A compact experimental machine for studying tunable Bose-Bose superfluid mixtures
P. C. M. Castilho, E. Pedrozo-Peñafiel, E. M. Gutierrez, P. L. Mazo, G. Roati, K. M. Farias, V. S. Bagnato
AA compact experimental machine for studying tunable Bose-Bose superfluid mixtures
P.C.M. Castilho, ∗ E. Pedrozo-Pe˜nafiel, † E.M. Gutierrez, P. L. Mazo, G. Roati, K.M. Farias, and V.S. Bagnato Instituto de F´ısica de S˜ao Carlos, Universidade de S˜ao Paulo, C.P. 369, 13560-970 S˜ao Carlos, SP, Brazil INO-CNR and LENS, University of Florence, via N. Carrara 1, 50019 Sesto Fiorentino, Italy
We present a compact and versatile experimental system for producing Bose-Bose superfluidmixtures composed of sodium and potassium atoms. The compact design combines the necessaryultra-high vacuum enviroment for ultracold atom experiments with efficient atomic fluxes by usingtwo-dimensional magneto-optical traps as independent source of atoms. We demonstrate the perfor-mance of this new machine by producing a Bose-Einstein condensate of Na with ∼ × atoms.The tunability of Na-K bosonic mixtures is particularly interesting for studies regarding the nucle-ation of vortices and quantum turbulence. In this direction, the large optical access of the sciencechamber along the vertical direction provides the conditions to implement high resolution opticalsetups for imaging and rotating the condensate with a stirring beam. We show the nucleation of avortex lattice with up to 14 vortices in the Na BEC, attesting the efficiency of the experimentalapparatus in studying the dynamics of vortices.
I. INTRODUCTION
Quantum degenerate mixtures created with either dif-ferent Zeeman sublevels [1–3] or with different atomicspecies [4–17] exihibit a rich physics that is not accessi-ble in a single component quantum gas. The existenceof different miscibility regimes [3, 8, 9, 11, 14, 16–18] di-rectly affects the statistical and dynamical properties ofthe system. The nucleation of vortices [19–21] and thesuperfluid current stability [22–24] are strongly modifiedby the interplay between the inter- and intraspecies in-teractions. In optical lattices, the phase diagram of two-component systems is far more complex than the simpleextension of the standard superfluid to Mott insulatortransition [25, 26]. Aditionally, the possibility of pro-ducing heteronuclear ground-state molecules with largedipole moment [15, 27, 28] could enable the study of evenstronger interacting dipolar gases than the ones recentlyobtained with lanthanide atoms [29, 30]. Large imbal-anced mixtures can shed light on the physics of impuri-ties coupled to a bosonic bath [31, 32], of fundamentalinterest in condensed matter physics. And beyond mean-field effects could be explored with the recent observationof quantum droplets in Bose mixtures composed of twohyperfine states of K [33, 34], as it was originally pro-posed in [35].The specific case of Na-K mixtures is of particular in-terest due to its large flexibility. Both, Bose-Bose andBose-Fermi mixtures could be easly produced by chang-ing the potassium isotope and the different miscibilityregimes explored with the tunning of the interspecies in-teractions via the Feshbach resonances for each combi- ∗ [email protected]; Current address: Laboratoire KastlerBrossel, Coll`ege de France, CNRS, 11 Place Marcelin Berthelot,75005 Paris, France † Current address: Department of Physics, MIT-Harvard Cen-ter for Ultracold Atoms and Research Laboratory of Electron-ics, Massachusetts Institute of Technology, Cambridge, Mas-sachusetts 02139, USA nation [36]. Due to the existence of chemically stableground-state molecules with large eletric dipole moment( ∼ .
72 Debye), the Bose-Fermi mixture has been vastlyexplored during the last few years [15].In this work, we present the realization of a compactexperimental machine to produce Bose-Bose superfluidmixtures composed of Na and K or K atoms withfast repetion rate. While the combination with K, re-cently produced in [17], could become a good platformfor the investigation of bosonic impurities, the combina-tion Na- K represents a fully-tunable Bose-Bose su-perfluid which remains still now unexplored. Thanksto its tunability, the nucleation of coupled vortex lat-tices [20, 21] and binary quantum turbulence [37, 38]configures one promissing path for such mixture. More-over, the large difference between their atomic transitions(with λ Na = 589 nm and λ K = 767 nm) makes it pos-sible to selectively nucleate vortices in one species evenwithout a magic wavelength . This could be done withthe use of an optical potential (i.e. stirring beam [39–41] and moving barrier) at 532 nm, which affets stronglysodium than potassium. The unperturbed species couldbe used to map the first species evolution revealling thetangling between vortex filaments. Similar experimentshad been developed in superfluid helium [42, 43], but noanalogous have been performed in quantum gases so far.In the following, we focus on describing the experimentalapparatus and the experimental sequence for producinga vortex lattice in a Bose-Einstein condensate of sodiumatoms after rotation by the stirring beam.This paper is structured as follows. Section II describesthe design of the new experimental system including thedetails of the vacuum system in Sec. II A, of the laser sys-tems for sodium and potassium atoms in Sec. II B andof the conservatives traps designed for simultaneouslytrap the two atomic species in Sec. II C. The magneto-optical traps (MOTs) for each species are described inSections III A and III B followed by the characterizationof the combined two-species MOT, in III C. Later, inSection IV, we focus on describing the experimental se-quence for producing the Na BEC. The intermediate a r X i v : . [ c ond - m a t . qu a n t - g a s ] J a n steps used to improve the transference of the atoms fromthe 3D-MOT to the optically plugged Quadrupole trapare described in Sec. IV A. Next, the Plug trap and theRF-forced evaporation of the sodium atoms are charac-terized in Sec. IV B. In Sec. IV C, we characterize the Na BEC obtained in the crossed optical dipole trap.Finally, a high resolution imaging and stirring setup isdescribed in Sec. V A and, in Sec V B, we presente thenucleation of a vortex lattice in the Na BEC.
II. EXPERIMENTAL SETUP FOR PRODUCINGTHE NA-K BOSE-BOSE SUPERFLUIDMIXTURES
In this section, we describe the design of each commonexperimental part in producing the Na-K Bose-Bose su-perfluid mixtures.
A. A compact two-species vacuum system
Cold atom experiments require the combination ofan ultra-high vacuum environment (with P ∼ − − − Torr) and efficient atomic sources. In the pastyears, compact sources of atoms have gained great at-tention due to the high atomic fluxes obtained from two-dimensional magneto-optical traps (2D-MOTs). Thesetraps, initially implemented for rubidium and potassiumisotopes in a vapor cell [44, 45], were later also able toproduce high atomic fluxes of lithium and sodium atomsby adding an adapted “Zeeman slower” [46] which pre-cool the atoms coming from an oven [47, 48]. For thelatter atomic species, a direct comparison between theloading of a standard three-dimensional MOT (3D-MOT)from pre-cooled atoms coming from a real Zeeman slowerand from the modified − and 10 − with respect tothe 2D-MOT chamber of sodium and potassium, respec-tively. Three ion pumps (Varian Vaclon Plus 75 L/s) areinstalled in the vacuum system pumping each of its threeregions in order to keep the desired ultra-high vacuumenvironment in the SC. The complete vacuum system isonly 1 . FIG. 1. Front view of the compact vacuum system designedfor the production of the Na-K Bose-Bose superfluid mixtures.
17 mm connects the bottom of the 2D-MOT chambersto an oven containing 5 g ampole of metallic sodium orpotassium. The ovens are heated to usual operating tem-peratures of 240 ◦ C for sodium and 30 ◦ C for potassiumresulting in a background pressure of 5 × − Torr and1 × − Torr, respectively. The 2D-MOT for potassium(K 2D-MOT) is loaded from the background vapor fillingthe whole chamber which is kept at ∼ ◦ C. Differentlyfrom the K 2D-MOT, a modified ◦ C avoiding de-posit of sodium.The Science chamber also consists of a one piece metal-lic chamber made of stainless steel 316L. It was speciallydesigned in an almost cylindrical shape with height of77 mm and maximum radius of 120 mm in order tomaximize the optical access. Therefore, besides the two2D-MOT chambers, six CF35 viewports were placed atthe xy -plane. Eight CF16 viewports were also placedon the same side but with an angle along the verticaldirection that orients them to the center of the cham-ber. Finally, two custom designed re-entrant viewportsfrom Torr Scientific with 89 mm of clear aperture wereplaced along the vertical direction with an internal sepa-ration of 31 mm. The resulting large numerical apertureenables the design of a high resolution imaging systemalong gravity. Besides the ion pump, a titanium subli-mation pump (Agilent - Titanium Sublimation Cartridge916-0050) is connected in the SC region (see cylinder inthe center of figure 1) enabling the achievement of anultra-high vacuum environment. B. Laser systems
In this part, we briefly describe the laser systems de-signed for sodium and potassium atoms.
TA-SHG pro
FIG. 2. Sketch of the optical setup designed to produce thelaser light used to cool, manipulate and image the sodiumatoms. The yellow lines represent the laser beams with fre-quency near the cooling transition, the orange lines representthe laser beams with frequency near the repumper transitionand the black lines represent laser beams with both frequen-cies. The green line represents the green light at 532 nm usedto pump the dye laser in order to produce the yellow light at589 nm. The frequencies used in each AOM/EOM are givenin MHz.
1. Sodium laser system
The laser light necessary for cooling, imaging and ma-nipulating the sodium atoms is obtained from a doubly-cavity laser (model DL-RFA-TA-SHG, from Toptica) sta-bilized to the 3 S / | F = 2 (cid:105) → P / transition. In fig-ure 2, we present the layout of the optical setup for thesodium laser system.Electro and acousto-optic modulators (EOMs andAOMs) are used to tune the different laser frequenciesand, in the case of the second, also as fast switchers.The laser light is initially divided into four laser beams.The first generates the cooling light for the 3D-MOT andthe imaging light resonant with the | F = 2 (cid:105) → | F (cid:48) = 3 (cid:105) transition. A double-pass AOM is used to perform thefine frequency adjustment needed during the experimen-tal sequence with minor misalignment of the laser beams.The second beam, used to generate the repumper lightof the 3D-MOT and the pump light resonant with the | F = 1 (cid:105) → | F (cid:48) = 2 (cid:105) transition, is obtained after pass-ing through a shifter acting at ∼ .
712 GHz. High fre-quency optical devices usually present very low efficiency( ≈ th -orderto produce the light needed for the push beam used totransfer the pre-cooled atoms at the 2D-MOT to the Sci-ence chamber. The third beam is used to generate the cooling and repumper lights necessary for the 2D-MOT.This is done by passing the light through an EOM with side-bands at ∼ .
712 GHz. Finally, the fourth beamis responsible for performing the adapted Zeeman slowerin the Na 2D-MOT. The repumper light is obtained bythe use of an EOM with side-bands at 1 .
713 GHz andan AOM at 220 MHz is used to bring both lights far reddetuned from the atomic transition.Polarization maintaining fibers deliver all the manipu-lated lights on the experimental apparatus decoupling thelaser sources from the optical table containing the vac-uum system. On the experiment table, all laser beamsare adjusted to have a beam diameter of 20 mm, besidesthe push beam, which has a beam diameter of 3 mm.The usual output laser powers for each fiber are specifiedin figure. 2.
2. A versatile laser system for bosonic potassium isotopes
The bosonic potassium isotopes ( K and K) havetransition frequencies separated by less than 310 MHzmaking it possible to design a laser system able to switchbetween these isotopes. In our setup, this can be easilydone by changing the lock-in point of each laser, as it isdescribed in the following.Due to the unresolved structure of the excited many-fold of the bosonic potassium isotopes, standard sub-Doppler laser cooling with light close to the D line is dif-ficult to implement and normally present a limiting tem-perature of more than 500 µ K. To overcome this limita-tion, schemes based on the D line transitions have beensuccessfully demonstrated with the Gray molasses pro-cedure [50–52]. Therefore, cooling and repumper lightson the D (at 767 nm) and D (at 770 nm) lines arenecessary during the experimental sequence.In figure 3, we present a sketch of the potassium lasersystem accounting for the lights of the two D -lines. Threelasers from Toptica, two TA-Pro and one DLX, are usedto generate the cooling and repumper lights from the D line and the light of the D line, respectively. The laserbeam of each D line laser is initially divided into twopaths providing the lights for the 2D-MOT/ imaging andfor the 3D-MOT. Double-pass AOMs are used to per-form the fine frequency adjustment of the lights duringthe experimental sequence. The DLX laser beam is alsodivided in two paths in order to provide the cooling and repumper lights at the D line.In order to achieve the necessary laser power to ef-ficiently cool the atoms during the MOT, we use twofinal stages of light amplification performed by home-made “master oscillator power amplifiers” (MOPAs)mounted with a tapered amplifier (TA) chip from Eagle-yard (EYP-TPA-0765-01500-3006-CMT03-0000) able toprovide 1 . cooling and repumper lights are simultaneously injected with a 50:50 ratio pro-viding 300 mW power at the output of the optical fiberfor performing the 2D-MOT and push beams. In theMOPA-3D, not only D cooling and repumper lights are FIG. 3. Sketch of the optical setup designed to produce the laser light used to cool, manipulate and image the potassiumatoms. The light red lines represent the laser beams with frequency near the D cooling transition, dark red lines representlaser beam with frequency near the D repumper transition, the pink lines represent the laser beam with frequency near the D cooling transition, the light green represent laser beams with frequency near the D repumper transition and the black linesrepresent laser beams with more than one frequency. The frequencies used in each AOM are given in MHz. simultaneously injected with a 10:1 ratio, but also the D light with a 5:1 ratio, which is switched on only during theGray molasses procedure while the D light remains off.With this configuration, around 320 mW and 210 mWof D and D , respectively, are obtained at the output ofthe 3D-MOT fiber.The D line lasers are frequency stabilized to the D ground-state crossover (C.O.) of the K isotope bymeans of the saturated absorption spectroscopy tech-nique. For selecting the potassium isotope we want towork with, AOMs are added to the saturated absorp-tion spectroscopy scheme shifting the lock-in point of thelasers in order to cover the frequency difference betweenthe cooling and repumper transitions of 308 MHz and108 MHz, respectively. The DLX laser is stabilized tothe D C . O . → | F (cid:48) = 2 (cid:105) transition also of the K iso-tope. For the D light, the choice between the bosonicisotopes is done combining the change in the lock-in pointby ∼
170 MHz with the addition of a single-pass AOMto the repumper light in order to make it resonant withthe K transition. With this configuration, no differencein the laser powers delivered to the experiment were ob-served. On the experiment table, all laser beams areadjusted to have a beam diameter of 18 mm, besides thepush beam, with d = 3 mm. C. Conservative traps to produce thetwo-component BEC
In this section, we discuss the trapping principles andthe design of the two conservative traps we will use toproduce the Bose-Bose superfluid mixture: the optically plugged Quadrupole trap [53, 54] and the crossed
ODT.In figure 4, we present a scheme of the configurations ofboth traps around the Science chamber.
1. The optically plugged Quadrupole trap
The optically plugged Quadrupole trap, or simply
Plug trap, is produced by a focused blue-detuned laser beamaligned through the center of a magnetic Quadrupole trap(QT), creating a barrier that repel the atoms from theregion where −→ B = 0, dramatically reducing the proba-bility of Majorana losses to happen [55, 56]. The use ofan “attractive” Plug trap, in which a red-detuned laserbeam is added to the Quadrupole trap, is less favorablefor sodium atoms due to the large detuning from theatomic transitions. The effective potential for the atomsin the plugged trap is: U Plug ( x, y, z ) = µB (cid:48) (cid:114) x y z + U
11 + ( x/x R ) e − r w
20 11+( x/xR )2 , (1)where µ is the atomic magnetic moment, B (cid:48) , the mag-netic field gradient along the coils axis (in this case, cho-sen to be along (cid:98) z ), U = 3 c Γ P/ω ∆ is the depth ofthe optical potential, c is the speed of light in vacuum, ω and Γ are, respectively, the angular frequency andthe decay rate of the atomic transition, ∆ = ω − ω isthe difference between the laser and the atomic transi-tion frequencies, named detuning of the laser, P is the FIG. 4. Vertical cut of the Science chamber with thequadrupole coils positioned along the (cid:98) z -axis, the plug beam(in green) propagating along (cid:98) x and aligned with the centerof the quadrupole trap and the crossed ODT laser beams (inred). laser power, w is the plug beam waist at the focus, x R is the Rayleigh length and r = (cid:112) ( y − y ) + ( z − z ) ,with ( y , z ) being the laser position with respect to thecenter of the Quadrupole trap at the x = 0 plane.From 1, one can easily see that the shape of the trap-ping potential is strongly affected by the plug beamalignment. Previous studies have shown that small mis-alignments of the plug beam from the center of the QT(smaller than a beam waist) results in an effective poten-tial with one single minimum [55, 56] in which the atomswould accumulate while decreasing its temperature. Forsmall displacements around this minimum, the potentialis approximately harmonic. When considering a plugbeam dislocated along (cid:98) y , the minimum of the effectivepotential occurs at (0 , y min ,
0) such that its frequenciescan be given by: ω x = (cid:115) g F m F µ B B (cid:48) my min , ω y = (cid:115) y w − ω x , ω z = √ ω x . (2)When designing a Plug trap for two different atomicspecies, it is important to repel both atoms from the re-gion where Majorana losses could happen. In figure 5 (a)and (b), we show the designed Plug trap potential fortrapping both Na and K atoms at the | F = 1 , m F = − (cid:105) hyperfine state. For simplicity, we considered the plug beam aligned with the center of QT in order to cre-ate the optical barrier that can be easily seen in fig-ure 5 (b), in which the potential along (0 , y,
0) is plot-ted. For these graphs, we used a magnetic gradient of B (cid:48) = 200 G/cm, a plug beam power of P = 4 W and awaist of w = 43 µ m. The height of the barrier for thepotassium atoms is a factor of ∼ . U Na0 = 245 µ K and U K0 = 105 µ K),due to the larger detuning between the plug beam and its U P l ug X - Z / k B ( µ K ) (a) -200 -100 0 100 200050100150200250 y Kmin U P l ug Y / k B ( µ K ) Position ( µ m) U PlugY Na U
PlugY K U
QuadY y Namin (b)
FIG. 5. Plug trap potential for sodium (in blue) and forpotassium atoms (in orange). The positions where the poten-tial is minimum is different for each species as it can be seenin (b) for the potential along (cid:98) y . The quadrupole potentialalong (cid:98) y without the addition of the Plug beam is representedby the dashed gray line. The potential along the (cid:98) x (solid lines)and (cid:98) z (dashed lines) are displaced in (a) and were calculatedfor the proper y = y min of each atomic species. atomic transitions. The resulting frequencies for sodium(potassium) are f x = 213(172) Hz, f y = 651(441) Hz and f z = 368(300) Hz.The magnetic field gradient is generated by a pair ofcircular coils in anti-Helmholtz configuration mountedalong the vertical axis (see figure 4) and separated by62 mm. These coils are also used to produce the MOTmagnetic field gradient. The blue-detuned light used toproduce the plug beam is generated by a Coherent VerdiV10 laser with λ = 532 nm and maximum output powerof 10 W.
2. The crossed optical dipole trap
Tuning the atomic interaction by means of magnet-ically induced Feshbach resonances [57] consists in in-troducing an external bias of magnetic field, which canonly be applied in pure optical dipole traps (ODTs). Inour experiment, the Bose-Bose superfluid mixture will beproduced in a crossed
ODT composed of two red-detunedfocused laser beams that perpendicularly cross near theminimum of the Plug trap potential (see figure 4).Single-beam optical dipole traps are described by thesecond term of 1. The 90 o crossed ODT trapping po-tential is therefore obtained by summing the potentialsof each individual laser beam resulting in a approx-imately harmonic potential with frequencies given by f i = (cid:113)(cid:80) j =1 , f i,j where the f i,j represents the i -axisfrequency related with the laser beam j . For the partic-ular case of identical laser beams with U = U = U , w = w = w and x R = y R = x R the trappingfrequencies can be simplified by: ω x (cid:48) ,y (cid:48) = (cid:115) U m (cid:20) x R + 2 w (cid:21) ≈ (cid:115) U mw ω z = (cid:115) U mw , (3)which presents a ratio of √ U cross0 = 2 U .The crossed ODT laser beams are generated by aMEPHISTO (MOPA-42W) laser with λ = 1064 nm andmaximum output power of 42 W. The laser beam is ini-tially divided in two parts in order to provide the twoODT laser beams desired for the crossed configuration.The power of each beam is controlled with an AOM,which are also used as fast switchers. After the AOMs,the diffracted beam is coupled into single-mode polariza-tion maintaining high power fibers. Around 5 . − . w ≈ µ m.Dichroic mirrors combine the ODT beams with the inplane MOT beams. III. THE TWO-SPECIES MOT
In this section, we describe the individual magneto-optical traps for sodium and potassium atoms and char-acterize the operation of the combined two-species MOT.
A. Sodium 2D and 3D-MOTs
The 3D-MOT of sodium in the SC is loaded fromthe pre-cooled atoms coming from the modified I ∼ I s , with I s being the satura-tion intensity I s = 6 .
26 mW/cm ) exits the 2D-MOTfiber with a central frequency near the cooling tran-sition ( δ cool-2D ∼ − . Na , where Γ Na = 9 .
79 MHzis the linewidth of the D line transitions) and side-bands at 1 .
712 GHz, providing δ rep-2D ∼ − . Na .This light is divided into two circularly polarized retro-reflected laser beams which perpendicularly cross in thecenter of the Na 2D-MOT vacuum chamber. The two-dimensional magnetic quadrupole field used for the 2D-MOT is produced by four sets of nine permanent magnets each (K&J Magnetic Inc. model BX082 with dimensionsof (3 . , . , .
4) mm and magnetization M = (10 . × , , d y = 6 cm and d z = 9 cm ,resulting in a magnetic field gradient along the beam’spropagation directions of 60 G/cm. Along the verticaldirection, in which travels the atomic flux coming fromthe oven, the residual magnetic field, together with a laserbeam counter-propagating with the atomic flux, is usedto perform an adapted Zeeman slower [47–49]. Around150 mW ( ∼ I s ) is used for the Zeeman laser beamwith cooling and repumper lights red-detuned from theatomic transitions by ∼
26 Γ Na . Its polarization is set tobe along the long axis of the 2D-MOT which, in combi-nation with the magnetic field, results in a circularly po-larized light for the atoms traveling along (cid:98) z [48]. Finally,the pre-cooled atoms in the 2D-MOT are guided to theSC by the use of a push beam with waist w ∼ µ m,power of 300 µ W ( ∼ . I s ) and frequency blue-detunedfrom the cooling transition ( δ push ∼ +1 . Na ).The 3D-MOT of sodium in the SC operates in theDark-SPOT MOT configuration [58]. We use a lineargradient of magnetic field ( ∼
11 G/cm) produced bythe Quadrupole coils, three circularly polarized retro-reflected laser beams with frequency near the coolingtransition ( δ cool-3D ∼ − . Na ) and one single pass laserbeam near the repumper transition ( δ rep ∼ − . Na ).The repumper beam has a “hole” (dark-SPOT) at thecenter of its intensity profile which is imaged into theatoms by a 1:1 telescope, such that only cooling light ar-rives in the center of the MOT. Therefore, the atoms inthe central region accumulate in the F = 1 ground-stateand stop to interact with the cooling light, decreasingthe re-scattered radiation and increasing the density ofthe atomic cloud. In our experiment, the dark-SPOT isproduced by a circular “mirror-mask” with 5 . ∝ N/T / ) of the atoms transferred to the magnetictrap. After a loading time of 5 s, around 5 × atomsat 350 µ K are trapped in the dark 3D-MOT.
B. Potassium 2D and 3D-MOTs
The 3D-MOT of potassium atoms in the SC is loadedfrom the pre-cooled atoms coming from the 2D-MOT per-formed in the K 2D-MOT chamber operating as a vapourcell. Thanks to the larger natural abundance of the Kisotope, we choose this isotope to perform the initial char-acterization of the system. Besides the atom number, wedo not expect considerable changes in switching to the K isotope [59].Around 300 mW ( ∼ I s with I s = 1 .
75 mW/cm )containing lights near the cooling ( δ cool-2D ∼ − . K ,where Γ K = 6 .
03 MHz is the linewidth of the D linetransitions) and the repumper ( δ rep-2D ∼ − . K ) tran-sitions in a 50:50 ratio exits the 2D-MOT fiber. A smallpart of this light ( ∼ . push beamwhile its main part is divided into two circularly po- (a) MOT KMOT Na F l uo r e sc en c e s i gna l ( a . u . ) Time (s)
Time (s) (b)
FIG. 6. Fluorescence signals from the potassium ( K, in or-ange) and sodium (in blue) MOTs as a function of the loadingtime. In (a), we show the dramatic decrease on the fluores-cence signal of the potassium MOT as soon as the MOT ofsodium is loaded. This decrease represents an atom loss ofmore than one order of magnitude (from ∼ × atomsto ∼ atoms, measured with absorption imaging). In (b),we show the opposite situation in order to observe that thefluorescence signal from the sodium MOT does not change inthe presence of the potassium atoms. larized retro-reflected laser beams which perpendicularlycross in the center of the K 2D-MOT chamber. Thetwo-dimensional magnetic quadrupole field is producedby four sets of four permanent magnets each (the samemodel used for the Na 2D-MOT) producing a magneticfield gradient along the beam’s propagation direction of30 G/cm. The pre-cooled atoms are transferred to theSC guided by the push beam. The resulting atomic fluxis of around 2 − × atoms/s.The 3D-MOT of K is produced with a linear gradi-ent of magnetic field of 16 G/cm and a total laser powerof 320 mW ( ∼ I s ) containing lights near the cool-ing ( δ cool-3D ∼ − K ) and the repumper ( δ rep-3D ∼− . K ) transitions in a 10:1 ratio. The potassium MOTalso operates in a retro-reflected configuration. After aloading time of 8 s, around 2 × atoms at 5 . C. The Na- K MOT
The first step in a two-species ultracold atom experi-ment consists in creating an efficient method to load andcool the different species prior the transference to a con-servative trap. The easiest approach is to perform a two-species MOT simultaneous loading both species. How-ever, light induced losses [60] could be a limiting factorwhile operating the two-species MOT.In the case of the Na- K MOT, we have observedthis kind of losses. Due to the large atom number dif-ference between the individual MOTs, the most affectedspecies is the potassium, contrary to the previous obser-vations in which the lightest species suffers the strongerlosses. In figure 6, we show the fluorescence signal ofthe sodium and potassium MOTs captured by indepen-dent photodiodes (sensitive to light at 767 nm or at 589 nm) for two different loading configurations: (a)the potassium MOT is fully loaded before turning onthe sodium MOT, showing the dramatic decrease in thepotassium fluorescence; and (b) with the opposite situ-ation, in which no difference in the sodium fluorescencewas observed. The drastic drop in the K MOT fluores-cence corresponds to a decrease of more than one order ofmagnitude in the number of atoms (from ∼ × atomsto ∼ atoms) making it difficult to perform the sub-sequent cooling procedures of the potassium cloud.In order to circumvent the atom loss resulted from thelight induced losses, one can implement a “Two-stageMOT loading” approach in a similar way as the one de-scribed by C.-H. Wu in [61]. It consists in performing theMOT of each species at different times of the experimen-tal sequence. Since this method has been demonstratedto be efficient for loading Na and K atoms, we areconfident that it will work also in the case of switchingfor the potassium bosonic isotopes, K and K. Thefirst attempts on this direction are under developmentin the laboratory. Moreover, the “Two-stage MOT load-ing” could be improved with a Gray molasses cooling ofthe sodium atoms [62] producing a colder cloud beforeloading the potassium MOT.
IV. PRODUCTION OF A NA BEC
In this section, we describe the experimental sequencefor producing a BEC of sodium with 1 × atoms. A. From the 3D-MOT to the magnetic trapping
We perform two intermediate steps before transferingthe atoms from the Na dark 3D-MOT to the Plug trap:a dark -molasses and a pre-pump stage. The first stage,used to cool the atoms below the Doppler limit, is donecombining the usual bright molasses [63] with the Dark-SPOT technique. At the beginning of the dark -molasses,the magnetic field is abruptly turned off and the detuningand power of the cooling light are ramped during 1 . δ cool-Mol ∼ − . Na and I cool-Mol ∼ . I s ), which are kept constant duringaditional 3 ms. The repumper light (detuning and power)is not changed during this stage. In the end of the dark -molasses we obtain 5 × atoms at 80 µ K.After the dark -molasses, we perform the pre-pumpstage by turning off the repumper light used for the dark-SPOT and letting the atoms expand during 250 µ s in thepresence of only cooling light. Since the cooling transi-tion is not closed, after a few cycles all the atoms arein the | F = 1 (cid:105) manifold equally distributed between thethree Zeeman sublevels. B. Evaporative cooling in the Plug trap
The transference of the pre-pumped Na atoms to theQuadrupole trap is done by abruptly switching on themagnetic field at B (cid:48) catch = 94 G/cm. This value was op-timized as the lowest magnetic field gradient that allowsall trappable atoms to remain trapped into the magnetictrap. After that, the field is adiabatically ramped upto its maximum value B (cid:48) QT = 190 G/cm during 500 ms.Once the atoms are trapped in the pure Quadrupole trap,the plug beam is turned on by ramping the laser lightintensity from zero to P Plug = 2 .
10 W in 100 ms [64].Around 1 . × atoms at 220 µ K are transferred to thePlug trap with a lifetime of 46 s.With the atoms in the Plug trap, forced radio-frequency (RF) evaporation is applied selectively remov-ing the hottest atoms [65]. The RF radiation is deliv-ered by a two-loop circular antenna with diameter of38 mm placed below the upper Quadrupole coil. Theevaporation ramp for producing a BEC of Na in thePlug trap lasts 12 . f RF = 45 MHz and final frequency between 1 . − . N vs. T in a log-log scale as it is shownin the graph of figure 7. Two different set of data, with(green open circles) and without (gray half-filled circles)the addition of the plug beam, are displayed in the graphwhile the solid curves are just used as guides for the eyes.The Majorana temperature is identified as the tempera-ture for which the two set of data points start to deviatedue to the occurrence of Majorana losses and it is around22 µ K for the sodium atoms in our system. For the greencircles, the efficiency of the evaporation procedure canbe estimated by the parameter s = log( N ) / log( T ) with s ≤ s = 0 .
89, ensuring itsefficiency. The onset of BEC is identified by the appear-ance of a bimodal density distribution of the atomic cloudobserved after 20 ms of time-of-flight (see the inset (a)of figure 7) for temperatures below T c = 1 . µ K and f RF = 1 . × atomscould be easily produced in the Plug trap by reducingeven further the RF-frequency between 0 . − . C. Final cooling in the crossed ODT
The transfer to the crossed
ODT is done after perform-ing the RF-evaporation procedure, as described in theprevious section, until f RF = 2 . t Evap = 9 . crossed ODT laser beams are adiabaticallyswitched on to its maximum power ( ∼ plug beam isabruptly switching off after the end of the magnetic fieldramp. Around 6 × atoms at ∼ µ K are trapped inthe crossed
ODT.
500 1000 1500 2000 25000,00,10,20,30,40,50,60,7 A t o m i c den s i t y p r o f il e ( a . u . ) Position along z -axis ( µ m)
500 1000 1500 2000 25000,00,10,20,30,40,50,60,7 A t o m i c den s i t y p r o f il e ( a . u . ) Position along z -axis ( µ m)
500 1000 1500 2000 25000,00,10,20,30,40,50,60,7 A t o m i c den s i t y p r o f il e ( a . u . ) Position along z -axis ( µ m) (b) (c) (d) T Maj ~ 22 µ KEnd of the RF-evaporationEnd of the RF-evaporation
Plug trapw/o Plugcrossed ODT N a a t o m nu m be r Temperature ( µ K) (a) FIG. 7. Log-log graph of
N vs. T for different points of theRF-evaporation of the sodium atoms. The optimized evap-oration procedure in the Plug trap (green circles), the samefrequency ramp performed only in the Quadrupole trap (graycircles) and the complete evaporation sequence for the BECin the crossed ODT (orange circles) are displayed in the graphas well as the Majorana temperature (green dashed line with T Maj ≈ µ K) identified as the temperature for which thetwo data points starts to deviate and the point in which theatoms are transferred to the ODT (orange dashed line).
With the atoms in the crossed
ODT, an optical evap-oration can continue to cool the atomic sample by slowlydecreasing the ODT depth. In our experiment, this doneby reducing the ODT laser beams powers with a seriesof six linear ramps for each beam resembling an expo-nential decay. The total optical evaporation procedurelasts 3 . /
10 for the ODT1 ( P final1 ≈
610 mW) andof 1 /
20 for the ODT2 ( P final2 ≈ Na atomsis U cross0 ≈ . µ K and the resulting frequencies are f x = 80(2) Hz, f y = 106(2) Hz and f z = 128(1) Hz, mea-sured combining the parametric heating technique [55]with the excitation of dipolar oscillations of the atomiccloud. All frequencies show a good agreement with thefrequencies obtained with 3. The route of the com-plete evaporation procedure for achieving the BEC in thecrossed ODT (forced-RF evaporation and optical evap-oration) can be seen on the log-log graph of N vs. T presented in figure 7.The achievement of the Na BEC in the crossed
ODTis also revealed with the appearance of a bimodal densityprofile observed after 20 ms of time-of-flight as illustratedin figure 7 (b-d) for different steps of the optical evap-oration. Almost pure BECs with ∼ × atoms areobtained by the end of the optical evaporation with life-times as long as 14 s. V. PRODUCTION OF A VORTEX LATTICE INTHE BEC OF SODIUM
In the direction of producing coupled vortex latticesand binary quantum turbulence in the Bose-Bose super-fluid mixtures produced in our setup, we developed alarge numerical aperture imaging system combined witha versatile stirring beam setup enabling the design of alarge variety of stirring patterns. In this section, we de-scribe the technical details of these two setups and profsits efficiency by producing a vortex lattice in the BEC ofsodium.
A. Vertical imaging and stirring setup
The stirring technique [39–41] vastly used in ultracoldatom experiments consists in the addition of a tightly fo-cused blue-detuned laser beam whose rotates along thesymetry axis of the BEC. The nucleated vortices are ori-ented with the rotation axis and an imaging beam co-propagating with the stirring beam is normally used toobserve the vortex lattice. In our experiment, the sym-metry axis of the Na BEC produced in the crossed ODTis along the gravity direction and we use a vertical setupcombined with the MOT beams for imaging and stirring.A scheme of the vertical setup along the science chamberis illustrated in figure 8. A thin wire-grid polarizer re-flects the vertical MOT beam and transmits the stirringand the imaging beams without significant deformation.The large clear aperture of the viewports along the (cid:98) z -axis enables the design of a high resolution setup. Atwo-inch achromatic 75 mm focal length lens (ThorlabsAC508-075-A) is used as a simple microscope objective.Despite its simplicity, we have measured an optical res-olution R ≈ µ m for 532 nm and 589 nm, stirring andimaging wavelengths, respectively. This optical resolu-tion gives the possibility of producing highly localizedpotentials with the green light. In the future, a cus-tom high numerical achromatic microscope will be in-stalled covering the range of the different wavelengthsnecessary for detecting the Bose-Bose mixture. A cus-tom designed dichroic mirror from Laseroptik combinesthe vertical imaging and the stirring beams. The verticalimaging magnification equal to × µ m in the atomic plane. FIG. 8. Cross-section view of the vertical MOT beams (lightyellow), the imaging beam (dark yellow) and the stirring beam(green) around the science chamber (gray). The positionof the BEC is indicated by a yellow circle in the center ofthe SC. The polarization of the MOT, imaging and stirringbeams are adjusted such that the wire-grid polarizer reflectsthe MOT beam and transmits the vertical imaging and thestirring beams.
FIG. 9. Lissajous figures produced by the stirring beam andimaged into a CCD camera with long exposure time. Theratio between the modulation frequencies of each AOM wasvaried and it is indicated by the number below each image.
In order to stir the laser beam, two crossed AOMs areused to produce a two-times diffracted beam, allowing ain-plane control of the stirring beam position. By mod-ulating the RF-frequency that control the AOMs withfrequency f Stirr , our system is able to produce the dif-ferent Lissajous figures shown in figure 9. The circle onthe left of the image is the usual pattern used for stirringand it is the one we applied to the atoms in the resultspresented in the next section.
B. Nucleation of a vortex lattice
The position of the stirring beam in the atomic planecan be directly measured by doing an in situ image of the0 o o o o o o o o xy FIG. 10. Mapping of the stirring beam position in the atomiccloud while simulating a circle with radius ∼ µ m. Thecentral image show the stirring positioned at the center ofthe cloud. atoms in the crossed ODT in the presence of the stirring.The repulsive potential that it creates results in a densitydip in the atomic density profile. Figure 10 shows a seriesof absorption images taken while simulating a circularpath with radius of ∼ µ m, used to nucleate vortices.The nucleation of a vortex lattice with the stirringbeam is obtained with a circular path with radius of 8 µ mand different modulation frequency values, ranging from40 to 85 Hz. After achieving an almost pure BEC of Na atoms in the end of the optical evaporation, thestirring beam power is adiabatically ramped up from 0to 75 µ W in 100 ms. During this time, the stirring beamis already rotating around the BEC. The BEC is rotatefor another 1 s at full stirring power, before decreasing itduring other 10 ms. The atomic cloud remains trappedin the ODT for another 100 ms before being released andimaged after 30 ms of time-of-flight. After this time, thesize of the vortices have sufficiently expanded in orderto a clear vortex lattice to be visible with our imagingsystem. In figure 11, we show the resulting vortex latticefor f Stirr = 80 Hz (b) in comparison with the static NaBEC (a).The number of nucleated vortices increases approxi-mately linearly with the rotation frequency approachingthe limiting case of rigid body rotation [41]. On the otherhand, the centrifugal force decreases the in-plane confine-ment creating an upper bound for f Stirr = f r for whichthe atoms are no longer confined. In our experiment, fre-quencies up to f Stirr = 85 Hz do not show any atom lossand by changing the stirring time, vortex lattices with14 vortices were produced with a lifetime of ∼
400 ms.Further investigations on the decay of the vortex latticeare on going to rule out the contributuion of the residualthermal component. (a) (b)
FIG. 11. Comparison between the usual BEC of sodium ob-tained in the crossed dipole trap (a) and the stirred BEC (b)with a vortex lattice.
VI. CONCLUSIONS AND PERSPECTIVES
In this paper, we have described a new experimen-tal machine for studying Bose-Bose superfluid mixturescomposed of Na and the bosonic isotopes of potassiumatoms ( K and K). The versatility of the experimentalapparatus surely opens up new prospects to the study ofBose-Bose mixtures.The first step in simultaneously trapping and coolingthe two atomic species was performed with a two-speciesMOT. Light induced losses strongly affected the potas-sium atoms preventing a successful transference of theatoms to the Plug trap. Next, we described the experi-mental sequence for producing an almost pure Na Bose-Einstein condensate in a crossed optical dipole trap with1 × atoms and lifetimes as long as 14 s. We describedthe implementation of a high resolution setup for imag-ing and stirring. A vortex lattices with up to 14 vorticesand lifetimes of ∼
400 ms were produced attesting theefficiency of the experimental apparatus in studying thedynamics of vortices.Further experiments focused on the role played by theresidual thermal component in the nucleation and decayof the vortex lattice as well as the search for new meth-ods of producing quantum turbulence [66] are of greatimportance. In the case of the Na-K bosonic mixtures,the presence of heteronuclear Feshbach resonances [36]will allow to explore different new scenarios [67]. Inparticular, the dynamics of coupled vortex lattices couldbe studied over the different miscibility regimes allowingthe observation of exotic vortex configurations [19–21].Relying on the large difference between the stirringpotential for sodium and potassium, a species selectivevortex nucleation method could also be realized in orderto study the transfer of vorticity between two superfluids.
VII. ACKNOWLEDGEMENTS