Optical transport and manipulation of an ultracold atomic cloud using focus-tunable lenses
Julian Léonard, Moonjoo Lee, Andrea Morales, Thomas M. Karg, Tilman Esslinger, Tobias Donner
OOptical transport and manipulation of an ultracold atomic cloud using focus-tunablelenses
Julian L´eonard, Moonjoo Lee, Andrea Morales, Thomas M. Karg, Tilman Esslinger, and Tobias Donner ∗ Department of Physics, ETH Z¨urich, 8093 Z¨urich, Switzerland (Dated: September 26, 2014)We present an optical setup with focus-tunable lenses to dynamically control the waist and focusposition of a laser beam, in which we transport a trapped ultracold cloud of Rb over a distanceof 28 cm. The scheme allows us to shift the focus position at constant waist, providing uniformtrapping conditions over the full transport length. The fraction of atoms that are transported overthe entire distance comes near to unity, while the heating of the cloud is in the range of a fewmicrokelvin. We characterize the position stability of the focus and show that residual drift ratesin focus position can be compensated for by counteracting with the tunable lenses. Beyond being acompact and robust scheme to transport ultracold atoms, the reported control of laser beams makesdynamic tailoring of trapping potentials possible. As an example, we steer the size of the atomiccloud by changing the waist size of the dipole beam.
The control of cold atomic gases with dipole potentialsproduced by far-off-resonance laser beams has provento be a uniquely powerful tool in the production andmanipulation of quantum gases [1]. Recently, substan-tial progress has been made by introducing experimen-tal techniques like high-resolution microscopy [2, 3] orholographic beam-shaping [4] to create atomic clouds inlocally structured [5, 6] or box-like potentials [7]. Yet,the ability to change optical potentials dynamically isnot very advanced. However, the most widely used im-plementation of dynamical potentials is the transport ofultracold atoms between two spatially separated regionsof an experiment, with one region optimized for the pro-duction of the cold atomic cloud and the other regionoptimized to investigate the cloud [8]. With the increas-ing interest in hybrid setups coupling cold gases to otherquantum systems [9–11], the transport of atomic cloudsnow has become a crucial technique.Optical transport can be performed by displacing thefocus of a dipole beam in which the atoms are trapped.This has been achieved with the focussing lens mountedon an air-bearing translation stage [8]. Compared tomagnetic transport, where the trap center is shifted ei-ther by a chain of overlapping coil pairs through which acurrent is applied sucessively [12], or by physically mov-ing one coil pair [13], this avoids to surround the vacuumchamber with a number of magnetic coils limiting theoptical access. Yet, it comes with the drawback of plac-ing an expensive and cumbersome translation stage closeto the vacuum chamber, which bears the risk of trans-ferring vibrations to the dipole trap or the optical table.Another method relies on trapping the atomic cloud ina one-dimensional optical lattice, which is then turnedinto a moving standing wave by detuning the frequenciesof two counterpropagating beams with respect to eachother [14]. However, for Gaussian beams this techniqueis only applicable on short distances or in the vertical ∗ [email protected] direction, because of the weak radial confinement com-pared to gravity [15].Here, we present a different approach based on focus-tunable lenses, which allows to move the position of adipole trap and additionally to tune its size. It combinesa compact arrangement with a static setup. The rapidprogress in the development of tunable and adaptiveoptics now allows to fabricate high-grade focus-tunablelenses, establishing them in an increasing number of fieldsof research and industry, such as material processing [16],photography [17], trapped nanoparticles [18] or bioimag-ing [19]. We use tunable lenses of the type EL-10-30 fromthe supplier Optotune . The lens surface is spherical withan aperture of 10 mm and a wavefront error of 0.1–0.2 λ (depending on the focal length), where λ = 1064 nm is FIG. 1. Setup to dynamically control size and position of adipole trap. (a) Transport at constant waist over a distanceof 28 cm. If the separation between the tunable lens T andthe static lens L equals the focal length f of the latter, thetwo beams can be transformed into each other by tuning f ,while maintaining the same divergence θ = d/f , thus thesame waist size, between A and B. (b) Independent controlover waist size and position of the focus. Replacing the firstlens with a tunable lens T allows to change the beam size at T , resulting in a different divergence behind L . a r X i v : . [ c ond - m a t . qu a n t - g a s ] S e p (d)(c) (b)(a) FIG. 2. Characterization of the optical transport. (a) The transfer fraction η = N B /N A and (b) the increase in temperature∆ T = T B − T A are shown for a dipole beam power of P = 3 . t anddipole beam power P . The small arrows indicate the columns for the line cuts in (a) and (b). the anti-reflection coating wavelength. The body of thelens is filled with a low-optical absorption liquid and thesurface is sealed off with an elastic polymer membrane.As indicated in the sketches in Fig. 1, an applied cur-rent in a coil can increase the membrane curvature bya magnetic ring mechanically pressing liquid from theouter area to the lens center. Thus the focal length canbe tuned within a range of 40–140 mm [20].We use these lenses to transport a cloud of ultracoldatoms over a distance of 28 cm from a first vacuum cham-ber A, where the atomic cloud is prepared, to a secondone B, which is our science chamber, as shown in Fig. 1.In principle, a focus displacement can be achieved usinga single tunable lens focussing a collimated beam. How-ever, increasing the focal length increases the waist sizeas well, thereby changing trapping frequencies and trapdepth during the transport. Instead, the setup presentedhere provides uniform trapping conditions over the fulltransport distance. This is preferrable, since only highconfinement and large trap depth allow for fast transport.The two beams in Fig. 1 (a) are focussed behind the staticlens L with focal length f = 300 mm at distances f and2 f . Their waist sizes are equal if their divergences are.This requires beam diameters of d and 2 d at L , respec-tively, resulting in the same divergence of θ = d/f for both. The beam with the focus at f must be collimatedbefore the lens, and the beam with the focus at 2 f musthave the same divergence θ before passing L . Thereforethe two beams have the same size at a distance f be-fore L . Placing a lens T with tunable focus f at thisposition allows to continuously transform one beam intothe other, resulting in a moving focus at constant waist.Since f > T . This canbe achieved by a first static lens, which in turn definesthe waist size behind L . In order to even gain indepen-dent control over position and waist size of the focus, thefirst static lens can be replaced by a tunable lens T , asshown in the extended setup in Fig. 1 (b). Calculationof the Gaussian beam propagation through the systemenables us to compute waist size and focus position forany focal length tuple ( f , f ).This extended setup is used in the following, choosingthe distances as indicated in Fig. 1. We send a collimatedlaser beam with a 1 /e diameter of 5 . λ = 1064 nm out of a photonic crystal fiber tothe tunable-lens setup. The lenses are steered via low-noise current sources. The focal lengths are first set to f A = 52 mm and f A = 88 mm, resulting in a measureddipole beam waist size of w = 47 . µ m with the focus atthe position A. For a dipole beam power of P = 4 . ω r / π = 802 Hz and U = k B × µ K, respectively.The ultracold atomic cloud is generated from initially5 × Rb atoms in a three-dimensional magneto-optical trap (MOT) loaded from a two-dimensionalMOT. After evaporative cooling in a hybrid trap formedout of the dipole beam potential and a magneticquadrupole trap [21], we entirely switch off the magneticpotential and end up with N A = 1 . × atoms at atemperature of T A = 4 . µ K in the dipole trap. Choos-ing a dipole beam power of P = 4 . f A with anamplitude of ∆ f A = 0 . z = 4 . ω z / π = 1 . / s, overallincreasing with laser power, which lie about a factor oftwo to six above the expected spontaneous emission rates.In light of our low longitudinal trapping frequency ω z , weattribute this additional heating to the susceptibility ofthe system to residual noise in the hertz range.Tuning the focal length of T , we now move the cloudposition. While keeping f = 52 mm constant, we applyan s-shaped position profile (parabolic velocity profile)from f A = 88 mm to f B = 138 mm and subsequentlymeasure the temperature at position B by time-of-flightabsorption imaging perpendicular to the transport axis.We confirm the temperature and atom number measure-ments in both imaging systems to be compatible withineach other by imaging the cloud at A, after the trans-port at B and after a double transport back at A. Wedo not observe any systematic difference in atom num-ber and temperature within our reproducibility of 4 %and 6 %, respectively. The imaging is carried out di-rectly after the transport is completed, neglecting resid-ual dipole oscillations that damp out with a time constantof τ dipole = 0 . P = 3 . η = N B /N A as a function of the trans-port duration t . Depending on t , transfer fractionsclose to unity can be reproducibly obtained. Fig. 2 (b) FIG. 3. Longitudinal drift of the cloud center position. Thered circles and the blue triangles represent the cloud positionwithout and with the compensated drift by tuning the focallength f over time. The dashed red line is a linear fit to thecloud position, giving a drift rate of 5 . × z / s, where z = 6 . shows the increase in temperature due to the transport,∆ T = T B − T A , where in addition the previously cali-brated heating rate for a static trap has been subtractedto get access to the pure heating caused by transportingthe atoms. For all values of t , the heating lies in therange of a few mikrokelvin, typically around 3 µ K. Weemphasize that since this data represent a difference, theactual standard deviation of the temperature data val-ues is smaller than the errorbars apparently suggest. Forboth atom number and temperature we observe the samereproducibility as before the transport, implying that thetunable-lens setup does not alter the reproducibility ofour experimental conditions.To further characterize the transport behaviour andto prove the flexibility on the choice of parameters, wevary both the transport duration t and the dipole beampower P over a broad range. Fig. 2 (c) shows the transferfraction η as a function of these parameters. We ob-serve values close to unity, i.e. η max = 97(3) %, whenchoosing sufficiently high laser powers and transport du-rations. For short transport durations and low laser pow-ers, we observe almost no transported atoms. This canbe explained by the small trap depth at low dipole beampowers, which is decreased below k B T A if the accelera-tion during the transport gets high for short transportdurations. The temperature increase ∆ T is shown inFig. 2 (d). For large trap depths, we observe an increasein temperature of ∆ T = 1–5 µ K. For short transportdurations and small laser powers, the finite trap depthcomes again into play and acts as an evaporative coolingstep for the atoms.The plots in Figs. 2 (c) and (d) both show diagonal pat-terns, indicating a highly nonlinear behaviour of ∆ T and η in the considered parameter space of t and P . We at- µ µ FIG. 4. Dynamic control over the trapping potential. Thecloud radius can be changed by increasing the waist size of thedipole beam trap at constant optical power (red data points).The grey shaded area spans the 2- σ confidence interval ofthe expected cloud size based on the independently measuredtemperature, taking into account the finite resolution of ourimaging setup with a numerical aperture of NA = 0 .
06. Thered dashed line predicts the cloud radius assuming an adia-batic expansion of the trap. Each data point represents theaverage of five pictures, the errorbars denote the statisticalerror of one standard deviation. tribute this to the nonadiabatic nature of our transport:Since the transport duration is comparable to the inverseof the trapping frequency, t ∼ /ω z , the cloud does notfollow adiabatically the trap position, but dipole oscilla-tions are excited. Depending on the specific relation of ω z and the transport duration, these dipole oscillationscan be of different amplitude or even fully suppressed[25]. They are converted to heat via collisions during thetransport and still continue afterwards. In combinationwith the finite trap depth, the oscillations in return leadto atom loss.The position stability of the dipole trap can be testedby measuring the drift behaviour for long hold times. Af-ter optical transport with the parameters t = 2 . P = 3 . . / s, correspond-ing to 5 . z = 6 . f B in the oppositedirection. During the hold time, we tune f B with the rate ∆ f B = − .
13 mm / s, corresponding to a real-spacechange in focus position of − .
37 mm / s. As shown inFig. 3, the drift rate can be almost entirely compensatedwhile maintaining the reproducibility in position [26]. Wealso check for position drifts in the radial direction whenholding the cloud at a constant position, but observe nomeasurable drift rate within an uncertainty of 1 µ m.Our optical setup allows us to dynamically and inde-pendently change the trap curvature and depth, withoutaffecting its position. So far, this was not possible, sincelowering the trapping frequency by decreasing the opti-cal power via ω r,z ∼ √ P was always accompanied by asmaller trap depth. Here, we tune the size of the cloudby changing the waist size with the focus-tunable lenses.During optical transport with P = 3 . t = 2 . f B , f B ), corresponding to dif-ferent waist sizes of 50–110 µ m at position B. The radialcloud size is subsequently measured by in situ absorptionimaging. As shown in Fig. 4, we observe a significant en-largement of the cloud radius for increasing waist size.At constant temperature, the cloud radius dependsquadratically on the waist size, σ r ∼ w . Taking intoaccount the adiabatic expansion of the cloud, the de-creased temperature leads to a linear dependency [27].We observe good agreement of the measurements withthat assumption for moderate waist sizes. Above waistsizes of ∼ µ m, the cloud radius increases faster thanlinearly, hinting towards nonadiabatic expansion alongthe long axis of the trap. Including time-of-flight tem-perature measurements to deduce the actual extensionof the cloud, we find good agreement of the cloud radiiover the whole range of examined waist sizes.In conclusion, we have demonstrated optical transportof ultracold atoms using focus-tunable lenses, achievingtransfer fractions close to unity at temperatures of a fewmicrokelvin. Furthermore, our setup offers the uniquepossibility to tune the waist size of the dipole beam,which allows to dynamically change the radius of thecloud at constant trap depth. As a consequence, a largerange of trap curvatures and densities can be exploredto optimize evaporative cooling [28] and trap transfer.The latter is particularly interesting for loading opticallattices to avoid heating due to density redistribution[29, 30]. Another possible application would be to pro-duce an interference pattern with tunable lattice constant[31] by injecting two off-centered beams into a tunable-lens setup. Finally, the unprecedented dynamic controlover size, density and collision rate realizable with tun-able lenses may be used to implement novel schemes forthe production and manipulation of ultracold gases.We would like to thank Laura Corman, ChristianZosel and Samuel H¨ausler for their contributions at anearly stage of the experiment. 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