Fast and efficient preparation of 1D chains and dense cold atomic clouds
Antoine Glicenstein, Giovanni Ferioli, Ludovic Brossard, Yvan R. P. Sortais, Daniel Barredo, Florence Nogrette, Igor Ferrier-Barbut, Antoine Browaeys
FFast and efficient preparation of 1D chains and dense cold atomic clouds
Antoine Glicenstein, Giovanni Ferioli, Ludovic Brossard, Yvan R. P. Sortais, Daniel Barredo,
1, 2
Florence Nogrette, Igor Ferrier-Barbut, and Antoine Browaeys Universit´e Paris-Saclay, Institut d’Optique Graduate School,CNRS, Laboratoire Charles Fabry, 91127, Palaiseau, France Nanomaterials and Nanotechnology Research Center (CINN-CSIC),Universidad de Oviedo (UO), Principado de Asturias, 33940 El Entrego, Spain
We report the efficient and fast ( ∼ Rb atomsand of dense atomic clouds trapped in optical tweezers using a new experimental platform. This platform isdesigned for the study of both structured and disordered atomic systems in free space. It is composed of twohigh-resolution optical systems perpendicular to each other, enhancing observation and manipulation capabil-ities. The setup includes a dynamically controllable telescope, which we use to vary the tweezer beam waist.A D1 Λ -enhanced gray molasses enhances the loading of the traps from a magneto-optical trap. Using thesetools, we prepare chains of up to ∼
100 atoms separated by ∼ n ∼ at / cm are obtained by compression of an initial cloud. This high density results into interatomicdistances smaller than λ / ( π ) for the D2 optical transitions, making it ideal to study light-induced interactionsin dense samples. I. INTRODUCTION
The optical response of an ensemble of atoms illuminatedby near-resonant light can be significantly different from theone of a single atom due to light induced dipole-dipole in-teractions [1]. They give rise to collective behaviors suchas modified decay rates or spectral linewidths [2–5], or res-onance shifts [6–8]. Recently these effects have drawn an in-creasing interest, for they can be relevant in fundamental op-tics and have possible applications ranging from optical latticeatomic clocks [9–11] to quantum technologies [12, 13].In order to enhance the collective optical response of anatomic ensemble, two different paths can be followed. Thefirst one consists in using high-density samples, so that theeffect of light-induced dipole interactions is large. This re-quires the preparation of atomic clouds with densities n ful-filling n / k ∼ k = π / λ with λ the atomic reso-nance wavelength. Fundamental questions arise concerningdisordered ensembles, such as the existence of Dicke super-radiance in small samples [14] or the saturation of the indexof refraction for high densities [15]. In disordered clouds, thefield radiated by each emitter acquires a random propagationphase that renders difficult the pristine control of interactioneffects. The second path thus consists in spatially structuringthe cloud at the sub-wavelength scale [16, 17]. In this way, theinterferences can be tailored, making it possible to enhance orsuppress the effect of dipole interactions. This second routecould pave the way to several applications: for example, mir-rors made by an atomic layer [16–18], as recently realized us-ing a 2D Mott insulator [5], controlled transport of excitations[19, 20] and light storage [13, 21] or in quantum metrology[12, 13, 22]. The investigation of collective effects in orderedensembles is also relevant for optical lattice clocks [9, 10, 23],as they could limit their accuracy.In this paper, we follow the two paths introduced above, re-lying on a new experimental platform, which we describe andcharacterize. This platform makes it possible to prepare 1D arrays [24] of Rb atoms, and disordered atomic ensembleswith peak densities reaching n / k ∼
1. This apparatus is anupgrade of our previous experimental setup [7]. It consists oftwo high-resolution optical systems with axes perpendicularto one another in a “maltese cross” geometry similar to [25].These two optical axes used together allow for the simultane-ous observation of the fluorescence light emitted by the atoms(incoherent response [26]) and the transmission through thecloud (coherent part [27]). One of the axes is used to focusa tight optical dipole trap (tweezer) to confine the atoms. Wehave placed in the tweezer beam path a telescope made oftwo lenses with tunable focal length to dynamically controlthe tweezer waist. We use this control to prepare chains ofatoms with variable length when retro-reflecting the tweezerlaser beam, and dense elongated samples after compressing aninitially loaded atomic cloud. The loading of the traps froma cloud of laser cooled atoms is enhanced by implementing Λ -enhanced gray molasses.The paper is organized as follows. Section II describes theoptical setup and its alignment, the imaging system, and the OptoTelescope that allows to produce optical tweezers withtunable waists. Section III presents the realization of a 1Dchain with controllable length and its characterization. Sec-tion IV details the enhancement of the trap loading using graymolasses. Section V introduces a new protocol to preparedense clouds using the tools described before.
II. OPTICAL SETUP, IN-VACUUM LENSES ALIGNMENTAND IMAGING SYSTEMA. Optical setup
Trapping individual atoms or preparing dense atomic sam-ples requires the waist of the dipole trap beam to be on theorder of a few micrometers [28, 29]. This imposes to workwith high numerical aperture (NA), diffraction-limited lenses[30]. As represented in Fig. 1, our apparatus is composed of a r X i v : . [ phy s i c s . a t o m - ph ] J a n OT λ trap =
940 nm fluo. λ = ˆ z ˆ x ˆ y ˆ x MOT ˆ y MOT // g ˆ x ˆ y FIG. 1. Schematic of the experimental setup. Two orthogonal high-resolution (NA=0.44) optical systems based on 4 in-vacuum asphericlenses (AL) create an optical dipole trap, which can be retroreflectedto realize a chain of single atoms in a 1D-optical lattice, and col-lect the scattered light on an electron-multiplying CCD (EMCCD) intwo perpendicular directions. On the tweezer axis, the fluorescenceis separated from the trapping light using a dichroic mirror (DM).The trap radial size is dynamically controlled with the
OptoTelescope (OT). All light enters and exits the vacuum chamber through CF40viewports (Vp). Insert : The x-axis is rotated by an angle of 45° withrespect to the plane containing the horizontal beams of the MOT andthe z-axis. It is therefore not superimposed to the vertical beam ofthe MOT, which is in the direction of gravity g . four in-vacuum aspheric lenses, forming two orthogonal axesin a quasi-confocal configuration. The lenses are manufac-tured by Asphericon ® [31] and feature effective NA = . ◦ with respect to the one containing horizontal MOT beams(see Insert Fig. 1): this gives an extra (vertical) access for theatomic beam entering the trapping region. This configurationallows the six MOT beams to be orthogonal, which facilitatesalignment and the overlapping with the dipole trap. This alsoreduces the stray light scattered in the chamber and collectedby the imaging system.The conjugated planes has been optimized using an opti-cal design software to minimize the aberrations of the twocrossed optical systems, at both the trapping wavelength λ trap =
940 nm and the Rb D2 line ( λ =
780 nm), the nu-merical aperture being fixed. Due to the dispersion propertiesof the glass of the aspheric lenses, the best performances at λ trap and λ are achieved at different focusing positions forinitially collimated beams. For this reason, we work in a trade-off configuration where the optical performances of the lensesare similar for the two different wavelengths. More precisely,we impose that the wavelength-dependent Strehl ratio ( S ) [32]is the same at λ trap and λ . In our specific case, we calcu-late S = .
93, at a distance d = +
285 µm away from the focalpoint of a lens at λ . For this configuration, we calculate that Laser λ B AC D CCDLaser λ d FIG. 2. Sketch of the alignment procedure. A CCD camera is placedat a fixed position d while we shine a λ = the image of an object emitting in vacuum at λ is located at d (cid:39) B. In-vacuum lenses alignment
The alignment procedure is detailed in [33]. It is exper-imentally challenging as it involves intersecting two opticalaxes with a precision much smaller than their field of view( ±
50 µm) [34]. We did the alignment in air, correcting for thedifference in index of refraction with respect to vacuum. Thebarrels holding the aspheric lenses are placed inside a metal-lic lens holder and separated from it with glass spacers. Thelens holder is designed such that the angle formed betweenthe two axes is 90° with a tolerance of ± . ± d away from one lens. A pinhole of diameter ( . ± . ) µm is then mounted on an XYZ translation stageand a rotation stage and placed inside the lens holder. Thispinhole is not small enough to be considered as a point sourcewhen illuminated by a laser beam at λ . We have taken itsfinite size into account for the characterization of the perfor-mance of the lenses [33]. The pinhole is first moved parallelto the lens axis to minimize the size of its image on the CCD.Once the pinhole is in the targeted object plane, we move it inthe transverse plane to maximize the Strehl ratio, thus placingit on the lens optical axis. The pinhole is then rotated by 90 ◦ toface another lens. This procedure is performed for each lensand by keeping track of the pinhole motion, we obtain a map-ping of the best foci. Finally, the spacers thickness is adjustedto bring all the foci at the same point. After the procedure,we obtain a satisfying alignment of the lenses and the opticalaxes cross with a residual offset (cid:46) C. Imaging system
The atoms held in the dipole trap are imaged with the twohigh-resolution axes (Fig. 1), with a diffraction-limited reso-lution of 1 . λ / ( NA ) (cid:39) ˆ z ,the fluorescence or the transmitted light is separated from thetrap light using a dichroic mirror and interferometric filters,and is collected by an electron-multiplying CCD (EMCCD)with pixel size 16 µm ×
16 µm [35]. The magnification of theimaging system along this axis is 6 .
4, leading to an effectivepixel size in the object plane of 2 . ˆ x -axis is collected on the samecamera, allowing for the observation of the atoms in two or-thogonal directions in a single image. The magnification onthe transverse axis is ∼
16, leading to an effective pixel sizeof 1 µm in the object plane. Both resolutions were verified us-ing calibrated pinholes in planes conjugate to the atoms plane.The magnification was confirmed by measuring simultane-ously the displacement of trapped atoms on both axes whenmoving the trapping beam by a known distance. The esti-mated collection efficiency of both imaging systems is ∼ λ =
780 nm). This value isconfirmed by the measurement of the fluorescence at satura-tion of a single Rb atom in a tight dipole trap. As detailedbelow, we use this atom as a probe to characterize the trap(size and depth), as was done in [30].
D. The
OptoTelescope
Our apparatus includes a telescope with tunable magnifica-tion, which we name here
OptoTelescope (OT). This telescopeis composed of a pair of 1 inch lenses with voltage-controlledfocal lengths, manufactured by OptoTune ® [36], and placed inan afocal configuration. Tunable lenses allow for the dynam-ical manipulation of dipole traps [37]. Here, using the OT,we dynamically change the size of the trapping beam beforethe aspherical lens and thus the optical tweezer waist. To limitaberrations from the OT, we use a beam diameter of (cid:39) × OptoTelescope by performing in situ measurements on a single atom trapped in the tweezer. For agiven magnification, the waist of the trap w is measured asfollows. For a fixed power P , the peak intensity and thus thelight-shift induced by the trap (proportional to the trap depth U ) are obtained by using a push-out beam expelling the atomfrom the trap. The light shift is measured from the detuning ofthis beam for which the push-out effect is the largest, recorded . . . λ trap =
940 nmOptoTelescope magnification D i po l e t r a p r a d i a l s i ze , w ( µ m ) FIG. 3. Dipole trap waist at 1 / e as a function of the OT magnifi-cation. The diffraction limit 1 . λ trap / NA (cid:39) . for various trap depths. The trap waist is then extracted using U ∝ P / w . The results were checked by independent mea-surements of the oscillation frequencies of individual trappedatoms [30]. We are able to dynamically change the size of thetrap between about 1 . . III. REALIZATION OF A CHAIN OF ATOMS WITHCONTROLLABLE LENGTH
In this section, we present the preparation and character-ization of one-dimensional atomic chains of cold Rb atoms,using the tools described in the previous section.As represented in Fig. 1, we produce the chain by retro-reflecting the tweezer beam using the second aspherical lensesplaced on the same axis, thus forming a 1D optical lattice withan inter-site spacing λ trap / =
470 nm [38]. The small beamwaist of the tweezer ensures a tight transverse confinement.This 1D array in then loaded from the MOT with a filling frac-tion averaged along the chain of (cid:39) .
25. We will show in thenext section that the loading can be improved up to ∼ . z R = π w / λ trap . Experi-mentally, we realize atomic chains with different lengths (andatom number) by tuning the waist of the trapping beam usingthe OT. As changing the waist also modifies the trap depth, weadapt its power to keep the depth at the center of the chain at ∼ ∼
100 µm (hence ∼
200 sites).
20 40 60 80 100 120 140 16000 .
51 Position (µm) F l uo r e s ce n ce ( a r b . un it s ) (a)(b) FIG. 4. (a) Averaged image of the fluorescence collected by the trans-verse imaging axis. (b) Cuts of the fluorescence along the chain forvarious chain lengths. p = p = p = p =
40 20 40 60 80 100 120 1400.080.511.522.5 Position (µm) T r a p m odu l a ti on fr e qu e n c y ( M H z ) . . . . . . A t o m l o ss e s ( a r b . un it s ) FIG. 5. Atom losses as a function of the position in the chain andthe modulation frequency of the trapping beam. The dashed lines arethe calculated axial oscillation frequencies. The multiple resonancescorrespond to 2 ω z / p with p integer. To characterize the chain, we measure the local transverseand longitudinal trapping frequencies ω r and ω z along thechain axis. To do so, we rely on parametric heating by modu-lating the intensity of the trapping beam at a given frequency,inducing losses at 2 ω r or 2 ω z . Since the trap depth variesalong the chain, the oscillation frequencies depend on the po-sition, and so do the resonant frequencies of the parametricheating. Experimentally, we first load a chain from the MOTand take a first reference fluorescence image. The trap beampower is then set at a value of 140 mW while, for this mea-surement, the waist is set to 3 . ω z (cid:39) π × ω r (cid:39) π ×
70 kHz at the centerof the chain. The beam intensity is then modulated with a rel-ative amplitude of 5% during 100 ms using an arbitrary wave-form generator. A second fluorescence image of the chain isthen taken and compared to the reference image to evaluatethe atom losses. This sequence is repeated 50 times to aver-age over the chain filling. Figure 5 shows the atom losses due to the axial excitation.The resonance frequencies extracted with this method are ingood agreement with the calculated oscillation frequencies(dashed lines), confirming the expected value of the waist.The different dashed lines reported in Fig. 5, are given by2 ω z / p with p integer. We observe losses at these frequenciessince the amplitude modulation is not perfectly sinusoidal andthus contains tones at multiples p of the driving frequency.We also observe losses on the chain edges where the trap isthe shallowest: these are due to the reference imaging lightexpelling atoms from the shallow traps, which are thus notrecovered in the second fluorescence image. The same ex-periment was done for radial oscillation frequencies, obtain-ing also in this case a good agreement between the measuredtrapping frequencies and the predicted ones. IV. OPTIMIZATION OF THE LOADING USING Λ -ENHANCED GRAY MOLASSES Gray molasses (GM) are commonly used to achieve sub-Doppler cooling of atoms using dark states [39–43]. Theuse of GM in a tight optical tweezer offers two interestingprospects. First, the low photon scattering rate in dark statesreduces light-induced collisions. This yields a higher densityof the atomic cloud the tweezer is loaded from, and hence alarger number of atoms in the tweezer. Second, their blue de-tuning with respect to the atomic frequency should permit totailor light-induced collisions to selectively remove a singleatom out of a pair, resulting into exactly one atom per trapwith high probability [44, 45].We first consider the loading of a single atom in a small(non-retroreflected) tweezer, and apply Λ -enhanced gray mo-lasses [46] on the Rb D2 line ( λ =
780 nm) [47]. Thecooling beam is blue-detuned from the ( S / , F = ) to ( P / , F (cid:48) = ) transition and superimposed with the six MOTbeams with intensity I ∼ I sat = .
67 mW cm − per beam. Thecoherent repumper is created from the same laser using anelectro-optical modulator with frequency equal to the groundstate hyperfine splitting ν = .
68 MHz. The intensity ofthe repumper is I ∼ I sat /
10 per beam, given by the sidebandamplitude. Since gray molasses rely on the blue detuningof the cooling lasers, the optimal detuning will depend onthe light-shift induced by the tweezer beam. After the MOTbeams are switched off, we study the loading of a single atomfrom the GM into the tweezer (waist w = . ∼
20 µK instead of 80 µK), and for amuch broader range of the tweezer depth. Also, when load-ing directly from the MOT, the atoms can be captured in trapswith depth U / k B ∼ U / k B ∼
200 µK. Furthermore, weobserve that the GM detuning does not significantly changethe temperature or the loading over a wide range of parame- . .
04 Number of counts on the EMCCD O cc u rr e n ce d e n s it y > FIG. 6. Histogram of the collected fluorescence of atoms in a traploaded with the GM (blue), in comparison with a trap loaded with asingle atom (red). The fluorescence is induced in both cases by 20msof MOT beams with detuning 3 Γ , where Γ is the natural linewidthof the Rb D2 line. A background image, without atom, has beensubtracted. ters for detunings between 50 and 120 MHz above the transi-tion and depths U / k B between 200 µK and 1 mK. For largertrap depths and small detunings, the GM frequency becomesresonant with the ( S / , F = ) to ( P / , F (cid:48) = ) transition,resulting in heating of the atom. However, while we observeefficient cooling when applying the GM, we have not foundloading probabilities significantly higher than 50% in a singletweezer, or 25% in chains of traps (retroreflected tweezers),similar to what we achieved with the MOT. This might bedue to the fact that the blue-detuned beam on the ( S / , F = ) to ( P / , F (cid:48) = ) transition is detuned to the red of the ( S / , F = ) to ( P / , F (cid:48) = ) transition (267 MHz higher infrequency), causing light-induced collisions, which may limitthe loading.To circumvent this issue, we have thus implemented graymolasses on the D1 line [ ( S / , F = ) to ( P / , F (cid:48) = ) transition]. In the single non-retroreflected tweezer, after op-timization, we were not able to obtain individual atoms witha probability significantly higher than 50%, whatever the de-tuning. This is in contrast to what was reported using a blue-detuned beam [44] or GM on the D1 line [45]. To explain thisobservation, we compare the volume of our tweezer to theone used in Ref. [45] and estimate ours to be a factor of > in-situ atom number.Finally, we have used D1 gray molasses to improve theloading of the atom chain. We are now able to load a chain oftraps with a 50% probability. This is likely due to the fact thaton average there are more than one atom per site following thegray molasses loading. The application of the MOT light forimaging then induces strong light-induced collisions, leavingeither 0 or 1 atom. Further investigations will be necessary tounravel the loading mechanism of this chain of closely-spacedtraps by D1 λ -enhanced gray molasses. We have also foundthat the loading using GM is more stable than the direct load-ing from the MOT in terms of daily fluctuations. V. PREPARATION OF DENSE ATOMIC CLOUDS
As mentioned in the introduction, one of the motivationsfor our new set-up is the study of light scattering in dense en-sembles. We present here a loading protocol based on the newtools of the setup that allows preparing dense enough samples.The main idea is to load as many atoms as possible into a largesingle-beam dipole trap using GM on the D1 line, and com-press the cloud by dynamically reducing the beam waist [49]using the
OptoTelescope .We start from a 3D-MOT, which is compressed in 15 ms byred-detuning the MOT beams from -3 Γ to -5 Γ . We then de-crease the magnetic field gradient by 50%. The MOT beamsare then switched off and the GM is applied for 200 ms, withthe dipole trap on. At this stage, the trap depth is U / k B (cid:39) . w (cid:39) . n ≈ . × at / cm . Theuse of GM is the key ingredient here that allows for the load-ing of this large number of atoms. The cloud has an aspectratio of about 12 along the trapping axis. The atom numberis evaluated from the fluorescence collected during the illumi-nation of the cloud with a 10 µs-pulse of resonant light and di-viding the signal by the same quantity measured with a singleatom. To avoid effects caused by light-induced interactions,the imaging pulse in sent after a time-of-flight of 10 µs dur-ing which the density drops by about an order of magnitude[51]. The temperature is measured by fitting the cloud size fora variable time-of-flight.The trap is then compressed to a waist w = . OptoTelescope in 30 ms,keeping the power constant. Next, the trap depth is increasedin 10 ms up to 7 . . n ∼ at / cm or equiva-lently to n / k = . ± .
3. This density is three times largerthan the one obtained in clouds of ∼
500 atoms [26, 29] withour previous apparatus which relied on a first, large dipole trap , ,
000 time (µs)a) Atom number N T (µK)0 50 100 150 2000 . .
52 time (µs)c) Peak density n / k FIG. 7. Time evolution in the final trap of atom number (a) and tem-perature (b). In (a) and (b), the solid lines correspond to the solutionsof (1) and (2) with L as single fit parameter. (c) Peak density n inthe trap, deduced from (a) and (b). acting as a reservoir to load a second small tweezer.Such a high density results in large 3-body losses and highelastic collision rates. To characterize them and confirm theextracted value of the density, we study its dynamics. To doso, we have measured the cloud atom number N and temper-ature T as a function of the time after the end of the com-pression. The results are shown in Fig. 7(a). The temporalevolution of N and T is described by the following systemof coupled equations that takes into account of 2- and 3-bodylosses [29, 52, 53]: dNdt = − γ N T − γ ( σ ( T ) , T ) N T (1) dTdt = T (cid:20) γ N T − ˜ γ ( σ ( T ) , T ) NT (cid:21) (2)where the parameter γ depends on the trap geometry and isproportional to the 3-body losses coefficient L . The coeffi-cients γ and ˜ γ depend on the temperature, the trap geom-etry and on the two-body elastic cross-section σ ( T ) , whosetemperature dependence takes into account the d -wave res-onance at 350 µK. We interpolate the data of [54] to finda functional form of σ ( T ) . We fit the decay of the atomnumber with the solution of Eq. (1), leaving solely L as afit parameter. We obtain L = ( ± ) × − cm / s. Thisvalue is larger [55] than those found in the literature [56, 57].Note that there exists no prediction for the effect of the d -wave resonance on 3-body losses, which could enhance L at T =
650 µK. We thus do not expect to find the literature val-ues, which were measured deep in the s -wave regime. We alsocompare the model prediction of the temperature evolution to the data [see Fig. 7(b)], and find a very good agreement. Thetemperature is almost constant, which justifies the assumptionof a temperature-independent L (and hence γ ) in the model.Combining the measurements of the atom number and of thetemperature, we calculate the cloud density. Its evolution isshown in Fig. 7(c).Our experiment is therefore able to efficiently produce mi-croscopic clouds containing up to a few thousand atoms atdensities n ∼ k . This corresponds to the regime wherethe atoms become strongly coupled by light-induced reso-nant dipole-dipole interactions (scaling as ¯ h Γ / ( kr ) α with α = , , VI. CONCLUSION
We have built an experimental setup that is well-suitedfor the study of light scattering in cold atom ensembles ei-ther in an ordered or disordered configuration. Our platformcombines two high-resolution optical systems perpendicularto each other, an optical tweezer with a dynamically tunablewaist and gray molasses on the D1 line. By retroreflectingthe optical tweezer we create an optical lattice of control-lable length, allowing for the preparation of atomic arrayswith an average interatomic distance 1 . λ . We recently usedthis feature to investigate a collective enhancement of light-induced interactions in 1D arrays [8, 59]. The same strategycan be applied with an optical lattice of shorter wavelength(e.g. combining a repulsive optical lattice at 532 nm with theinfrared tweezer for confinement). This would increase col-lective effects even further, enabling the observation of sub-radiant modes in ordered arrays [21, 60]. Furthermore, wepresented a protocol for preparing dense clouds in a tightlyfocused optical tweezer that exploits the dynamical tunabil-ity of the OT. In this way we create clouds with a peak den-sity larger than k at a rate > ACKNOWLEDGMENTS
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