Ultracold atom interferometry in space

ABSTRACT Bose-Einstein condensates (BECs) in free fall constitute a promising source for space-borne interferometry. Indeed, BECs enjoy a slowly expanding wave function, display a large

spatial coherence and can be engineered and probed by optical techniques. Here we explore matter-wave fringes of multiple spinor components of a BEC released in free fall employing

light-pulses to drive Bragg processes and induce phase imprinting on a sounding rocket. The prevailing microgravity played a crucial role in the observation of these interferences which not

only reveal the spatial coherence of the condensates but also allow us to measure differential forces. Our work marks the beginning of matter-wave interferometry in space with future

applications in fundamental physics, navigation and earth observation. SIMILAR CONTENT BEING VIEWED BY OTHERS PATHFINDER EXPERIMENTS WITH ATOM INTERFEROMETRY IN THE COLD ATOM LAB ONBOARD THE

INTERNATIONAL SPACE STATION Article Open access 13 August 2024 QUANTUM GAS MIXTURES AND DUAL-SPECIES ATOM INTERFEROMETRY IN SPACE Article 15 November 2023 A SPACE-BASED QUANTUM GAS

LABORATORY AT PICOKELVIN ENERGY SCALES Article Open access 22 December 2022 INTRODUCTION Interference of two BECs constitutes the hallmark of macroscopic coherence. The first observation1 of

the corresponding fringes has ushered in the new era of coherent matter-wave optics. The condensates can be engineered and probed by optical techniques2,3,4,5 making them a promising source

for precision measurements. In addition, their large spatial coherence and their slow expanding wave function6 allow for experiments on macroscopic time scales. Indeed, space displays an

enormous potential for advancing high-precision matter-wave interferometry because the size of the device is no longer determined by the dropping height required on ground7. Additionally,

low external influences and the reduced kinematics of the source allow us to control systematic effects. For these reasons quantum tests of general relativity8,9,10, the search for the

nature of dark matter and energy9,11,12,13,14, the detection of gravitational waves9,15,16 and satellite gravimetry17,18,19,20,21 represent only a few of the many promising applications of

atom interferometry in space. Being at the very heart of the aforementioned proposals, our experiments set the beginning of space-borne coherent atom optics. They have benefited from our

earlier studies on BEC interferometry at the drop tower in Bremen22,23 exploring methods for high-precision inertial measurements. Moreover, in other groups interferometry with laser-cooled

atoms was performed on parabolic flights24 and a cold-atom clock was studied on a satellite25. Exploration of degenerate quantum gases is currently continued with the Cold Atom Laboratory

(CAL) in orbit26. In this article we report on the first interference experiments performed during the recent space flight of the MAIUS-1 rocket27 demonstrating the macroscopic coherence of

the BECs engineered in this microgravity environment. RESULTS In contrast to1 which used an optical double-well potential to interfere two BECs, we employ Bragg processes as well as phase

imprinting simultaneously in different magnetic spinor components. The resulting rich interference pattern stretches across the complete spatial distribution of the wave packets. We analyse

its contrast as its temporal evolution can be exploited to detect forces acting differently on the spinor components. Applied to three dimensions, this arrangement could serve as a vector

magnetometer. Moreover, due to the higher achievable spatial resolution, our method compares favourably to the determination of the BEC position based on a fit of the envelope of its spatial

density distribution. The latter was e.g. proposed for the measurement of gravity gradients in the STE-QUEST8 mission designed as a space-borne quantum test of the equivalence principle.

SETUP Our interferometer is based on an atom-chip apparatus for trapping and cooling of the atomic ensembles delivering BECs of about 105 rubidium-87 atoms within 1.6 seconds28,29. The atom

chip enables a very compact and robust design required by the demanding constraints of the rocket in terms of mass, volume, power consumption as well as vibrations and accelerations during

launch. The necessary autonomous experimental control is realised by a customised onboard software allowing for image analysis, self-optimisation of parameters, operation of a decision tree

and real time interaction with the ground control. The BECs are created in the magnetic hyperfine ground state F = 2, mF = +2 and then released from the trap. We transfer the freely falling

matter-wave packet into a superposition of several spinor components by employing radio frequencies30, or by changing the magnetic field orientation. Optionally, we spatially separate them

after the interferometry sequence by a Stern–Gerlach arrangement. The experiments reported here were performed with a superposition of atoms in the three spinor components mF = ±1 and 0,

which are synchronously and identically irradiated by a single or sequential light pulses creating spatial matter-wave interferences. Figure 1a depicts the arrangement of the light fields,

which are detuned by 845 MHz with respect to the D2 transition in rubidium, and drive several processes detailed in Fig. 1b–d. Perpendicular to the direction of absorption imaging (green

circle) along _z_, two counterpropagating light beams A and B run parallel to the atom chip, and induce Bragg diffraction in the _x_-direction such that the diffracted wave packets gain two

photon recoils in momentum. The direction of momentum transfer is tilted with respect to the longitudinal axis of the sounding rocket, which is oriented along the diagonal of the _x_–_z_

plane. 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° to the latter. Bragg diffraction (Fig. 1b)

is resonantly driven by tuning the frequency difference, _ν__A_ − _ν__B_, between the two light beams to create an optical lattice travelling with half of the speed of the diffracted wave

packets. Timing and duration as well as frequency difference and power adjustment are performed autonomously via acousto-optical modulators during space flight. Reflections of the Bragg

beams on the optical viewports of the vacuum chamber create additional low-intensity light beams with a tilt of about two degrees determined by comparing experiments and simulations. They

interfere with the original beams A and B giving rise to an additional spatial intensity modulation moving approximately along the _y_-direction. This effect leads to an averaged phase

imprinting on the wave function2 (Fig. 1c) as well as to Bragg double-diffraction of the wave packets, which is comparably weak due to the low intensities of the reflections. In addition,

the light beams A and B are diffracted at the edges of the atom chip, and hence, feature a spatial intensity modulation, which also causes phase imprinting roughly oriented along the

_y_-direction (Fig. 1d). For a systematic analysis we implemented numerical simulations of our experiments. The theoretical images of the spatial density distributions depict simulations

modelling the evolution of the different spinor components of the wave packets including the atom-light interaction in position space31,32. Parameters, such as relative intensities,

frequencies and the geometry, are independently determined by the experimental setup. The 2° beam angle and an overall intensity adjustment were adapted. COHERENT MANIPULATION BY LIGHT

PULSES The key processes of our interference experiments can be understood by analysing the effect of a single light-pulse on the multi-spinor BECs. Figure 2 compares the experiments in

space (left column) and on ground (right column), in which the light fields interact for 60 μs with a multi-component wave packet 15 ms after its release. Moreover, the experimental results

obtained with multiple spinor components are contrasted with the corresponding simulations, which serve as a reference and consider a single wave packet in the state F = 2, mF = 0. The

figure shows the spatial density distribution of the wave packets and its Bragg diffracted parts. The experimental images were obtained by absorption imaging 31 ms and 86 ms after release on

ground and during the rocket flight, respectively. Most strikingly, the results obtained in space feature a pronounced horizontal stripe pattern, which is oriented almost along the

y-direction with a period of roughly 60 μm. In contrast, the pictures on ground do not display such a pattern. We identify four reasons for this clear distinction between ground and space

experiments: (i) In order to cope with the gravitational pull on ground, a time of flight shorter than in space had to be chosen as to ensure that the wave packet is detected close to the

focal plane of the imaging. (ii) The corresponding shorter expansion time leads to a smaller size of the wave packet, and the fringe spacing imprinted onto the wave packet by the diffraction

of the Bragg beams at the edges of the atom chip is below the image resolution. (iii) On ground, the frequencies of the Bragg beams were adjusted to compensate the projection of the

gravitational pull. Therefore, the interference pattern of the reflected and incoming light fields moves with a larger speed than in space and wash out the related phase imprint. (iv)

Double-Bragg process are suppressed as they are non-resonant. However, in the microgravity environment of the sounding rocket, the frequency difference of the light beams tuned to the Bragg

resonance results in an optical interference pattern travelling with a lower speed and a temporal periodicity close to the recoil frequency. This motion is slow enough to leave a phase

imprint albeit with lower amplitude due to temporal averaging over the 60 µs of interaction. Our simulations of the experiments with and without gravity confirm this difference and allow us

to deduce the reflection angle from the fringe spacing. In our space experiments the observed fringe contrast is still much lower than predicted by our simulations based on a single spinor

component. This deviation becomes even more prominent when we consider a slice through the intensity modulation along the _y_-direction indicated by the orange line in Fig. 2. The existence

of several spinor components in presence of a residual magnetic field gradient explains this reduction. Indeed, the latter suffices to accelerate the individual components relative to each

other according to their different magnetic susceptibilities. Since our imaging does not distinguish between the different components we arrive at a lower contrast. INTERFERENCE EXPERIMENTS

This assumption is confirmed by the experiments summarised in Fig. 3. Here we study interferences generated by three sequential light pulses acting synchronously and identically on all

spinor components. Moreover, we perform a Stern–Gerlach analysis of the interferometer output ports, which can be clearly distinguished by their kinetic momenta due to the use of BECs as a

source. Figure 3a depicts the interferometric arrangement to coherently split, deflect and recombine the different spinor components leading to a grid-like stripe pattern detailed in Fig. 

1b–d. The sequence of pulses is reminiscent of a Mach–Zehnder-type interferometer but our Bragg processes were weak and a momentum transfer occurred only to a small fraction of a BEC. The

pictures were taken 50 ms after exposure of the released BECs to the magnetic field gradient for state separation, and 67 ms after the third light-pulse. This choice of parameters guaranteed

that the exit ports were spatially separated on the absorption images according to their momenta and spinor components at as indicated by the red lines in Fig. 3a. Moreover, the time

between the light pulses was 1 or 2 ms and, hence short enough, that the wave packets largely overlap at the exit ports giving rise to interference fringes modulated approximately along the

_x_-direction. Therefore, the experimental arrangement resembles a shearing interferometer probing the spatial coherence of the different spinor components. Figure 3b, c depicts the enlarged

view of the output port corresponding to the mF = −1 state together with the line integral along a fringe, and our theoretical simulations of both, respectively. Indeed, the pattern

analysis shares similarities with point-source interferometry23,33. While theory and experiment feature the same spatial periodicity, we had to add an inhomogeneous field in our simulation

to obtain agreement of the tilts of the fringe pattern. Such a residual field is also required to explain the orientation of the phase imprint discussed below. The low contrast observed in

the experiment, of about 20% in the line integral, can be explained by inhomogeneities of the light beams used for Bragg diffraction leading to a spread of Rabi frequencies. In these

experiments we have benefited from the point-source character of the BEC as our theoretical simulation reveals that the spatial interference pattern would vanish already for a thermal cloud

of atoms with temperatures of a few hundred nK. The interaction of the BEC with the three light fields also leads to phase imprinting, and hence, to a notable stripe pattern along the

_y_-direction as confirmed by our simulations. According to our theory such a pattern can originate from a repetitive imprint by light diffracted at the chip edge as discussed in Fig. 1d.

Even more remarkably and despite the averaging, our theory also reveals that, for our optical arrangement depicted in Fig. 1a, the moving amplitude modulation detailed in Fig. 1c, leads to a

phase imprint featuring the observed fringe spacing. Without the Stern–Gerlach analysis and therefore spatially overlapping spinor components, the absorption images and simulations of the

patterns exemplified by Fig. 3d, e, show a low contrast. In comparison, the Stern–Gerlach separation leads to a higher fringe contrast, and allows us to selectively visualise the fringe

patterns for the different spinor components as illustrated in Fig. 3f. In order to separate the effect of the fringe tilts and inhomogeneities we restrict our analysis to vertical segments

along the orange line. Indeed, the patterns corresponding to mF = ±1 are rotated in opposite direction which can be explained by a magnetic field curvature. While a homogeneous magnetic

field gradient would just lead to a translation of the mF = ±1 components with respect to the mF = 0 component, a curvature induces tilts. Our simulations shown in Fig. 3g–i confirm this

effect and feature corresponding patterns for a value of 3.5 µT/mm2 for the curvature of the magnetic field. DISCUSSION Hence, simultaneous imprinting of a stripe pattern onto a

multi-component or multi-species wave packet formed from a BEC using a spatially modulated far-detuned light beam allows us to analyse differential forces due to external electric or

magnetic field gradients and curvatures, or to detect a differential velocity of the components. While a pure translation can be observed by the resulting loss of contrast, the detection of

tilts would preferably be combined with a Stern–Gerlach separation. To detect forces by tracking the motion of the center-of-mass of the wave packets is a frequently used technique. For

example, it was exploited in drop tower experiments22, is studied with CAL26, and proposed for STE-QUEST8 to characterise the environment and movement of the atomic ensemble. Our method

improves the sensitivity for wave packet displacements by fitting the smaller spatial fringe period instead of the envelopes. The principle of using an interference modulation in the signal

is reminiscent of the increased resolution in the Michelson stellar interferometer34. We foresee several extensions of the imprint method: (i) adaption to gravity in order to avoid loss of

modulation depth due to the moving grating, (ii) application to three dimensions by spectral spatial light modulators for a 3D imprint and (iii) measurements of inertial forces acting on a

single species or multiple ones in cases where Mach–Zehnder interferometers are not available, or their dynamic measurement range is surpassed. In conclusion, we have employed light-pulse

interferometry induced by Bragg processes as well as phase imprinting to investigate and exploit the spatial coherence of multi-component BECs on a sounding rocket. Our experiments mark the

beginning of matter-wave interferometry in space and lay the groundwork for future in-orbit interferometry performed with CAL and its future successor BECCAL35, for the next MAIUS missions,

and generally, for high-precision interferometry in space. METHODS The optical setup for interferometry consists of two collimated and counterpropagating light beams A and B as well as their

reflections with an angle of two degrees with respect to A and B as shown in Fig. 1a. Their frequencies are detuned by 845 MHz from the Rubidium-87 D2 line. To fulfil the Bragg condition,

both beams need a relative detuning which at the beginning of the flight was set to _ν__A_ − _ν__B_ = 15.1 kHz. Unfortunately, a residual movement of the atoms after release from the

magnetic trap reduced the diffraction efficiency. Therefore, it was adjusted during flight to a value of 18.8 kHz for later measurements. The light pulse has a length of 60 µs and beam A an

intensity of 4.1 mW/cm2 while the beam B has an intensity of 8.0 mW/cm2 for the analysis of single interactions. In the three-pulse sequences the intensity of beam A remains the same,

whereas the intensity for beam B is doubled for the second pulse leading to an increased diffraction ratio. Approximately 5% of both light beams are reflected on the optical viewports of the

vacuum chamber. On ground, the interferometry axis is tilted by 45° with respect to gravity. In free fall the Doppler shift leads to a detuning of _ν__A_ − _ν__B_ = 259.4 kHz. For this

reason, double diffraction is suppressed. DATA AVAILABILITY The image data for Figs. 2 and 3 are provided under https://doi.org/10.25835/0062691. The analysed data are available from the

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condensate and cold atom laboratory. _EPJ Quantum Technol._ 8, 1 (2021). Article  Google Scholar  Download references ACKNOWLEDGEMENTS We thank all members of the QUANTUS-collaboration for

their support and acknowledge fruitful discussions with M. Cornelius, P. Stromberger and W. Herr. This work is supported by the DLR Space Administration with funds provided by the Federal

Ministry for Economic Affairs and Energy (BMWi) under grant numbers DLR 50WM1131-1137, 50WM0940, 50WM1240, 50WM1556, 50WM1641, 50WM1861, 50WM1956, 50WP1431-1435 and 50WM2060, and is funded

by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967. W.P.S. thanks Texas A&M University for a

Faculty Fellowship at the Hagler Institute for Advanced Study at Texas A&M University and Texas A&M AgriLife for support of this work. The research of the IQST is financed partially

by the Ministry of Science, Research and Arts Baden-Württemberg. H.A. acknowledges financial support from “Niedersächsisches Vorab” through “Förderung von Wissenschaft und Technik in

Forschung und Lehre” for the initial funding of research in the new DLR-SI Institute. N.G. acknowledges funding from “Niedersächsisches Vorab” through the Quantum- and Nano-Metrology

(QUANOMET) initiative within the project QT3. We thank ESRANGE Kiruna and DLR MORABA Oberpfaffenhofen for assistance during the test and launch campaign. FUNDING Open Access funding enabled

and organized by Projekt DEAL. AUTHOR INFORMATION Author notes * Aline N. Dinkelaker Present address: Leibniz-Institut für Astrophysik Potsdam, Potsdam, Germany * Hauke Müntinga Present

address: Institute for Satellite Geodesy and Inertial Sensing, German Aerospace Center (DLR), Bremen, Germany * Stephan T. Seidel Present address: Airbus Defense and Space GmbH, Taufkirchen,

Germany * Benjamin Carrick Present address: MORABA, German Aerospace Center (DLR), Weßling, Germany * These authors contributed equally: Maike D. Lachmann, Holger Ahlers. AUTHORS AND

AFFILIATIONS * Institute of Quantum Optics and QUEST-Leibniz Research School, Leibniz University Hannover, Hannover, Germany Maike D. Lachmann, Holger Ahlers, Dennis Becker, Stephan T.

Seidel, Thijs Wendrich, Naceur Gaaloul, Wolfgang Ertmer & Ernst M. Rasel * Department of Physics, Humboldt-Universität zu Berlin, Berlin, Germany Aline N. Dinkelaker, Vladimir Schkolnik,

 Markus Krutzik & Achim Peters * Center of Applied Space Technology and Microgravity (ZARM), University of Bremen, Bremen, Germany Jens Grosse, Hauke Müntinga, Claus Braxmaier & 

Claus Lämmerzahl * Department of Enabling Technologies, German Aerospace Center (DLR), Bremen, Germany Jens Grosse & Claus Braxmaier * Institute of Laser-Physics, University Hamburg,

Hamburg, Germany Ortwin Hellmig & Klaus Sengstock * Institute of Physics, Johannes Gutenberg University Mainz (JGU), Mainz, Germany André Wenzlawski & Patrick Windpassinger *

Institute for Software Technology, German Aerospace Center (DLR), Brunswick, Germany Benjamin Carrick & Daniel Lüdtke * Institut für Quantenphysik and Center for Integrated Quantum

Science and Technology (IQST), Ulm, Germany Wolfgang P. Schleich * Institute of Quantum Technologies, German Aerospace Center (DLR), Ulm, Germany Wolfgang P. Schleich * Hagler Institute for

Advanced Study at Texas A&M University; Texas A&M AgriLife Research; Institute for Quantum Science and Engineering (IQSE) and Department of Physics and Astronomy, Texas A&M

University, College Station, TX, USA Wolfgang P. Schleich * Ferdinand-Braun-Institut, Leibniz-Institut für Höchstfrequenztechnik, Berlin, Germany Andreas Wicht Authors * Maike D. Lachmann

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Google Scholar CONTRIBUTIONS 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 simulations. E.M.R., W.P.S., M.D.L. and H.A. wrote the manuscript, with contributions from all authors. C.B., W.E., M.K., C.L., D.L., A.P.,

W.P.S., K.S., A.Wi. and P.W. are the co-principal investigators of the project, and E.M.R. its principal investigator. CORRESPONDING AUTHOR Correspondence to Ernst M. Rasel. ETHICS

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