Ultracold atom interferometry in space
Maike D. Lachmann, Holger Ahlers, Dennis Becker, Aline N. Dinkelaker, Jens Grosse, Ortwin Hellmig, Hauke Müntinga, Vladimir Schkolnik, Stephan T. Seidel, Thijs Wendrich, André Wenzlawski, Benjamin Weps, Naceur Gaaloul, Daniel Lüdtke, Claus Braxmaier, Wolfgang Ertmer, Markus Krutzik, Claus Lämmerzahl, Achim Peters, Wolfgang P. Schleich, Klaus Sengstock, Andreas Wicht, Patrick Windpassinger, Ernst M. Rasel
UUltracold atom interferometry in space
Maike Diana Lachmann, ∗ Holger Ahlers, † Dennis Becker, Stephan Tobias Seidel, ‡ Thijs Wendrich, Naceur Gaaloul, Wolfgang Ertmer, and Ernst Maria Rasel
Institut f¨ur Quantenoptik, Leibniz Universit¨at Hannover, Welfengarten 1, 30167 Hannover, Germany
Aline Nathalie Dinkelaker, § Vladimir Schkolnik, Markus Krutzik, and Achim Peters
Institut f¨ur Physik, Humboldt-Universit¨at zu Berlin, Newtonstraße 15, 12489 Berlin, Germany
Jens Grosse, ¶ Hauke M¨untinga, ∗∗ Claus Braxmaier, †† and Claus L¨ammerzahl Zentrum f¨ur angewandte Raumfahrttechnologie und Mikrogravitation,Universit¨at Bremen, Am Fallturm, 28359 Bremen, Germany
Ortwin Hellmig and Klaus Sengstock
Institut f¨ur Laserphysik, Universit¨at Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany
Andr´e Wenzlawski and Patrick Windpassinger
Institut f¨ur Physik, Johannes Gutenberg-Universit¨at, Staudingerweg 7, 55128 Mainz, Germany
Benjamin Weps ‡‡ and Daniel L¨udtke Institute for Software Technology, Deutsches Zentrum f¨ur Luft und Raumfahrt e.V.,Lilienthalplatz 7, 38108 Braunschweig, Germany
Andreas Wicht
Ferdinand-Braun-Institut, Leibniz-Institut f¨ur H¨ochstfrequenztechnik, Newtonstraße 15, D-12489 Berlin, Germany
Wolfgang P. Schleich
Institut f¨ur Quantenphysik and Center for Integrated Quantum Science and Technology (IQ ST ),Ulm, Germany; Institute of Quantum Technologies,German Aerospace Center (DLR) S¨oflinger Str. 100, 89081 Ulm,Germany; Hagler Institute for Advanced Study at Texas A&M University; TexasA&M AgriLife Research; Institute for Quantum Science and Engineering (IQSE) andDepartment of Physics and Astronomy, Texas A&M University, College Station, USA (Dated: January 6, 2021) Bose-Einstein condensates (BECs) in free fallconstitute a promising source for space-bornematter-wave interferometry. Indeed, BECs enjoya slowly expanding wave function [1, 2], display alarge spatial coherence [3] and can be engineeredand probed by optical techniques [4–7]. On asounding rocket, we explore matter-wave fringes ∗ [email protected]; these authors contributedequally to this work † these authors contributed equally to this work ‡ Now at Airbus Defense and Space GmbH, Willy-Messerschmitt-Str. 1, 82024 Taufkirchen, Germany § Now at Leibniz-Institut f¨ur Astrophysik Potsdam, An der Stern-warte 16, 14482 Potsdam, Germany ¶ Also at Institut f¨ur Raumfahrtsysteme, Deutsches Zentrum f¨urLuft und Raumfahrt e.V., Linzerstr.1, 28359 Bremen, Germany ∗∗ Now at Institute for Satellite Geodesy and Inertial Sensing, Ger-man Aerospace Center (DLR), Am Fallturm 9, 28359 Bremen,Germany †† Also at Institut f¨ur Raumfahrtsysteme, Deutsches Zentrum f¨urLuft und Raumfahrt e.V., Linzerstr.1 ,28359 Bremen, Germany ‡‡ now at MORABA, Deutsches Zentrum f¨ur Luft und Raumfahrte.V., M¨unchener Straße 20, 82234 Weßling, Germany of multiple spinor components of a BEC releasedin free fall employing light-pulses to drive Braggprocesses and induce phase imprinting. The pre-vailing microgravity played a crucial role in theobservation of these interferences which not onlyreveal the spatial coherence of the condensatesbut also allow us to measure differential forces.Our work establishes matter-wave interferometryin space with future applications in fundamentalphysics, navigation and Earth observation [8]. Interference of two BECs constitutes the hallmark ofmacroscopic coherence. The first observation [3] of thecorresponding fringes has ushered in the new era of co-herent matter-wave optics. In this article we report onthe first interference experiments performed during therecent space flight of the MAIUS-1 rocket [2] demonstrat-ing the macroscopic coherence of the BECs engineered inthis microgravity environment.In contrast to [3] which used an optical double-wellpotential to interfere two BECs, we employ Bragg pro-cesses as well as phase imprinting simultaneously in dif-ferent magnetic spinor components. The resulting richinterference pattern stretches across the complete spatial a r X i v : . [ phy s i c s . a t o m - ph ] J a n Figure 1. Optical arrangement for space-borne light-pulse interferometry employing a multi-component rubidium Bose-Einsteincondensate (BEC) and associated diffraction processes. a , b , After release of the BEC two light beams, A and B, with differentfrequencies ν A and ν B , and intensities travel in opposite directions parallel to the atom chip and generate a moving opticallattice driving Bragg processes which coherently transfer momentum to the atomic wave packet along the x-direction ( b ). Twoadditional light beams tilted by two degrees emerge due to reflections of the beams A and B on the optical viewports. c , Theirinterference with the lattice beams gives rise to a traveling spatial intensity modulation in the y-direction modifying the BECwave function as well as inducing weak double Bragg processes in x-direction (not shown). d , In addition, the light beamsare diffracted at the atom chip and the arising interference modulates their intensity in y-direction. The various effects of thelight pulses on the multi-component wave packet are detected by a CCD-camera recording the shadow of the BEC irradiatedby light (green circle) from the z-direction. Earth gravity pulls along the x-direction during space flight, and along the x-zdiagonal on ground. distribution of the wave packets. We analyse its contrastas its temporal evolution can be exploited to detect forcesacting differently on the spinor components. Applied tothree dimensions, this arrangement could serve as a vec-tor magnetometer. Moreover, due to the higher achiev-able spatial resolution, our method compares favourablyto the determination of the BEC position based on a fitof the envelope of its spatial density distribution. Thelatter was e.g. proposed for the measurement of gravitygradients in the STE-QUEST mission [9] designed as aspace-borne quantum test of the equivalence principle.Indeed, space displays an enormous potential for ad-vancing high-precision matter wave interferometry be-cause the size of the device is no longer determined by thedropping height required on ground [10]. Additionally,low external influences and the reduced kinematics of thesource allow us to control systematic effects. For thesereasons quantum tests of general relativity [9, 11, 12], thesearch for the nature of dark matter and energy [11, 13–16], the detection of gravitational waves [11, 17, 18], andsatellite gravimetry [19–22] represent only a few of themany promising applications of atom interferometry inspace. Being at the very heart of the aforementioned propos-als, our experiments mark the beginning of space-borne coherent atom optics. They have benefited from our ear-lier studies on BEC interferometry at the drop towerin Bremen [23, 24] exploring methods for high-precisioninertial measurements. Moreover, in other groups in-terferometry with laser-cooled atoms was performed onparabolic flights [25] and a cold-atom clock was studiedon a satellite [26]. Exploration of degenerate quantumgases is currently continued with the Cold Atom Labo-ratory (CAL) in orbit [27].Our interferometer is based on an atom-chip apparatusfor trapping and cooling of the atomic ensembles deliv-ering BECs of about 10 rubidium-87 atoms within 1.6seconds [28, 29]. The atom chip enables a very com-pact and robust design required by the demanding con-straints of the rocket in terms of mass, volume, powerconsumption as well as vibrations and accelerations dur-ing launch. The necessary autonomous experimental con-trol is realised by a customised onboard software allowingfor image analysis, self-optimization of parameters, oper-ation of a decision tree and real time interaction with theground control.The BECs are created in the magnetic hyperfineground state F = 2, m F = +2 and then released from thetrap. We transfer the freely falling matter wave packetinto a superposition of several spinor components by em-ploying radio frequencies [30], or by changing the mag-netic field orientation. Optionally, we spatially sepa-rate them after the interferometry sequence by a Stern-Gerlach arrangement.The experiments reported here were performed with asuperposition of atoms in the three spinor componentsm F = ± a depicts thearrangement of the light fields which are detuned by 845MHz with respect to the D2 transition in rubidium, anddrive several processes detailed in Fig. 1 b , c , and d .Perpendicular to the direction of absorption imag-ing (green circle) along z, two counterpropagating lightbeams A and B run parallel to the atom chip, and in-duce Bragg diffraction in the x-direction, such that thediffracted wave packets gain two photon recoils in mo-mentum. The direction of momentum transfer is tiltedwith respect to the longitudinal axis of the soundingrocket which is oriented along the diagonal of the x-zplane. This configuration is chosen such that in space,the separation points along Earth’s gravitational pull g,and on ground, at an angle of 45 degrees to the latter.Bragg diffraction (Fig. 1 b ) is resonantly driven by tun-ing the frequency difference, ν A - ν B , between the two lightbeams to create an optical lattice travelling with half ofthe speed of the diffracted wave packets. Timing andduration as well as frequency difference and power ad-justment is performed autonomously via acousto-opticalmodulators during space flight.Reflections of the Bragg beams create additional low-intensity light beams with a tilt of about two degreesdetermined by comparing experiments and simulations.They interfere with the original beams A and B givingrise to an additional spatial intensity modulation movingapproximately along the y-direction. This effect leads toan averaged phase imprinting on the wave function [4](Fig. 1 c ) as well as to double Bragg diffraction of thewave packets which is comparably weak due to the lowintensities of the reflections. In addition, the light beamsA and B are diffracted at the edges of the atom chip,and hence, feature a spatial intensity modulation whichalso causes phase imprinting roughly oriented along they-direction (Fig. 1 d ).For a systematic analysis we implemented numericalsimulations of our experiments. The theoretical images ofthe spatial density distributions depict simulations mod-elling the evolution of the different spinor componentsof the wave packets including the atom-light interactionin position space [31, 32]. Parameters such as relativeintensities, frequencies and the geometry are indepen-dently determined by the experimental setup. The twodegree beam angle and an overall intensity adjustmentwere adapted. The key processes of our interference experiments canbe understood by analysing the effect of a single lightpulse on the multi-spinor BECs. Fig. 2 compares theexperiments in space (left column) and on ground (rightcolumn), in which the light fields interact for 60 µ s witha multi-component wave packet 15 ms after its release.Moreover, the experimental results obtained with mul-tiple spinor components are contrasted with the corre-sponding simulations which serve as a reference and con-sider a single wave packet in the state F = 2, m F = 0.The figure shows the spatial density distribution of thewave packets and its Bragg diffracted parts. The exper-imental images were obtained by absorption imaging 31ms and 86 ms after release on ground and during therocket flight, respectively.Most strikingly, the results obtained in space featurea pronounced horizontal stripe pattern which is orientedalmost along the y-direction with a period of roughly 60micrometres. In contrast, the pictures on ground do notdisplay such a pattern.We identify four reasons for this clear distinction be-tween ground and space experiments: (i) In order to copewith the gravitational pull on ground, a time of flightshorter than in space had to be chosen as to ensure thatthe wave packet is detected close to the focal plane of theimaging. (ii) The corresponding shorter expansion timeleads to a smaller size of the wave packet, and the fringespacing imprinted onto the wave packet by the diffrac-tion of the Bragg beams at the edges of the atom chip isbelow the image resolution. (iii) On ground, the frequen-cies of the Bragg beams were adjusted to compensate theprojection of the gravitational pull. Therefore, the inter-ference pattern of the reflected and incoming light fieldsmove with a larger speed than in space and wash outthe related phase-imprint. (iv) Double Bragg process aresuppressed as they are non resonant.However, in the microgravity environment of thesounding rocket, the frequency difference of the lightbeams tuned to the Bragg resonance results in an opticalinterference pattern travelling with a lower speed and atemporal periodicity close to the recoil frequency. Thismotion is slow enough to leave a phase imprint albeit withlower amplitude due to temporal averaging over the 60 µ sof interaction. Our simulations of the experiments withand without gravity confirm this difference and allow usto deduce the reflection angle from the fringe spacing.In our space experiments the observed fringe contrast isstill much lower than predicted by our simulations basedon a single spinor component. This deviation becomeseven more prominent when we consider a slice throughthe intensity modulation along the y-direction indicatedby the orange line in Fig. 2. The existence of severalspinor components in presence of a residual magneticfield gradient explains this reduction. Indeed, the lat-ter suffices to accelerate the individual components rel-ative to each other according to their different magneticsusceptibilities. Since our imaging does not distinguishbetween the different components we arrive at a lower Figure 2. Experimental observations (two upper panels) and theoretical simulations (lower panels) of the impact of a singlelight-pulse simultaneously inducing Bragg processes and phase imprinting on a matter-wave packet released from the trap inthe low gravity environment of space (left column), and on ground (right column). Each picture shows the undiffracted and thediffracted parts due to Bragg and weak double-Bragg processes. In space, the striking feature is the amplitude modulation ofall BECs along the y-direction which in our ground experiments was not visible, in accordance with our theoretical simulations.On ground, the free expansion time of the BECs was short (31 ms) to keep them in the Bragg beams and the focal regionof the detection. In space, the longer expansion times (86 ms) lead to a larger fringe spacing which allows us to resolve theimprint. In addition, the phase imprinting due to the moving amplitude modulation vanishes on ground due to the Dopplershift caused by the larger detuning between the light beams A and B, resulting in a much larger velocity of the light pattern.In contrast to our model assuming a single BEC component, the experimental fringe patterns feature spatial distortions as wellas a much lower contrast. The latter holds even in the case when only a segment of the picture along the y-direction (orangeline) is analysed. contrast.This assumption is confirmed by the experiments sum-marised in Fig. 3. Here we study interferences generatedby three sequential light pulses acting synchronously andidentically on all spinor components. Moreover, we per-form a Stern-Gerlach analysis of the interferometer out-put ports which can be clearly distinguished by their mo-menta due to the use of BECs as a source.Fig. 3 a depicts the interferometric arrangement to co-herently split, deflect and recombine the different spinorcomponents leading to a grid-like stripe pattern detailedin Figs. 3 b - d . The sequence of pulses is reminiscent ofa Mach-Zehnder-type interferometer but our Bragg pro-cesses were weak and a momentum transfer occurred onlyto a small fraction of a BEC.The pictures were taken 50 ms after exposure of thereleased BECs to the magnetic field gradient for stateseparation, and 67 ms after the third light pulse. Thischoice of parameters guaranteed that the exit ports werespatially separated on the absorption images accordingto their distinct momenta and spinor components as in- dicated by the red lines in Fig. 3 a .Moreover, the time between the light pulses was 1 msor 2 ms and, hence short enough, that the wave pack-ets largely overlap at the exit ports giving rise to in-terference fringes modulated approximately along the x-direction. Therefore, the experimental arrangement re-sembles a shearing interferometer probing the spatial co-herence of the different spinor components.Figs. 3 b and c depict the enlarged view of the outputport corresponding to the m F = -1 state together withthe line integral along a fringe, and our theoretical sim-ulations of both, respectively. Indeed, the pattern anal-ysis shares similarities with point-source interferometry[24, 33]. While theory and experiment feature the samespatial periodicity, we had to add an inhomogeneous fieldin our simulation to obtain agreement of the tilts of thefringe pattern. Such a residual field is also required toexplain the orientation of the phase imprint discussedbelow.The low contrast observed in the experiment, of about20 % in the line integral, can be explained by inhomo- Figure 3. Experimental and simulated spatial matter-wave fringes created in a multi-component BEC by a sequence of three lightpulses applied after release. a , The associated Bragg processes create several spatially displaced, but still largely overlappingwave packets, resulting in an interference pattern in the three output ports of the interferometer corresponding to a transferof either +1, - 1 or 0 effective photon recoils. The fringes are recorded with and without a prior Stern-Gerlach-type spatialseparation of the different spinor components. We model the experiment by solving the 2D-Gross-Pitaevskii equation of a BECinteracting with the light fields discussed in Fig. 1. b , c , A close up of one output port is shown with the corresponding lineintegrals along the red line (bottom) as well as their theoretical counterparts. The experiment displays a lower contrast due tospatially varying Rabi frequencies. The temporal sequence of the three light pulses also leads to an effective phase imprinting. d - i , The stripe pattern (left) and contrast for a data slice (right) observed with and without the Stern-Gerlach separator aredepicted. Without Stern-Gerlach separation the stripe pattern obtained for the slice along the orange line ( d ) features a lowercontrast than our model ( e ) which might result from the relative motion of the spinor components. We observe a highercontrast for separated magnetic states ( f ) . Indeed, the components m F = ± F = 0 which points to a residual magnetic field with a curvature in agreement with our numerical simulations( g - i ). geneities of the light beams used for Bragg diffractionleading to a spread of Rabi frequencies. In these experi-ments we have benefited from the point-source characterof the BEC as our theoretical simulation reveals that thespatial interference pattern would vanish already for athermal cloud of atoms with temperatures of a few hun-dred nK.The interaction of the BEC with the three light fieldsalso leads to phase imprinting, and hence, to a notablestripe pattern along the y-direction as confirmed by oursimulations. According to our theory such a pattern canoriginate from a repetitive imprint by light diffracted atthe chip edge as discussed in Fig. 1 d . Even more remark-ably and despite the averaging, our theory also revealsthat, for our optical arrangement depicted in Fig. 1 a ,the moving amplitude modulation detailed in Fig. 1 c ,leads to a phase imprint featuring the observed fringespacing.Without the Stern-Gerlach analysis and therefore spa-tially overlapping spinor components, the absorption im-ages and simulations of the patterns exemplified by Figs.3 d , e show a low contrast. In comparison, the Stern-Gerlach separator leads to a higher fringe contrast, andallows us to selectively visualise the fringe patterns forthe different spinor components as illustrated in Fig. 3 f .In order to separate the effect of the fringe tilts and inhomogeneities we restrict our analysis to vertical seg-ments along the orange line. Indeed, the patterns corre-sponding to m F = ± F = ± F = 0 component, a curvature inducestilts. Our simulations shown in Figs. 3 g - i confirm thiseffect and feature corresponding patterns for a value of3.5 µ T/mm for the curvature of the magnetic field.Hence, simultaneous imprinting of a stripe patternonto a multi-component or multi-species wave packetformed from a BEC using a spatially modulated far-detuned light beam allows us to analyse differential forcesdue to external electric or magnetic field gradients andcurvatures, or to detect a differential velocity of the com-ponents. While a pure translation can be observed bythe resulting loss of contrast, the detection of tilts wouldpreferably be combined with a Stern-Gerlach separation.To detect forces by tracking the motion of wave pack-ets is a frequently used technique. For example, itwas exploited in drop tower experiments [23], is studiedwith CAL [27], and proposed for STE-QUEST [9]. Ourmethod improves the sensitivity for wave packet displace-ments by fitting the smaller spatial fringe period insteadof the envelopes. The principle of using an interferencemodulation in the signal is reminiscent of the increasedresolution in the Michelson stellar interferometer [34].We foresee several extensions of the imprint method:(i) adaption to gravity in order to avoid loss of modula-tion depth due to the moving grating, (ii) application tothree dimensions by spectral spatial light modulators fora 3D imprint, and (iii) measurements of inertial forcesacting on a single species or multiple ones in cases whereMach-Zehnder interferometers are not available, or theirdynamic measurement range is surpassed.In conclusion, we have employed light-pulse interfer-ometry induced by Bragg processes as well as phase-imprinting to investigate and exploit the spatial coher-ence of multi-component BECs on a sounding rocket.Our experiments mark the beginning of matter-wave in-terferometry in space and lay the groundwork for futurein-orbit interferometry performed with CAL and its fu-ture successor BECCAL [35], for the next MAIUS mis-sions, and generally, for high-precision interferometry inspace. I. METHODS
The optical setup for interferometry consists of twocollimated and counterpropagating light beams A and Bas well as their reflections with an angle of two degreeswith respect to A and B as shown in Fig. 1 a . Their fre-quencies are detuned by 845 MHz from the Rubidium-87 D2 line. To fulfil the Bragg condition, both beams needa relative detuning which at the beginning of the flightwas set to ν A − ν B = 15.1 kHz. Unfortunately, a residualmovement of the atoms after release from the magnetictrap reduced the diffraction efficiency. Therefore, it wasadjusted during flight to a value of 18.8 kHz for later mea-surements. The light pulse has a length of 60 µ s and thebeam A an intensity of 4.1 mW/cm while the beam Bhas an intensity of 8.0 mW/cm for the analysis of singleinteractions. In the three-pulse sequences the intensityof beam A remains the same, whereas the intensity forbeam B is doubled for the second pulse leading to anincreased diffraction ratio. Approximately 5 % of bothlight beams are reflected on the optical viewports of thevacuum chamber. On ground, the interferometry axisis tilted by 45 ° with respect to gravity. In free fall theDoppler shift leads to a detuning of ν A − ν B = 259.4 kHz.For this reason, double diffraction is suppressed. II. DATA AVAILABILITY
The image data for Figs. 2 and 3 are provided withthe paper. The analysed data are available from the cor-responding authors on reasonable request.
III. CODE AVAILABILITY
The simulation code is available from the correspond-ing authors on reasonable request. [1] M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E.Wieman, E. A. Cornell,
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M.D.L., H.A., D.B., A.N.D., J.G., O.H., H.M., V.S.,T.W., A.We. and B.W., with S.T.S. as scientific lead,planned and executed the campaign. M.D.L. and H.A.evaluated the data. H.A. and N.G. carried out the sim-ulations. E.M.R., W.P.S., M.D.L. and H.A. wrote themanuscript, with contributions from all authors. C.B.,W.E., M.K. C.L., D.L., A.P., W.P.S., K.S., A.Wi. andP.W. are the co-principal investigators of the project, andE.M.R. its principal investigator.
V. ACKNOWLEDGEMENTS