumping tube (DP), and Zeeman slower (ZS). The insetshows the trajectory of the two atomic beams for reference.Inset A shows the location of the MOT, as indicated by thered circle, within the science section connected to the end ofthe slower. Inset B shows co-propagating atomic beams fromthe effusive sources. permanent magnets [46] design. Simultaneous slowingof the Li and Rb has been demonstrated, but it requiresthe magnetic field to be tailored such that specific regionsalong the slower cool different species [26]. Alternatively,one could use multiple Zeeman slowers at the expense ofreduced optical axis [47]. Instead, we chose to dynami-cally switch the magnetic field profile to load the MOTand optical dipole trap (ODT) sequentially. Althoughthis results in slightly longer experimental cycle time, wecan achieve much larger loading rates as we can indepen-dently tune the MOT and Zeeman slower to the opti-mal loading parameters for both species. This sequentialloading technique has been shown to be an effective ap-proach to trapping Li and Rb in an ODT [48].We elected to use a σ + design as the decreasing mag-netic field has two main advantages. First, as a result ofthe atoms moving fastest in the large magnetic field re-gion where the Zeeman effect almost cancels the Dopplershift, the required detuning of slowing beam is smalland can be easily derived from our MOT lasers using anacousto-optic modulator. Second, the decreasing mag-netic field of the slower can be mated with the magneticfield from the quadrupole coils of the MOT such that theslower length can be made significantly shorter as theatoms complete the final stage of slowing after enteringthe MOT trapping region. Using the MOT field to pro-vide slowing has been used in our previous experimentalapparatus [43] and in similar dual species slowers [29].Critical to the success of our design, where the end ofthe slower and the MOT region are not in close prox-imity (required for smooth field matching between theend of the slower and the MOT region as demonstratedpreviously [29]), is our use of a coil at the end of theslower to produce a magnetic field with opposite polar-ity to disengage atoms from the slower by violating theadiabatic slowing condition. By varying the current, wecan control the velocity at the point of disengagement toensure the atoms are resonant with slowing laser whenthey reach the MOT region. As discussed earlier, usingthe MOT field for slowing has the added benefit that thefinal stage of slowing is done close to the trapping re-gion which helps to mitigate the blooming of the atomicbeam. Blooming occurs because the slower reduces thevelocity component parallel to the axis of the slower whileheating the radial velocity distribution due to sponta-neous re-emission of the absorbed light. This leads to anincreasing divergence of the atomic beam as the atomsdecelerate. The result of this is that the divergence an-gle of the beam upon leaving the slower (proportional toratio of initial velocity to the final velocity) is continu-ously increased with more slowing and this counteractsthe benefit of lengthening the slower in order to captureand slow atoms with even higher initial velocities.To produce the Zeeman slower field, we elected to useeight solenoids with computer controlled currents allow-ing for automated optimization of the magnetic field.Motivated by the fact that elongating the slower to in-crease the capture velocity leads both to increasing powerdissipation and to diminishing returns due to beam diver-gence, we elected to build a relatively short slower mea-suring 24 cm which is easily air cooled using the metalfins which separate the coils. The slower is typically op-erated with less than a fifty percent duty cycle, but wefind that the fins provide sufficient heat transfer to theair such that the slower can be operated continuously atthe largest required currents with the hottest coil onlyreaching a temperature of 60 ◦ C.One drawback of the σ + design compared to a σ − andspin-flip slower, is that the slowing beam is much lessdetuned resulting in a larger radiation pressure exertedon the MOT. To reduce the radiation pressure, we focusthe slowing beam at the entrance of the slower such thatthe beam is large at the MOT and the divergence moreclosely matches that of the atomic beam. This focussinghas the added benefit that the beam curvature helps toprovide some radial confinement. In other work, adding ahole in the slowing beam has shown to effectively addressthis drawback [49].Prior to constructing the slower, we simulated theatom trajectories as they decelerated within the slow-ing and trapping fields. The virtual slower adopts a twolevel model for the atom and solves the equation of mo-tion subject to a positionally dependent radiation pres-sure. The result of the simulation is a bunching of atomsin phase space and can be used to estimate the propercurrent for the disengagement coil and slowing beam pa-rameters. If the atoms leave the slower going too slowlythey risk the possibility of being turned around, while ifthey are traveling too fast they will not be captured bythe MOT. The first effect is more likely for Rb as itsexit velocity is lower than that of Li. These effects areillustrated in the phase space plots shown in Figure 3. C. Vacuum System
The Zeeman slower separates the science section of theexperimental apparatus from the effusive source section.By decreasing the length of the slower, the isolation be- L i S p ee d ( m / s ) − . − . − . − . − . − . − . . Distance from the MOT (m) R b S p ee d ( m / s ) − . − . − . − . − B F i e l d ( G ) − . − . − . − . − B F i e l d ( G ) FIG. 3. Phase space trajectories for both species in theZeeman slower and quadruple field of the MOT coils. Themagnetic field was chosen to illustrate how improper choice ofthe disengagement coil current can cause atoms to either passdirectly through without further slowing (top panel) becausethey leave the slower moving too quickly, or turn around be-fore reaching the trap (bottom panel) because the atoms leavethe slower moving too slowly. Inset figures show the magneticfield produced by the MOT coils and Zeeman slower. tween the section is reduced requiring the addition ofa differential pumping tube with an estimated hydro-gen conductance of 1 L/s immediately before the slower.Both the source and science side are pumped by an Agi-lent VacIon Plus 20 Starcell ion pump and SAES Capac-iTorr D 400-2 non-evaporatable getter.The Li effusive source is loaded with Li and baked sep-arately at 500 ◦ C for 6 hours in order to remove any re-maining mineral oil or contaminants from the loadingprocess before being back filled with argon and attachedto the main apparatus. The entire apparatus is thenbaked for one week at 200 ◦ C.Long term exposure of the ion pumps to a signifi-cant background pressure of Rb generates filaments that,through field emission, produce large leakage currents.This emission and heating limit the pumping perfor-mance by vaporizing the Rb and other materials origi-nally stored in the pump. It has been suggested that thelifetime of an ion pump exposed to a high vapor pressureof Rb can be prolonged by heating it continuously aboveits melting temperature [50]; however, we choose here toprotect the pump by introducing a cold finger just afterthe Rb oven. Therefore, a copper feed through is placedinside the source section which is cooled externally usinga TEC in order to condense Rb [51].Not shown in Fig. 2 is an additional UHV cross towhich is connected the Agilent VacIon Plus 20 Star-cell ion pump and SAES CapaciTorr D 400-2 non-evaporatable getter. Also on the cross is a windowthrough which the Zeeman slowing light is introduced.In order to minimize the coating of that window due tothe Li atomic beam, we heat the window and we close thebeam shutter (shown in Fig. 2) immediately after load-ing the MOT to minimize the time during which the Libeam is incident on the window.
II. RESULTS AND DISCUSSIONA. The Effusive Source
Prior to assembling the entire apparatus, we measuredthe transverse velocity distribution of the emitted fluxfrom the Li effusive source. To characterize the source,the emission was probed using a transverse laser whichwas scanned over the atomic D2 transition for the twoground hyperfine states. The flange containing the mi-crotubes was heated to 450 ◦ C using metal band heaterswhile the opposite end was kept at approximately 15 ◦ Ccooler. We developed a model [52] for the expected fluo-rescence signal based on the predicted angular and veloc-ity distribution of the atoms leaving the effusive source.The expected angular distribution of a transparent chan-nel of a given aspect ratio has been discussed in lengthin literature [32, 53, 54] and the velocity distribution, F BeamMB ( v ), within the atomic beam emitted from a reser-voir at a temperature T is [55] F BeamMB ( v ) = m v k T exp (cid:34) − (cid:18) kT vm (cid:19) (cid:35) . (5)Based on the experimental data shown in Fig. 4, themodel estimates an average beam divergence of approxi-mately 3 ◦ which corresponds to a microtube aspect ratioof approximately 20; half the expected value of 40 giventhe microtube diameter (250 µ m) and length (1 cm). Apossible explanation could be a slight misalignment be-tween microtubes or emission from gaps between tubeswhere they are not well packed. The total flux of atoms atthis operational temperature was measured to be 9 × atoms/s while the predicted value using Equation 1 is4 × atoms/s which is in reasonable agreement as itneglects any emission from the gaps between tubes or un-certainty in source temperature. The Rb source was nottested prior to installation into apparatus as it requiredbreaking the ampule.Characterization of the effusive source with respect toatom loading rate, MOT lifetime, steady state atom num-ber, and the lifetime of Li atoms loaded into an ODT atvarious operation temperatures was performed with op-timized settings for the Zeeman slower. We note that thelifetime of atoms in the ODT (given by the inverse single-particle loss rate) is a better and more relevant proxy FIG. 4. Oven florescence (black circles) produced by theprobe beam and the best fit of the numerical model (solidline, see text for details). The inset shows the experimentalsetup with the atomic beam going from right to left whileprobed by a transverse beam. In practice, the photodiodeviewport is coated by Li during operation and it is best toplace the detector along the other available axis orthogonalto the probe and atomic beams. for the quality of the vacuum than the MOT lifetime asthere are additional loss mechanisms present in the MOTother than just collisions with background gases. Theseadditional losses include light assisted collisions such asradiative escape and fine structure changing collisions,and they become more pronounced for larger MOT atomnumbers where the atomic density is higher.The Li oven temperature was increased while the Rbsource was kept at room temperature. As the temper-ature increased, the loading rate and steady state atomnumber in the MOT increased while the ODT lifetimedecreased steadily. At the lowest operating temperature(346 ◦ C), the Li MOT lifetime is more than a factor of 2longer than the ODT lifetime. This is expected given theMOT trap depth is is more than three orders of magni-tude larger than the ODT [56]. However, as the sourcetemperature is increased, the MOT number and densitygrows, and the light assisted collisional losses in the MOTbecome the dominant loss mechanism. The MOT lifetimeis observed to then drop below the ODT trap lifetime.Once the steady-state number is large enough, the MOTgrows in size with a constant density and the contribu-tion to the single-particle loss rate (i.e. lifetime) fromlight assisted losses becomes constant. As the oven tem-perature is further increased, the ODT lifetime is reduceddue to increased collisions with background gases emit-ted by the oven. Because the ODT depth is less than theMOT, the lifetime reduction is larger for the ODT thanfor the MOT [57].To characterize the Rb slower, the Rb oven temper-ature was increased while the Li source was kept at aconstant 356 ◦ C. The loading rate and steady state atomnumber increase monotonically while the ODT lifetimedecreases. For the Rb MOT, the light assisted collisionallosses are already dominant at the very lowest atom num-
340 360 380 400 420 440
Li Oven Temperature ( o C) L i L o a d i n g R a t e ( a t o m s / s ) L i S t e a d y S t a t e N u m b e r ( a t o m s ) L i OD TL i f e t i m e ( s ) L i M O TL i f e t i m e ( s ) FIG. 5. The effect of Li source temperature of Li loading rate(black dots), steady state atom number (blue trianges), MOTlifetime (red diamonds), and ODT lifetime (green squares).Due to density dependent loss mechanism within the MOT,the lifetime of ODT is a better estimate of the backgroundpressure inside the science section of the apparatus. Here,the Rb source is kept fixed at room temperature (20 ◦ C, i.e.,“off”). Note the typical operating temperature of the Rbsource is 100 ◦ C
40 60 80 100 120
Rb Oven Temperature ( o C) R b L o a d i n g R a t e ( a t o m s / s ) R b S t e a d y S t a t e N u m b e r ( a t o m s ) L i OD TL i f e t i m e ( s ) R b M O TL i f e t i m e ( s ) FIG. 6. The effect of Rb source temperature of Rb loadingrate (black dots), steady state atom number (blue triangles),MOT lifetime (red diamonds), and lifetime for Li confined ina ODT (green squares). For rubdium, light assisted collisionallosses are dominant for even the lowest density traps result-ing in lifetimes shorter than those observed for the Li ODT.Here the Li source was held fixed at its standard operationaltemperature of 360 ◦ C. bers (achieved at the lowest source temperature) and thusthe lifetime of a Rb atom in the MOT is always less thanthat of a Li atom in the ODT. Note that for these mea-surements, the Rb MOT was not present. Therefore, theLi lifetimes in the ODT only represent the loss rate in-duced by collisions from atoms in the atomic beam andbackground gas and do not include any additional lossesthat might occur due to hetero-atomic light assisted col-lisions if the atomic clouds were well overlapped [38]. B. The Zeeman Slower
Of interest for the design of the Zeeman slower is theeffect of slower length and the intensity of the slowinglight on loading rate. In addition, the necessity of addi-tional repump light needed to optically pump atoms outof other ground states should be considered. While wetarget with our σ + polarized light a closed (i.e. cycling)transition for the slowing of both Rb and Li atoms, im-perfect polarization can lead to off resonant excitationto excited state levels that can decay back to differentground states that are no longer in resonance with theslowing light and therefore are no longer decelerated ef-fectively. Empirically, we find that for the operation ofthe Rb Zeeman slower, an additional repump laser wasrequired. We find that such additional repumping lightis not needed for Li, and we believe this is, in part, be-cause the off resonant excitation to other levels is muchmore strongly suppressed than in Rb because of the muchlarger slowing magnetic fields used. This is discussedmore below.For optimizing the MOT loading rate, the expecteddetuning and field profile was set based on the virtualslower simulations, then each coil was scanned about itsset point to optimize the loading rate. In all cases, the op-timal setpoint was within a few percent of the predictedvalue. This process was repeated for increasing η untila decrease in loading rate was observed. Table I showsthe relevant operational parameters used for testing. Wewere able to observe small MOTs for both species whenthe slowing beam is off. Activating the slowing beamand using the magnetic field produced by the quadrupolecoils of the MOT as the sole Zeeman slower leads to a fac-tor of 6-8 improvement in loading rate for both species.Activating the remaining Zeeman slower field further im-proved the loading by a factor of 5 and 12 for Li and Rb,respectively. TABLE I. Loading parameters for both MOTs.Rb LiSlowing Beam Pump Detuning (MHz) a -85 -76Slowing Beam Pump Power (mW) 15 40Slowing Beam Repump Detuning (MHz) b c
35 30MOT Repump Beam Detuning (MHz) 0 -40MOT Repump Beam Power (mW) c
10 40MOT Axial Gradient (G/cm) 15.4 49 a The pump detuning for Rb is with respect to the F = 3 → F (cid:48) = 4 D2 transition while for Li it is with respect tothe F = 3 / → F (cid:48) = 5 / b The repump detuning for Rb is with respect to the F = 2 → F (cid:48) = 3 D2 transition while for Li it is with respect tothe F = 1 / → F (cid:48) = 5 / c Beams have a radius of 9 mm, and the power is split betweenthree retroflected arms of the MOT
To change the slower length, the number of coils acti-vated was varied while monitoring the loading rate. Topredict the loading rate, the flux of slowed atoms pass-ing through the MOT was calculated by integrating overthe angular and velocity distribution of atoms leavingthe effusive source. For each velocity, there is a criti-cal exit angle for atoms leaving the effusive source abovewhich they will miss the MOT after slowing. This angleis determined from basic kinematics given the constantdeceleration along the slower and does not account forthe added reduction in captured atoms due to transverseheating. This angle, along with the capture velocity ofthe slower, sets the limits of integration which in turndetermine the flux that the MOT can capture. The scal-ing of loading rate with length is highly sensitive to thevelocity group within the distribution being slowed. ForLi, the velocity distribution is peaked at 1700 m/s, whilethe maximum capture velocity is approximately 600 m/s.As a result, the atoms slowed are from the the low ve-locity tail of the distribution. Directly integrating theMaxwell-Boltzmann distribution up to capture velocityfor small velocities leads to v scaling. Combining thiswith the √ L scaling for the capture velocity, one mayexpect to see quadratic scaling of the loading rate withinitial increases in slower length if the divergence of theatomic beam is disregarded. In contrast, for Rb the dis-tribution is peaked at much lower velocity of 300 m/s andatoms are predominantly captured from the linear regionof distribution resulting in linear scaling of capture veloc-ity with slower length using the same argument. Experi-mentally, we observe linear scaling of the loading rate forboth species, and not quadratic for Li, which is in goodagreement with our numerical simulation. The reducedloading rate for Li is a result of the larger divergence ofthe atomic beam upon exiting the slower, as comparedto Rb, given its much higher initial velocity and lightermass.It is challenging to accurately predict the loading ratefor two reasons: 1) it is difficult to properly estimate theactual area of the effusive source outlet and account formicrotube misalignment and the atomic emission fromgaps and 2) it is difficult to know the exact source tem-perature to which the flux is exponentially sensitive. InFigures 7 and 8, we compare the measured and predictedloading rates on slower length, and we find that the modelprovides reasonable estimates for the expected flux givenour uncertainty in the source temperature and a micro-tube array assembly (10% uncertainty in microtube num-ber).Finally the effect of the slowing beam intensity on load-ing rate was investigated. For Li, we observed an im-proved loading rate with beam power while for Rb wesaw decrease in loading rate at higher intensities. Weattribute the roll over of the Rb loading rate as resultingfrom atoms being stopped prior to reaching the MOTat the higher slower intensities. The Rb beam is moresusceptible to this than the Li beam because of its muchlower exit velocity and smaller slowing field. FIG. 7. The MOT loading rate for Li as function slowerlength at a source temperature of 360 ◦ C. The shaded regionis the expected loading rate based on our model given a ± ◦ Ctemperature uncertainty and 10% uncertainty in microtubenumber. .
02 0 .
04 0 .
06 0 .
08 0 .
10 0 .
12 0 .
14 0 .
16 0 . Slower Length (m) L o a d i n g R a t e ( a t o m s / s ) FIG. 8. The MOT loading rate for Rb as function slowerlength at a source temperature of 100 ◦ C. The shaded region isthe expected loading rate based on our model given a ± ◦ Ctemperature uncertainty and 10% uncertainty in microtubenumber.
Slowing Beam Pump Power (mW) . . . . . . . . . R b L o a d i n g R a t e ( a t o m s / s ) . . . . . L i L o a d i n g R a t e ( a t o m s / s ) FIG. 9. The effect of slowing beam power on the MOTloading rate for Li (red squares) and Rb (black dots). Weattribute the roll over of the Rb loading rate as resulting fromatoms being stopped prior to reaching the MOT at the higherslower intensities.
III. THE ROLE OF REPUMPING
With this decreasing field slower, σ + polarized lightis used and the magnetic field profile is optimized foratoms in the cycling (i.e. closed) transition on the D2line (2 S / → P / for Li and 5 S / → P / forRb) between the ground and excited stretched states.These states correlate at zero magnetic field to | F =3 , m F = +3 (cid:105) and | F (cid:48) = 4 , m (cid:48) F = +4 (cid:105) for Rb and | F = 3 / , m F = +3 / (cid:105) and | F (cid:48) = 5 / , m (cid:48) F = +5 / (cid:105) for Li. For strong magnetic fields, large enough thatthe energy shift due to the magnetic field is large com-pared to the hyperfine splitting, the hyperfine couplingbetween J and I is disrupted and F is no longer a goodquantum number. In this case, the nuclear spin is de-coupled from the electron and m I will not be changedby the absorption or emission of a photon for an electricdipole transition. This limit is referred to as the hyper-fine Paschen-Back regime and it occurs at fields aboveabout 100 G for Li and above about a thousand Gaussfor Rb. For most of the initial slowing, Li is in thislimit whereas Rb is not. Thus the ground and excitedstretched states in Li are more accurately labeled by their m J and m I quantum numbers: | m J = 1 / , m I = +1 (cid:105) and | m (cid:48) J = 3 / , m (cid:48) I = +1 (cid:105) .The stretched-to-stretched state transitions are closedsince a Rb(Li) atom that absorbs a photon and is ex-cited into the | F (cid:48) = 4 , m (cid:48) F = +4 (cid:105) ( | m (cid:48) J = 3 / , m (cid:48) I = +1 (cid:105) )state can only decay back to the stretched ground state | F = 3 , m F = +3 (cid:105) ( | m J = 1 / , m I = +1 (cid:105) ). However,leakage out of this cycling transition can occur if the po-larization is not perfectly σ + . In this case, off resonantexcitation to other excited states can occur, and subse-quent decay out of these states may not necessarily bringthe atom back to the stretched state but rather to otherground states. In general, the optical transitions fromthese other ground states to the excited state manifoldwill not be in resonance with the slowing beam leadingto a sharp drop in the photon scattering rate, and as aresult the atoms will not be slowed properly as the adia-batic slowing condition will be broken.In the case of Rb, when the polarization is not perfectly σ + , off resonant excitation can occur from the stretchedground state to the | F (cid:48) = 4 , m (cid:48) F = +3 or + 2 (cid:105) states(these transitions are quite likely since their frequenciesat fields below 100 G are different from the stretched-to-stretched state transition by only a few tens of MHzcorresponding to only a few natural linewidths, Γ Rb =2 π × . | F (cid:48) = 3 , m (cid:48) F = +3 or + 2 (cid:105) states (the rate of these transitions is significantly lowerthan those to the F (cid:48) = 4 manifold because their resonantfrequencies are different from the stretched-to-stretchedstate transition by a few hundred MHz at 100 G, butless than 50Γ Rb ). Decay from the F (cid:48) = 4 states willreturn the atoms to the F = 3 ground state, and at lowmagnetic fields (below 100 G) the transition frequenciesfrom these states back to the F (cid:48) = 4 excited state are nomore than a 5Γ Rb away from the slowing light frequency. In this case, the scattering rate is still relatively highand atoms are optically pumped back into the stretchedstate before they have time to fall out of the slowingcycle by moving into a different region where they areoff resonant with the slowing light. In the case that offresonant excitation to the F (cid:48) = 3 manifold occurs, decayback to the F = 3 or F = 2 manifold is possible. Asdiscussed above, decay back to non-stretched states inthe F = 3 manifold does not lead to significant atom loss.However, decay back to the F = 2 manifold leads to acatastrophic drop in scattering rate from the slowing lightsince the transition frequency from the F = 2 manifoldto the F (cid:48) = 3 excited states is more than 3 GHz away(500Γ Rb ) from the slowing light frequency. Without lightto move them back to the F = 3 ground state manifold,the atoms are lost from the slowing.We note that for σ − (field decreasing) based Zeemanslowers where the opposite stretched states are targeted,the leakage out of the cycling transition due to imperfectpolarization can be dramatically intensified. This furthernecessitates the need for repumping atoms back to thecycling transition. In Rb, this enhancement has beenobserved and occurs at a magnetic field of 120 G whenthe | F (cid:48) = 3 , m (cid:48) F = − (cid:105) excited state crosses the | F (cid:48) =2 , m (cid:48) F = − (cid:105) excited state and the transition frequenciesto this other excited state is exactly equal to the slowinglight frequency [58]. In Rb, this crossing occurs below100 G and for Li it is irrelevant as it occurs below 10 G.Figure 10 shows the impact of adding repumping lightto the Zeeman slower beam on the loading rate of the RbMOT. In order to make this measurement, some of therepump light for the MOT was redirected into the slow-ing beam; however, since the slowing beam also traversedthe MOT and had a similar size as the MOT beamsat that location, redirecting light did not substantiallychange the total repump light provided to the MOT.The frequency of the repump light added to the slowingbeam was not frequency shifted as we the pump light.Rather, the repump light was exactly on resonance forthe F = 2 → F (cid:48) = 3 transition at zero magnetic field. Itis important to note that the Zeeman shift of this repumptransition varies with the m F value in the ground stateand it does not follow that of the stretched-to-stretchedstate transition, so there is no optimal detuning for therepump light. Despite not being frequency shifted tocompensate for the atomic beam’s Doppler shift and theZeeman shift, the repump light is nevertheless effective inreturning the atoms to the cycling transition when theyfall out of the stretched state. In particular, we observe astrong dependence of the captured flux on repump power.For a repump power of 12 mW we obtain the maximumin captured flux and additional light at this frequencydoes not further improve the loading rate.In the case of lithium, we observed a large capturedflux without any repump light added to the slowingbeam. While the same off resonant excitation mecha-nisms are present for lithium, there are several reasonswhy the leakage out of the stretched-to-stretched cy-0 Slowing Beam Repump Power (mW) . . . . . . N o r m a li z e d R b L o a d i n g R a t e FIG. 10. The effect of adding hyperfine repumping light tothe slowing beam on the loading rate of the Rb MOT. Thesedata were taken using the parameters listed in Table I, andthe rate is normalized to the peak loading rate. cling transition is smaller than in Rb. Firstly, Li is inthe hyperfine Paschen-Back limit for the slowing withinthe Zeeman slower itself. In this limit, the m I quan-tum number is unchanged by the absorption of a pho-ton and therefore none of the other excited states (with m (cid:48) J = 3 /
2) are excited by the slowing beam. In fact,there is only one other excited state (other than thestretched excited state, | m (cid:48) J = 3 / , m (cid:48) I = +1 (cid:105) ) to whichthe atom can go. This is the | m (cid:48) J = 1 / , m (cid:48) I = +1 (cid:105) state. From this state, atoms can decay back to the initialstretched state or to the | m J = − / , m I = +1 (cid:105) groundstate. The transition frequency from this m J = − / m (cid:48) J = 1 / | m J = 1 / , m I = +1 (cid:105) → | m (cid:48) J = 1 / , m (cid:48) I = +1 (cid:105) transi-tion is approximately 1 GHz (more than 150Γ Li ) differentfrom the slowing light frequency at 650 G, thus suppress-ing the rate of this off-resonant excitation by a factor ofmore than 2000 compared with the resonant scatteringrate on the stretched-to-stretched transition (assuming abeam intensity of 40 mW/cm ). During the final stageof slowing where the magnetic field is much smaller, theresulting suppression of these off resonant transitions issmaller. However, in our design, this final stage occursinside the MOT region where repump light for the LiMOT may help to mitigate this effect.We conclude by noting that we did not observe anyimprovement in the captured flux when the atomic beamwas exposed to repump light just after the oven output.In this case, the optical beam was perpendicular to theatomic beam and thus there was a negligible Dopplershift. We performed this test for both Rb and Li tocheck if the captured flux could be increased by optically pumping the atoms into upper hyperfine levels (and thusincrease the population of atoms in the stretched states)before they entered the Zeeman slowing region. We didnot observe an appreciable change in the captured flux. IV. COMPLICATIONS OF SIMULTANEOUS,MULTI-SPECIES OPERATION
There are a number of complications inherent to allmulti-species laser cooling experiments when simultane-ous trapping of the species is performed. For our applica-tion, the loading of the two species into an optical dipoletrap, all of the complications arising from simultaneousslowing and simultaneous containment of both species inthe MOTs can be avoided. In short, the sequential load-ing of the MOT and transfer of the atoms into the ODTis very effective, and this approach was used successfullyin prior measurements of the Feshbach resonances in theLi+Rb mixture [48]. In that work, the ODT and MOTswere not overlapped until the moment of transfer, and theonly atom loss incurred for the first species transferredwas due to background collisions during the loading ofthe second species. For high loading rates (less than asecond) and long trap lifetimes (more than 10 seconds)the loss from waiting for the other species to load is onthe order of 10% or less.However, there are applications for which simultaneousloading and storage in the MOT may be necessary. Twoexamples are photoassociation studies with the atomsheld in the MOT and the transfer of the laser cooledmixture to a magnetic trap for which sequential transfermade not be possible.For simultaneous slowing and trapping of multiplespecies, the first and most obvious complication is thatthe optimal Zeeman slower field profile and the optimalMOT magnetic field gradient may be different to thepoint of being incompatible for different species. For ex-ample, here we find empirically that the optimal MOTaxial field gradients for Rb and Li are 15.4 and 49 G/cmrespectively, differing by more than a factor of 3, andthe optimal initial field of the Zeeman slower for Li andRb differs by a factor of 6 due to the different adiabaticconditions. Consistent with prior observations, the LiMOT performance at the detunings and power listed inTable I showed dramatic improvements at high field gra-dients (above 30 G/cm) and the Rb atom number in theMOT is dramatically suppressed when operated at fieldgradients above about 28 G/cm [38]. These differencesarise from an interplay between the homonuclear light as-sisted collisional loss rates and the trap-depth recaptureprobability of the products of inelastic collisions (see thework of Ladouceur et al. and references therein [38]).Of course, if simultaneous operation of the MOTs is re-quired, a new field gradient and MOT parameters canbe found that are acceptable yet non–optimal for eachspecies.An additional complication arises in simultaneous op-1eration of the MOTs when the atom clouds overlap. Inthat case, heteronuclear light-assisted losses can occurfurther suppress the steady state atom numbers in theMOT. Prior work has shown that, under certain condi-tions, the Li atom number is more dramatically reducedthan the Rb atom number presumably due to differencesin the MOT trap depths and the re-capture probabilitiesof the collision partners accelerated by these these binaryinelastic collisions [38]. In the work presented here, be-cause we use a retro-reflection configuration for the MOTbeams and the return beams are less intense, the radi-ation pressure is imbalanced and the Rb and Li MOTsare observed to be offset from one another by a distancemore than their diameters. This offset is even more pro-nounced due to the different offsets produced by the Zee-man slowing beams. Thus we do not observe significantlight assisted losses when both species are present in theMOT.
V. CONCLUSION
We have presented a design for a multi-species effusivesource and slower which is applicable to the slowing of awide variety of species, even those with large mass differ-ences, and demonstrated the design with Li and Rb. Ourchoice of slower length was made to balance the marginalreturns on performance (as there is a linear scaling offlux with slower length) with the goal of creating a de-sign that is simple (for example, compact and without the need for water cooling) and easily adaptable to otheratomic species. By utilizing the quadruple magnetic fieldfor the MOT as a secondary slowing field, we were ableto further shorten the length of the slower. While it ap-pears that a longer slower would improve Li loading rates,we achieved comparable or higher loading rates to priorwork at similar oven operating temperatures. In partic-ular, we observe loading rates of 8 × atoms/s for aRb oven temperature of 120 ◦ C and 1 . × atoms/sfor a Li reservoir at 450 ◦ C, corresponding to reservoirlifetimes for continuous operation of 10 and four yearsrespectively. Based on simulations, we believe that forLi, the linear scaling was a result of divergence of theatomic beam, while for Rb it was due to the peaking ofthe thermal distribution of velocities leaving the source.
VI. ACKNOWLEDGMENTS
The authors also acknowledge financial support fromthe Natural Sciences and Engineering Research Councilof Canada (NSERC / CRSNG), and the Canadian Foun-dation for Innovation (CFI). W.B. would also like to alsoacknowledge NSERC support through the Canada Grad-uate Scholarships-Master’s program. This work was doneunder the auspices of the Center for Research on Ultra-Cold Systems (CRUCS). Finally, the authors would alsolike to thank Florian Schreck for his generosity with su-perb technical advice and the microtubes used for bothsources. [1] M. Taglieber, A. Voigt, T. Aoki, T. W. H¨ansch, andK. Dieckmann, Phys. Rev. Lett. , 010401 (2008).[2] A. Trenkwalder, C. Kohstall, M. Zaccanti, D. Naik, A. I.Sidorov, F. Schreck, and R. Grimm, Phys. Rev. Lett. , 115304 (2011).[3] G. Roati, F. Riboli, G. Modugno, and M. Inguscio, Phys.Rev. Lett. , 150403 (2002).[4] S. Ospelkaus, C. Ospelkaus, L. Humbert, K. Sengstock,and K. Bongs, Phys. Rev. Lett. , 120403 (2006).[5] I. Titvinidze, M. Snoek, and W. 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MOT magneto-optical trap