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Space-based research can provide a major leap forward in the study of key open questions in the fundamental physics domain. They include the validity of Einstein’s Equivalence principle, the origin and the nature of dark matter and dark energy, decoherence and collapse models in quantum mechanics, and the physics of quantum many-body systems. Cold-atom sensors and quantum technologies have drastically changed the approach to precision measurements. Atomic clocks and atom interferometers as well as classical and quantum links can be used to measure tiny variations of the space-time metric, elusive accelerations, and faint forces to test our knowledge of the physical laws ruling the Universe. In space, such instruments can benefit from unique conditions that allow improving both their precision and the signal to be measured. In this paper, we discuss the scientific priorities of a space-based research program in fundamental physics.

Atom interferometry enables precision measurements with outstanding sensitivities in a broad field of applications, ranging from fundamental physics to applications in geodesy or navigation. The development of robust and mobile devices paves the way for future satellite missions, e.g. striving for improved spaceborne gravimetry or a precision test of the universality of free fall. The sensitivity of an atom interferometer scales quadratically with the interrogation time. Consequentially, exceptional sensitivities can be reached for interferometry with free evolving ensembles on time scales of several seconds, achievable by operating on a microgravity platform. Such long interrogation times necessarily require ensembles with ultra-low expansion rates, making collimated Bose-Einstein condensates (BEC) the ideal input states. Therefore a method called magnetic lensing is used to narrow the momentum distribution. Together with the very good coherence properties of BECs, this reduces uncertainties in the interferometric measurement and enables high-fidelity beam splitter processes like Bragg diffraction. Within the scope of this thesis, a novel matter-wave lens system is presented to lower the internal kinetic energy of a BEC to the picokelvin regime, which is then used to perform interferometric measurements in microgravity. This is achieved with the QUANTUS-2 apparatus, a high-flux rubidium BEC machine based on atom chip technology, which operates at the drop tower in Bremen. Exploiting the excitation of a quadrupole mode in combination with a magnetic lens attains three-dimensional collimation of the BEC. With this technique, an unprecedented residual kinetic energy of $\sfrac{3}{2}k_B\cdot38\,$pK is achieved, where the ensemble is observed after an interrogation time of 2$\,$s with a high signal-to-noise ratio. Upgrading the experiment to realize single and double Bragg diffraction enables the first demonstration of a double Bragg-based interferometer in microgravity with a retro-reflection setup. The symmetric splitting achieved with the double Bragg process doubles the enclosed interferometer area and reduces systematic effects compared to single diffraction techniques. A complete characterization is performed to optimize the beam splitting process and verify the feasibility of atom chip setups for interferometric measurements. The potential of magnetically lensed BECs for interferometric measurements is investigated by probing the spatial coherence. To this end, a novel application of shear interferometry is developed to investigate the divergence of the magnetically lensed ensemble in analogy to an optical shear plate. Based on the interferometry pattern, the imperfections of the magnetic lens potential are studied, and the lens strength is optimized. Shear interferometry even enables the spatially resolved determination of the BEC's velocity field based on the interferometry pattern. Consequentially, the internal kinetic energy can be deduced from a single absorption image. Especially compact, ground-based atom interferometers can profit from this characterization method since extended times of flight are not required. This shear interferometry represents a versatile tool to study BEC dynamics independently of the application in matter-wave optics. The first demonstration of interferometry with picokelvin atomic ensembles and the tools developed in this work provide the basis to realize atom interferometry on extended time scales of several seconds. This will ultimately enable future space missions to employ cold atom interferometry at unrivalled levels of precision.

Abstract Quantum sensors based on light pulse atom interferometers allow for measurements of inertial and electromagnetic forces such as the accurate determination of fundamental constants as the fine structure constant or testing foundational laws of modern physics as the equivalence principle. These schemes unfold their full performance when large interrogation times and/or large momentum transfer can be implemented. In this article, we demonstrate how interferometry can benefit from the use of Bose–Einstein condensed sources when the state of the art is challenged. We contrast systematic and statistical effects induced by Bose–Einstein condensed sources with thermal sources in three exemplary science cases of Earth- and space-based sensors. Graphic abstract

On its maiden flight on Jan 23, 2017 the MAIUS-1 mission was able to demonstrate the first creation of a Bose-Einstein Condensate in space. During about 360 s of microgravity, around 100 experiments were carried out to characterize the behaviour of the condensate and its usability for atom interferometry in this environment. To achieve these goals in the limited timeframe of a sounding rocket flight, the payload was equipped with an autonomous control system. The system was designed to optimize the experiment and decide on the next experimental sequences based on environmental conditions and previous experimental results. This includes an image evaluation algorithm and a model-based description of the experimental sequences available. To allow monitoring and control of the instrument from the ground station, a Mission Control System was developed built entirely on Open Source technologies. This includes flow control of the experimental sequences, monitoring of housekeeping and scientific data (time-series data and images) as well as defining experimental sequences. All data are distributed via network sockets to several workstations and a timeseries database. Furthermore, the Mission Control System provides tools to plan, create and edit experimental sequences as well as sanity checks and simulations. In this talk, we will give an overview of the architecture of these systems with a focus on the Mission Control System and its application in future space missions on sounding rockets and the ISS.

The stability of matter-wave sensors benefits from interrogating large-particle-number atomic ensembles at high cycle rates. The use of quantum-degenerate gases with their low effective temperatures allows constraining systematic errors towards highest accuracy, but their production by evaporative cooling is costly with regard to both atom number and cycle rate. In this work, we report on the creation of cold matter-waves using a crossed optical dipole trap and shaping it by means of an all-optical matter-wave lens. We demonstrate the trade off between residual kinetic energy and atom number by short-cutting evaporative cooling and estimate the corresponding performance gain in matter-wave sensors. Our method is implemented using time-averaged optical potentials and hence easily applicable in optical dipole trapping setups., Comment: 10 pages, 5 figures

A major challenge common to all Galilean drop tests of the Universality of Free Fall (UFF) is the required control over the initial kinematics of the two test masses upon release due to coupling to gravity gradients and rotations. In this work, we present a two-fold mitigation strategy to significantly alleviate the source preparation requirements in space-borne quantum tests of the UFF, using a compensation mechanism together with signal demodulation. To this end, we propose a scheme to reduce the gravity-gradient-induced uncertainties in an atom-interferometric experiment in a dedicated satellite mission and assess the experimental feasibility. We find that with moderate parameters, the requirements on the initial kinematics of the two masses can be relaxed by five orders of magnitude. This does not only imply a significantly reduced mission time but also allows to reduce the differential acceleration uncertainty caused by co-location imperfections below the $10^{-18}$ level., Comment: 12 pages, 3 figures

We present a source engineering concept for a binary quantum mixture suitable as input for differential, precision atom interferometry with drift times of several seconds. To solve the non-linear dynamics of the mixture, we develop a set of scaling approach equations and verify their validity contrasting it to the one of a system of coupled Gross-Pitaevskii equations. This scaling approach is a generalization of the standard approach commonly used for single species. Its validity range is discussed with respect to intra- and inter-species interaction regimes. We propose a multi-stage, non-linear atomic lens sequence to simultaneously create dual ensembles with ultra-slow kinetic expansion energies, below 15 pK. Our scheme has the advantage of mitigating wave front aberrations, a leading systematic effect in precision atom interferometry., Comment: 38 pages, 7 figures

Abstract Out of a single Bose-Einstein condensate (BEC), we create two simultaneous interferometers, as employed for the differentiation between rotations and accelerations. Our method exploits the precise motion control of BECs combined with the precise momentum transfer by double Bragg diffraction for interferometry. In this way, the scheme avoids the complexity of two BEC sources and can be readily extended to a six-axis quantum inertial measurement unit. Graphical abstract

Full author list: B Canuel, S Abend, P Amaro-Seoane, F Badaracco, Q Beaufils, A Bertoldi, K Bongs, P Bouyer, C Braxmaier, W Chaibi, N Christensen, F Fitzek, G Flouris, N Gaaloul, S Gaffet, C L Garrido Alzar, R Geiger, S Guellati-Khelifa, K Hammerer, J Harms, J Hinderer, M Holynski, J Junca, S Katsanevas, C Klempt, C Kozanitis, M Krutzik, A Landragin, I Làzaro Roche, B Leykauf, Y-H Lien, S Loriani, S Merlet, M Merzougui, M Nofrarias, P Papadakos, F Pereira dos Santos, A Peters, D Plexousakis, M Prevedelli, E M Rasel, Y Rogister, S Rosat, A Roura, D O Sabulsky, V Schkolnik, D Schlippert, C Schubert, L Sidorenkov, J-N Siemß, C F Sopuerta, F Sorrentino, C Struckmann, G M Tino, G Tsagkatakis, A Viceré, W von Klitzing, L Woerner and X Zou, Gravitational waves (GWs) were observed for the first time in 2015, one century after Einstein predicted their existence. There is now growing interest to extend the detection bandwidth to low frequency. The scientific potential of multi-frequency GW astronomy is enormous as it would enable to obtain a more complete picture of cosmic events and mechanisms. This is a unique and entirely new opportunity for the future of astronomy, the success of which depends upon the decisions being made on existing and new infrastructures. The prospect of combining observations from the future space-based instrument LISA together with third generation ground based detectors will open the way toward multi-band GW astronomy, but will leave the infrasound (0.1-10 Hz) band uncovered. GW detectors based on matter wave interferometry promise to fill such a sensitivity gap. We propose the European Laboratory for Gravitation and Atom-interferometric Research (ELGAR), an underground infrastructure based on the latest progress in atomic physics, to study space-time and gravitation with the primary goal of detecting GWs in the infrasound band. ELGAR will directly inherit from large research facilities now being built in Europe for the study of large scale atom interferometry and will drive new pan-European synergies from top research centers developing quantum sensors. ELGAR will measure GW radiation in the infrasound band with a peak strain sensitivity of 3.3 × 10-22/√Hz at 1.7 Hz. The antenna will have an impact on diverse fundamental and applied research fields beyond GW astronomy, including gravitation, general relativity, and geology., This work was realized with the financial support of the French State through the ‘Agence Nationale de la Recherche’ (ANR) in the frame of the ‘MRSEI’ program (Pre-ELGAR ANR-17-MRS5-0004-01) and the ‘Investissement d’Avenir’ program (Equipex MIGA: ANR11-EQPX-0028, IdEx Bordeaux—LAPHIA: ANR-10-IDEX-03-02). AB acknowledges support from the ANR (project EOSBECMR), IdEx Bordeaux—LAPHIA (project OE-TWR), the QuantERA ERA-NET (project TAIOL) and the Aquitaine Region (projets IASIG3D and USOFF). The work was also supported by the German Space Agency (DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grant Nos. 50WM1556, 50WM1956 and 50WP1706 as well as through the DLR Institutes DLR-SI and DLR-QT. XZ thanks the China Scholarships Council (No. 201806010364) program for financial support. JJ thanks ‘Association Nationale de la Recherche et de la Technologie’ for financial support (No. 2018/1565). PA-S, MN, and CFS acknowledge support from contracts ESP2015-67234-P and ESP2017-90084-P from the Ministry of Economy and Business of Spain (MINECO), and from contract 2017- SGR-1469 from AGAUR (Catalan government). LAS thanks Sorbonne Universit´es (Emergence project LORINVACC) and Conseil Scientifique de l’Observatoire de Paris for funding. RG acknowledges Ville de Paris (Emergence programme HSENS-MWGRAV), ANR (project PIMAI) and the Fundamental Physics and Gravitational Waves (PhyFOG) programme of Observatoire de Paris for support. We also acknowledge networking support by the COST actions GWverse CA16104 and AtomQT CA16221 (Horizon 2020 Framework Programme of the European Union). DS gratefully acknowledges funding by the Federal Ministry of Education and Research (BMBF) through the funding program Photonics Research Germany under contract number 13N14875. SvAb, NG, SL, EMR, DS, and CS gratefully acknowledge support by ‘Nieders¨achsisches Vorab’ through the ‘Quantum- and Nano-Metrology (QUANOMET)’ initiative within the project QT3, and through ‘Förderung von Wissenschaft und Technik in Forschung und Lehre’ for the initial funding of research in the new DLRSI Institute, the CRC 1227 DQ-mat within the projects A05, B07 and B09, the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy—EXC-2123 QuantumFrontiers—390837967 (B2), and the German Space Agency (DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grants No. DLR 50WM1641 (PRIMUSIII), 50WM1952 (QUANTUS-V-Fallturm), and 50WP1700 (BECCAL), 50WM1861 (CAL), 50WM2060 (CARIOQA) as well as 50RK1957 (QGYRO). FS, GMT and AV gratefully acknowledge support by the Italian ‘Ministero dell’Istruzione, Universit`a e Ricerca’ through the funding program PRIN, under contract number 2015L33WAK_003. BL, VS, MK, and AP gratefully acknowledge support by the Berlin School of Optical Sciences and Quantum Technology (BOS.QT) and by the German Space Agency (DLR) with funds provided by the Federal Ministry for Economic Affairs and Energy (BMWi) due to an enactment of the German Bundestag under Grants No. 50WP1432 (QUANTUS-IV-MAIUS), 50WP1953 (QUANTUS-V-Fallturm), and 50WP1702 (BECCAL).

Inertial sensors based on matter-wave interferometry are currently approaching the precision and accuracy of state-of-the-art classical sensors. While these devices are often realised with ultracold but not Bose-condensed atoms as matter waves, employing Bose-Einstein Condensates (BEC) promises to overcome certain limitations, especially those related to the ensemble's expansion. The point-source like character of BECs also enables utilising spatial interference patterns to measure e.g. rotation rates in single-shot experiments. Matter wave-based inertial sensors are considered for experiments ranging from Gravitational Wave detection to tests of the Universality of Free Fall (UFF) to gain insight into the joint between Quantum Mechanics and General Relativity. In the scope of this thesis, matter-wave interferometry with BECs was demonstrated for the first time in a microgravity environment with the QUANTUS-1 apparatus. The same instrument was then employed as a quantum tiltmeter utilising a novel beam-splitting mechanism known as Bragg Double Diffraction. To this end, the QUANTUS-1 apparatus designed as a BEC instrument to be operated in the drop tower at ZARM at University of Bremen was equipped with optics and laser systems required for performing matter-wave interferometry based on Bragg Diffraction. The apparatus employs an atom chip to create BECs of around 10000 Rubidium 87 atoms within 15 s. With a Mach-Zehnder like interferometer scheme, spatial interference fringes were observed after a free evolution time in the interferometer of up to 677 ms. To achieve these long time scales, a method known as Delta-Kick Collimation (DKC) was adapted to slow the expansion of the BEC to a kinetic energy equivalent below 1 nK, and the atoms were transferred to a non-magnetic Zeeman state via an adiabatic rapid passage (ARP). A similar interferometer scheme with a newly developed beam-splitter mechanism known as Bragg Double Diffraction was used to measure the tilt of the instrument on ground with a precision of up to 4.4 AA rad. This thesis presents an overview of the apparatus including ground-based characterisations of all required experimental steps. Results from over 400 free fall experiments are evaluated for expansion studies of the BEC and matter-wave interferometry in microgravity. The time-evolution of first and second order Bragg Double Diffraction beam splitters is studied, and an interferometer sensitive to the tilt of the instrument is implemented. Based on this work, a gravimeter with a new launch mechanism comprising Bragg beam splitters and Bloch oscillations to enable atomic fountains in atom-chip based devices was developed. The microgravity experiments were adapted for the MAIUS-1 sounding-rocket instrument to create the first man-made BEC in outer space and study the feasibility of operating matter-wave interferometers on space-borne platforms. The results of this thesis lay the groundwork for future space-borne missions using matter-wave interferometry for precision measurements of inertial forces.

Trägheitssensoren (Inertialsensoren) dienen der Messung von Beschleunigungen und Drehungen zur Bestimmung der Bewegung mobiler Plattformen. Als Komponenten von Navigationssystemen ermöglichen sie - zu einem gewissen Grad - eine Unabhängigkeit von Satellitennavigationssystemen, deren Signale nicht überall empfangbar sind bzw. auch absichtlich gestört werden können. Äußerst genaue und langzeitstabile Trägheitsnavigationssysteme sind im Prinzip auf der Grundlage der Atominterferometrie realisierbar. Allerdings ist noch beträchtliche Forschungs- und Entwicklungsarbeit zu leisten, bis sich derartige auf quantenphysikalischen Phänomenen basierende Systeme in der Praxis einsetzen lassen.

We present a simple derivation of the interference pattern in matter-wave interferometry as predicted by a class of master equations, by using the density matrix formalism. We apply the obtained formulae to the most relevant collapse models, namely the Ghirardi-Rimini-Weber (GRW) model, the continuous spontaneous localization (CSL) model together with its dissipative (dCSL) and non-markovian generalizations (cCSL), the quantum mechanics with universal position localization (QMUPL) and the Di\'{o}si-Penrose (DP) model. We discuss the separability of the collapse models dynamics along the 3 spatial directions, the validity of the paraxial approximation and the amplification mechanism. We obtain analytical expressions both in the far field and near field limits. These results agree with those already derived in the Wigner function formalism. We compare the theoretical predictions with the experimental data from two relevant matter-wave experiments: the 2012 far-field experiment and the 2013 Kapitza Dirac Talbot Lau (KDTL) near-field experiment of Arndt's group. We show the region of the parameter space for each collapse model, which is excluded by these experiments. We show that matter-wave experiments provide model insensitive bounds, valid for a wide family of dissipative and non-markovian generalizations., Comment: 49 pages,16 figures

Matter-wave interferometry is a direct test of the quantum superposition principle for massive systems, and of collapse models. Here we show that the bounds placed by matter-wave interferometry depend weakly on the details of the collapse mechanism. Specifically, we compute the bounds on the CSL model and its variants, provided by the the KDTL interferometry experiment of Arndt's group [Phys. Chem. Chem. Phys., 2013, 15, 14696-14700], which currently holds the record of largest mass in interferometry. We also show that the CSL family of models emerges naturally by considering a minimal set of assumptions. In particular, we construct the dynamical map for the colored and dissipative Continuous Spontaneous Localization (cdCSL) model, which reduces to the CSL model and variants in the appropriate limits. In addition, we discuss the measure of macroscopicity based on the cdCSL model., 9 pages, 5 figures; accepted for publication in Physics Letters A (2017)

Quantum sensors based on coherent matter-waves are precise measurement devices whose ultimate accuracy is achieved with Bose-Einstein condensates (BEC) in extended free fall. This is ideally realized in microgravity environments such as drop towers, ballistic rockets and space platforms. However, the transition from lab-based BEC machines to robust and mobile sources with comparable performance is a challenging endeavor. Here we report on the realization of a miniaturized setup, generating a flux of $4 \times 10^5$ quantum degenerate $^{87}$Rb atoms every 1.6$\,$s. Ensembles of $1 \times 10^5$ atoms can be produced at a 1$\,$Hz rate. This is achieved by loading a cold atomic beam directly into a multi-layer atom chip that is designed for efficient transfer from laser-cooled to magnetically trapped clouds. The attained flux of degenerate atoms is on par with current lab-based BEC experiments while offering significantly higher repetition rates. Additionally, the flux is approaching those of current interferometers employing Raman-type velocity selection of laser-cooled atoms. The compact and robust design allows for mobile operation in a variety of demanding environments and paves the way for transportable high-precision quantum sensors., 22 pages, 6 figures