A compact single-chamber apparatus for Bose-Einstein condensation of 8 7 Rb
Igor Gotlibovych, Tobias F. Schmidutz, Stuart Moulder, Robert L. D. Campbell, Naaman Tammuz, Richard J. Fletcher, Alexander L. Gaunt, Scott Beattie, Robert P. Smith, Zoran Hadzibabic
AA compact single-chamber apparatus for Bose-Einstein condensation of Rb Igor Gotlibovych, Tobias F. Schmidutz, Stuart Moulder, Robert L. D. Campbell, Naaman Tammuz,Richard J. Fletcher, Alexander L. Gaunt, Scott Beattie, Robert P. Smith, and Zoran Hadzibabic
Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom (Dated: September 5, 2018)We describe a simple and compact single-chamber apparatus for robust production of Rb Bose-Einsteincondensates. The apparatus is built from off-the-shelf components and allows production of quasi-pure conden-sates of > × atoms in < s. This is achieved using a hybrid trap created by a quadrupole magnetic fieldand a single red-detuned laser beam [Y.-J. Lin et al. , Phys. Rev. A , 063631 (2009)]. In the same apparatus wealso achieve condensation in an optically plugged quadrupole trap [K. B. Davis et al. , Phys. Rev. Lett. , 3969(1995)]; we show that as little as mW of plug-laser power is sufficient for condensation, making it viableto pursue this approach using inexpensive diode lasers. While very compact, our apparatus features sufficientoptical access for complex experiments, and we have recently used it to demonstrate condensation in a uniformoptical-box potential [A. Gaunt et al. , arXiv:1212.4453 (2012)]. PACS numbers: 67.85.-d, 37.10.De
I. INTRODUCTION
Atomic Bose-Einstein condensates (BECs) are now widelyused for studies of many-body physics [1] and as brightsources for atom optics and interferometry [2]. Since the firstdemonstrations of condensation in magnetic [3–5] and opti-cal [6] traps, the development of experimental setups for BECproduction has generally taken two parallel routes. On onehand, some applications require ever more complex setups;these, for example, include multi-species experiments [7],single-particle detection [8] or hybrid systems combining neu-tral atoms and ions [9]. On the other hand, there has also beena continuing effort to design simple and inexpensive machinesthat are still suitable for many experiments [10–17].In this paper, we describe a particularly simple apparatus,built exclusively from off-the-shelf components, and our cool-ing procedure for production of Rb BECs. While beingcompact and consisting of a single vacuum chamber for bothlaser and evaporative cooling (see Fig. 1), our setup featuresBEC atom numbers and production rates comparable to mostmulti-chamber Rb setups, as well as sufficient optical ac-cess for complex experiments. By evaporative cooling in a hy-brid magnetic-optical trap introduced by Lin et al. [18], we re-liably produce quasi-pure BECs of > × atoms in < s.Using the same setup, we also explored condensation in an op-tically plugged quadrupole trap [5]. Specifically, we study theplugging laser power requirements for a range of plug-laserwavelengths and show that it is possible to achieve condensa-tion using as little as mW of plug power. This opens thepossibility of implementing this approach using inexpensivediode lasers. Recently, we have used this apparatus (in thehybrid-trap configuration) to demonstrate Bose-Einstein con-densation in a uniform optical-box potential [19]. This un-ambiguously shows that this simple and inexpensive setup issufficient for many non-trivial experiments requiring signifi-cant optical access to the atomic cloud.The article is structured as follows. In Sec. II we outline ourexperimental setup. In Sec. III we provide details of the lasercooling stage of our experiments. Evaporative cooling andcondensation in a hybrid trap are described in Sec. IV, while FIG. 1: Vacuum system: 1 - turbo pump port, 2 - valve, 3 - ion pump,4 - Rb dispensers, 5 - viewport, 6 - glass cell. We also show themagnetic coils for creating: 7 - quadrupole field, 8 - bias field, 9 -guide field, 10 - RF field. All coils except 9 and 10 are paired (onlyone coil per pair is shown). experiments with an optically plugged trap are discussed inSec. V. Finally, in Sec. VI we summarise our results. II. EXPERIMENTAL SETUPA. Vacuum System
BEC production in a single-chamber vacuum system is sub-ject to two contradicting requirements: while a higher Rb vapour pressure facilitates loading of the magneto-optical trap(MOT), a lower background gas pressure increases the life-time and evaporation efficiency during later cooling stages.Condensation is achieved by carefully balancing these two re- a r X i v : . [ c ond - m a t . qu a n t - g a s ] D ec quirements. In our experiments this balance is improved byusing isotopically pure Rb vapour sources (purchased fromAlvatec).Our vacuum system is shown in Fig. 1. A quartz cell byTriad Technology allows optical access via two
50 mm (topand bottom) and eight
25 mm anti-reflection coated windows.The vacuum is maintained by a single
45 l / s ion pump. Af-ter moderate baking of the system, at ◦ C for a week, weachieve magnetic trap lifetimes of over
20 s . The Rb pres-sure typically reduces this to about
10 s . B. Magnetic Coils
The magnetic quadrupole field for both the MOT and themagnetic trap is created by an anti-Helmholtz pair of 16-turnwater-cooled coils wound from 4 mm copper tubing (“7” inFig. 1). These create an axial gradient of B (cid:48) = 400 G / cm when carrying
200 A .The quantisation axis for optical pumping and imaging isprovided by a magnetic field along the imaging axis. We use alow-inductance planar 10 turn coil wound from copperwire (“9” in Fig. 1), providing a field of at the atoms.Gravity compensation during time-of-flight (TOF) mea-surements is achieved by combining a quadrupole field (cre-ated by the MOT coils) with a homogeneous vertical bias field.Residual potential curvature is minimised by a high bias fieldstrength. We use two 50-turn coils in a Helmholtz configura-tion (“8” in Fig. 1), providing a bias field of
70 G when run at10 A.A radio-frequency (RF) field for forced evaporative coolingis created by a three-turn coil mounted against the top view-port of the cell. For transitions between neighbouring m F states separated by up to
15 MHz , we achieve Rabi frequen-cies above
20 kHz using
600 mW of RF power.
C. Laser-Cooling System
Magneto-optical trapping of Rb requires two laser fre-quencies of its D line (near
780 nm) . We use two grating-stabilised external-cavity diode lasers (DL Pro from TopticaPhotonics). They are referenced to separate vapor cells to gen-erate cooling light close to the | F = 2 (cid:105) → | F (cid:48) = 3 (cid:105) cyclingtransition and repumping light resonant with the | F = 1 (cid:105) →| F (cid:48) = 2 (cid:105) transition. Cooling light is amplified using a taperedamplifier (BoosTA from Toptica). The cooling and repumpinglight pass through acousto-optic modulators (AOMs) and arecombined in a two- to six-way free-space fiber port cluster,built in-house from OFR components (distributed by Thor-labs).The spatial arrangement of our laser beams is shown inFig. 2. The six MOT beams are delivered to the glass cell viaoptical fibers. A total of
120 mW of cooling light and
10 mW of repumping light reaches the atoms. We use large diameter(
25 mm ) beams which do not need to be realigned for months.The light for optical pumping and absorption imaging of theatoms is derived from the cooling light. The pumping and to CCD O D T M O T bea m s pump beamimaging beamplug FIG. 2: Top view of the glass cell, showing the arrangement of thelaser beams. imaging beams are controlled by additional AOMs and enterthe chamber via the “back” viewport (5 in Fig. 1).
D. Single-Beam Dipole Trap
The optical-dipole-trap (ODT) beam used for the hybridtrap is derived from a
20 W ytterbium fiber laser (YLR-20-LP from IPG Photonics). After passing through an AOM,the beam is focused by a concave-convex pair of lenses, al-lowing the adjustment of both waist size and position. Wetypically use a beam waist of µ m and a maximum powerof at the atoms. Higher powers lead to excessive atomlosses, which can be attributed to two-photon transitions [20];these transitions are caused by the large linewidth of the trap-ping laser ( . in our case). The focal point is positionedapproximately a beam waist below the zero of the magneticquadrupole field. The beam power is controlled in the range . − using a feedback loop consisting of a photodi-ode, a proportional-integral-derivative (PID) controller, andthe AOM. Throughout this range, we achieve an rms powernoise below over a bandwidth of . E. Optical-Plug Beam
In our experiments, for the optical-plug light we used aTi:Sapphire laser (Coherent MBR-110) in order to explore arange of plug wavelengths and powers. However, since weshow that as little as
70 mW of plug power is sufficient toachieve quantum degeneracy, in future experiments the pluglight could be generated using a simple diode laser.The plug beam is focused to a waist of µ m and alignedto overlap with the zero of the magnetic quadrupole field, asshown in Fig. 2. F. Imaging
We image the atoms with a collimated, circularly polarisedbeam, resonant with the | F = 2 , m F = 2 (cid:105) → | F (cid:48) =3 , m F (cid:48) = 3 (cid:105) transition. The imaging efficiency was calibratedto account for the deviations of the absorption cross-sectionfrom the theoretical value, primarily due to imperfections inthe polarisation of the imaging light. We compared the mea-sured atom number at the BEC critical point ˜ N c with the the-oretically predicted critical number N c . ˜ N c was measured byextrapolating the non-saturation slope of the thermal compo-nent to the condensation point as described in [21, 22]. Wefound an imaging efficiency of (1 . ± . − , which lies inthe range typical of other experiments [23, 24]. III. LASER COOLING
For the MOT we use an axial field gradient of B (cid:48) =13 G / cm and a cooling-light detuning of −
25 MHz . Typi-cally, we load the MOT to ≈ atoms in
15 s . Note, how-ever, that s of loading are sufficient to produce BECs with > atoms. In daily operation, MOT atom numbers are de-duced from the intensity of fluorescence light collected on aphotodiode, which was calibrated using absorption imaging.Following the initial loading stage, we compress the MOTby increasing B (cid:48) to
64 G / cm for
20 ms , and then detune thecooling light to −
68 MHz for (CMOT, [25]). We foundthat these steps reduce the temperature and improve transferinto the magnetic trap. These steps are followed by ofoptical molasses during which the magnetic field is switchedoff and the cooling-light detuning of −
68 MHz is maintained.This cools the cloud to ≈ µ K . IV. CONDENSATION IN A HYBRID TRAP
Following molasses, the atoms are optically pumped intothe | F, m F (cid:105) = | , (cid:105) hyperfine ground state, using a combi-nation of resonant | F = 2 (cid:105) → | F (cid:48) = 2 (cid:105) σ + light and repumplight. We pump > of the atoms into the | , (cid:105) state in µ s , while heating the cloud to µ K .The atoms are then captured in a magnetic potential by sud-denly turning on the quadrupole field with B (cid:48) = 64 G / cm (matching the gradient of the CMOT) and then ramping B (cid:48) to
80 G / cm over
200 ms . Finally, the trap is further compressedby raising B (cid:48) to
200 G / cm over
500 ms .From this point on, the evaporative cooling to condensa-tion can be divided into three stages: ( I ) RF evaporation, ( II )transfer into the hybrid trap, and ( III ) ODT evaporation.Fig. 3 summarises the evolution of the relevant experimen-tal parameters during the evaporation sequence, while Fig. 4displays the evolution of the atom number N , the temperature T , and the calculated phase-space density D . N and T are measured using time-of-flight (TOF) absorp-tion imaging and D is calculated from a semiclassical model[18], using an analytical expression for the hybrid trappingpotential. We verified the parameters of the model (such as B ' (cid:72) G c m (cid:45) (cid:76) f (cid:72) M H z (cid:76) P (cid:72) W (cid:76) (cid:72) s (cid:76) I II III
FIG. 3: Evaporation sequence in the hybrid trap. We show the evolu-tion of (top to bottom) the magnetic field gradient B (cid:48) , RF frequency f , and ODT power P . The sequence has three stages: ( I ) RF evapo-ration, ( II ) transfer into the hybrid trap, and ( III ) ODT evaporation.
I II III (cid:72) (cid:76) Evaporation time (cid:72) s (cid:76) Γ(cid:61)
Γ(cid:61) (cid:45) (cid:45) (cid:45) (cid:45) (cid:45) P h a s e S p ace D e n s it y T e m p e r a t u r e (cid:72) Μ K (cid:76) (cid:172) Μ m (cid:174) FIG. 4: BEC production. We plot the temperature T (blue opencircles, left axis) and phase-space density D (red crosses, right axis)versus atom number N (bottom) and time t (top) throughout the cool-ing sequence. See Fig. 3 and text for details of stages I - III . Alsoshown are an absorption image of a partially condensed cloud after
50 ms of time-of-flight expansion [optical density varies between 0(blue) and 3 (red)] and its integrated profile. Fits to the thermal andcondensed components are indicated. beam waist) by measuring trapping frequencies and compar-ing them with theoretical predictions. We omit the calculatedvalues of D in stage II , where they are unreliable because thetrapping potential varies slowly over large volumes. A. RF Evaporation
During the initial evaporation stage in the compressed trap( I in Figs. 3 and 4), we ramp the RF frequency linearly from
15 MHz to in . We achieve a 30-fold increase inthe peak phase space density, with an evaporation efficiency γ = − d[ln D ] / d[ln N ] = 2 . .At the end of this stage the cloud typically contains N =50 × atoms at T = 90 µ K . B. Loading of the Hybrid Trap
In stage II the magnetic field gradient is decompressed tojust below the gravity-compensating value, B (cid:48) g = mg/µ B =15 . / cm , where m is the atom mass, g is the gravitationalacceleration and µ B is the Bohr magneton. From this pointon, the atoms are supported against gravity by optical forcesonly, while the confinement along the ODT axis is dominatedby the magnetic forces [18]. Note that the ODT beam is onfrom the beginning of the magnetic trapping (see Fig. 3), butinitially does not have a dominant role.We decompress B (cid:48) to
80 G / cm over
100 ms while keep-ing the RF frequency constant, then decompress further to B (cid:48) = 40 G / cm while sweeping the RF frequency linearlyto . in . ; this provides a good gain in phase-spacedensity despite the weak magnetic confinement. Finally, themagnetic field is decompressed from B (cid:48) to B (cid:48) = 14 . / cm .In this step we sweep the field gradient according to B (cid:48) ( t ) = B (cid:48) × (1 + t/τ ) − , where τ = t B (cid:48) / ( B (cid:48) − B (cid:48) ) and the sweepduration is t = 800 ms . This changes the RF-limited trapdepth approximately linearly with time, with the approxima-tion being exact in the case of no ODT and B (cid:48) = B (cid:48) g .At the end of this stage we typically have × atomsat µ K . C. Optical Evaporation
For B (cid:48) < B (cid:48) g , evaporation is no longer driven by the RFfield. Instead, the trap depth is limited by the potential heightat a saddle point vertically below the magnetic-field zero [26].Evaporation can thus be forced efficiently by lowering theODT power, P , albeit at the cost of a small reduction in thetrapping frequencies.We ramp P exponentially to its final value, P end , with atime constant of .
25 s and total ramp duration of . (Bothparameters have been optimised empirically.) We achieve anevaporation efficiency of γ = 3 . , leading to condensation at P end = 0 .
16 W .At the critical point, N ≈ and T ≈
250 nK . At thispoint, the trapping frequency is about 30 Hz along the ODTaxis and about 90 Hz radially.Lowering the ODT power further results in quasi-pure con-densates of > × atoms. The lifetime of the quasi-pureBEC is ∼ , consistent with the expected 3-body losses [27]. V. CONDENSATION IN A PLUGGED QUADRUPOLETRAP
Our experiments with the optically plugged quadrupole trapwere performed before we could introduce the isotopicallypure Rb vapour sources into the setup. For this reason theatom numbers in the hybrid and plugged traps cannot be di-rectly compared. The abundance of Rb in the naturalisotopic mixture means that for the same background pres-sure, hence the same MOT loading time and cloud lifetimein the magnetic trap, the MOT loading rate is about 4 timessmaller. The collisional rate, which determines the efficiencyof evaporative cooling, is then also correspondingly lower. Asa result of these effects, we could produce only smaller BECs,containing up to ∼ × atoms.Our goal here, however, was not to maximise the atom num-ber, but to investigate the minimal requirements on the plug-laser power. The improvements brought about by using iso-topically pure Rb sources should equally increase the de-generate sample size in plugged-trap experiments.In the first plugged-trap experiment, W of 532 nm laserpower was used [5], while later it was shown that by reducingthe plug size this requirement can be reduced to W [12].Here we show that bringing the laser wavelength closer to theatomic resonance can reduce this value to as little as mW. A. Cooling Sequence
In these experiments, the laser-cooling stage was essen-tially the same as in Sec. III, except that the optimisationof the rubidium pressure for best BEC production resulted in ∼ . × atoms being loaded into the MOT.The atoms were then loaded into the plugged quadrupoletrap with an axial gradient of
360 G / cm . The strong magneticconfinement compensates for the smaller initial atom numberand allows the initiation of evaporative cooling. RF evapora-tion started at f = 16 MHz . After holding f constant for ,we swept it linearly to in . At this point the cloudwas sufficiently dense for the losses due to three-body recom-bination to become relevant [28]. We thus decompressed thetrap to
160 G / cm in
300 ms . The RF frequency was thenswept exponentially from to ∼
180 kHz in . . B. Effects of Plug Power and Wavelength
In the above cooling sequence, the plug laser beam was onfrom the moment the atoms were loaded into the quadrupolemagnetic trap. However, its efficiency in preventing Majoranalosses depends on its power and wavelength. Reducing thebeam detuning from the atomic resonance increases both theoptical dipole forces and the spontaneous light scattering, thusallowing smaller powers to be used, but at the cost of moreheating and shorter lifetimes.To study this effect quantitatively, we varied the plug-laserwavelength in the range −
775 nm and the beam power, (a) (cid:72) mW (cid:76) N u m b e r o f a t o m s (cid:72) (cid:76) (b) (cid:72) Μ K (cid:76) N u m b e r o f a t o m s (cid:72) (cid:76) FIG. 5: Condensate atom number for different plug parameters. (a)Atom number versus plug power for two different wavelength. At771 nm only 70 mW of plug power are necessary for condensation.(b) Atom number versus the peak potential created by the plug. P plug , in the range mW - , while keeping the beamgeometry fixed.Fig. 5(a) shows the number of atoms in the condensed cloud as a function of P plug for two different wavelengths. At nm we achieve condensation for P plug (cid:38) mW; in-creasing P plug beyond 300 mW leads to only a slow increasein the atom number. At nm, as little as 70 mW of plugpower is sufficient for condensation. Note, however, that inthis case one should use the minimum necessary laser power,since increasing P plug further actually has adverse effects dueto the increased spontaneous light scattering.In Fig. 5(b) we plot the number of atoms at the end of theevaporation versus the peak value of the repulsive potentialcreated by the plug beam. We see that the threshold poten-tial is in fact the same for a range of wavelengths. This alsoshows that (for this range of wavelengths) the spontaneouslight scattering is not relevant for powers up to the thresh-old value. Only for higher peak potentials we see that longerwavelengths (closer to resonance) lead to lower atom numbersdue to the spontaneous scattering. VI. CONCLUSION
We have described a simple single-chamber apparatus forproducing Bose-Einstein condensates of Rb by evaporativecooling in either a hybrid magnetic-optical trap or an opti-cally plugged quadrupole trap. With the hybrid-trap approachwe achieve BECs with > × atoms, comparable to mostmulti-chamber setups. In our experiments with the opticallyplugged trap the main result is that as little as 70 mW of plugpower is sufficient to achieve condensation. This makes it pos-sible to pursue this approach using inexpensive diode lasers.We hope that our description of both experimental ap-proaches will benefit groups wanting to design simple andcost-efficient BEC machines for various applications. Acknowledgments
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