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Atom interferometry enables quantum sensors for absolute measurements of gravity (1) and gravity gradients (2). The combination with classical sensors can be exploited to suppress vibration noise in the interferometer, extend the dynamic range, or to remove the drift from the classical device (3). These features motivate novel sensor and mission concepts for space-borne earth observation e.g. with quantum gradiometers (4) or hybridised atom interferometers (5). We will discuss developments of atom optics and atom interferometry in microgravity in the context of future quantum sensors (6) and outline the perspectives for applications in space (4,5).The presented work is supported by by the CRC 1227 DQmat within the projects B07 and B09, the CRC 1464 TerraQ within the projects A01, A02 and A03, by "Niedersächsisches Vorab" through "Förderung von Wissenschaft und Technik in Forschung und Lehre" for the initial funding of research in the new DLR-SI Institute, and through the "Quantum and Nano- Metrology (QUANOMET)" initiative within the project QT3.(1) V. Ménoret et al., Scientific Reports 8, 12300, 2018; A. Trimeche et al., Phys. Rev. Appl. 7, 034016, 2017; C. Freier et al., J. of Phys.: Conf. Series 723, 012050, 2016; A. Louchet-Chauvet et al., New J. Phys. 13, 065026, 2011; A. Peters et al., Nature 400, 849, 1999.(2) P. Asenbaum et al., Phys. Rev. Lett. 118, 183602, 2017; M. J. Snadden et al., Phys. Rev. Lett. 81, 971, 1998.(3) L. Richardson et al., Comm. Phys. 3, 208, 2020; P. Cheiney et al., Phys. Rev. Applied 10, 034030, 2018; J. Lautier et al., Appl. Phys. Lett. 105, 144102, 2014.(4) A. Trimeche et al., Class. Quantum Grav. 36, 215004, 2019; K. Douch et al., Adv. Space. Res. 61, 1301, 2018.(5) T. Lévèque et al., arXiv:2011.03382; S. Chiow et al., Phys. Rev. A 92, 063613, 2015.(6) M. Lachmann et al., arXiv:2101.00972; K. Frye et al., EPJ Quant. Technol. 8, 1, 2021; D. Becker et al., Nature 562, 391, 2018; J. Rudolph et al., New J. Phys. 17, 065001, 2015; H. Müntinga et al., Phys. Rev. Lett. 110, 093602 , 2013.

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

Space offers virtually unlimited free-fall in gravity. Bose-Einstein condensation (BEC) enables ineffable low kinetic energies corresponding to pico- or even femtokelvins. The combination of both features makes atom interferometers with unprecedented sensitivity for inertial forces possible and opens a new era for quantum gas experiments. On January 23, 2017, we created Bose-Einstein condensates in space on the sounding rocket mission MAIUS-1 and conducted 110 experiments central to matter-wave interferometry. In particular, we have explored laser cooling and trapping in the presence of large accelerations as experienced during launch, and have studied the evolution, manipulation and interferometry employing Bragg scattering of BECs during the six-minute space flight. In this letter, we focus on the phase transition and the collective dynamics of BECs, whose impact is magnified by the extended free-fall time. Our experiments demonstrate a high reproducibility of the manipulation of BECs on the atom chip reflecting the exquisite control features and the robustness of our experiment. These properties are crucial to novel protocols for creating quantum matter with designed collective excitations at the lowest kinetic energy scales close to femtokelvins., 6 pages, 4 figures

Inertial sensors based on cold atoms have great potential for navigation, geodesy, or fundamental physics. Similar to the Sagnac effect, their sensitivity increases with the space-time area enclosed by the interferometer. Here, we introduce twin-lattice atom interferometry exploiting Bose-Einstein condensates of rubidium-87. Our method provides symmetric momentum transfer and large areas offering a perspective for future palm-sized sensor heads with sensitivities on par with present meter-scale Sagnac devices. Our theoretical model of the impact of beam splitters on the spatial coherence is highly instrumental for designing future sensors., Atom interferometers can be useful for precision measurement of fundamental constants and sensors of different type. Here the authors demonstrate a compact twin-lattice atom interferometry exploiting Bose-Einstein condensates (BECs) of 87 Rb atoms.

We demonstrate a quantum gravimeter by combining the advantages of an atom chip for the generation, delta-kick collimation, and coherent manipulation of freely falling Bose-Einstein condensates (BECs) with an innovative launch mechanism based on Bloch oscillations and double Bragg diffraction. Our high-contrast BEC interferometer realizes tens of milliseconds of free fall in a volume as little as a one centimeter cube and paves the way for measurements with sub-μGal accuracies in miniaturized, robust devices.

Clouds of ultra-cold atoms and especially Bose–Einstein condensates (BEC) provide a source for coherent matter-waves in numerous earth bound experiments. Analogous to optical interferometry, matter-wave interferometers can be used for precision measurements allowing for a sensitivity orders of magnitude above their optical counterparts. However, in some respects the presence of gravitational forces in the lab limits experimental possibilities. In this article, we report about a compact and robust experiment generating Bose–Einstein condensates in the drop tower facility in Bremen, Germany. We also present the progress of building the succeeding experiment in which a two species atom interferometer will be implemented to test the weak equivalence principle with quantum matter.

The weak equivalence principle (EP) represents a corner stone in the general theory of relativity [1] . The validity of this postulate was and is currently tested in different groups with different systems. Among this multitude of methods atom interferometry is considered to be one of the most promising tools in performing high-precision measurements [2] . Using two atom species in free fall with different masses allows comparing two independent measurements of g. This is made possible by creating a mixture of two atomic species at a temperature close to absolute zero. This regime is suitable for the observation of matter waves at long time scales needed for high-precision quantum tests. In this letter an overview of the developments of our quantum sensor devices is done. The up-to-date progress and future prospects in our group of these ambitious and technically challenging projects are briefly presented as well.

Going Down the Tube Two pillars of modern physics are quantum mechanics and general relativity. So far, both have remained apart with no quantum mechanical description of gravity available. Van Zoest et al. (p. 1540 ; see the Perspective by Nussenzveig and Barata ) present work with a macroscopic quantum mechanical system—a Bose-Einstein condensate (BEC) of rubidium atoms in which the cloud of atoms is cooled into a collective quantum state—in microgravity. By dropping the BEC down a 146-meter-long drop chamber and monitoring the expansion of the quantum gas under these microgravity conditions, the authors provide a proof-of-principle demonstration of a technique that can probe the boundary of quantum mechanics and general relativity and perhaps offer the opportunity to reconcile the two experimentally.

We employ light-induced double Bragg diffraction of delta-kick collimated Bose-Einstein condensates to create three symmetric Mach-Zehnder interferometers. They rely on (i) first-order, (ii) two successive first-order, and (iii) second-order processes which demonstrate the scalability of the corresponding momentum transfer. With respect to devices based on conventional Bragg scattering, these symmetric interferometers double the scale factor and feature a better suppression of noise and systematic uncertainties intrinsic to the diffraction process. Moreover, we utilize these interferometers as tiltmeters for monitoring their inclination with respect to gravity.

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

Atom interferometers have a multitude of proposed applications in space including precise measurements of the Earth's gravitational field, in navigation & ranging, and in fundamental physics such as tests of the weak equivalence principle (WEP) and gravitational wave detection. While atom interferometers are realized routinely in ground-based laboratories, current efforts aim at the development of a space compatible design optimized with respect to dimensions, weight, power consumption, mechanical robustness and radiation hardness. In this paper, we present a design of a high-sensitivity differential dual species $^{85}$Rb/$^{87}$Rb atom interferometer for space, including physics package, laser system, electronics and software. The physics package comprises the atom source consisting of dispensers and a 2D magneto-optical trap (MOT), the science chamber with a 3D-MOT, a magnetic trap based on an atom chip and an optical dipole trap (ODT) used for Bose-Einstein condensate (BEC) creation and interferometry, the detection unit, the vacuum system for $10^{-11}$ mbar ultra-high vacuum generation, and the high-suppression factor magnetic shielding as well as the thermal control system. The laser system is based on a hybrid approach using fiber-based telecom components and high-power laser diode technology and includes all laser sources for 2D-MOT, 3D-MOT, ODT, interferometry and detection. Manipulation and switching of the laser beams is carried out on an optical bench using Zerodur bonding technology. The instrument consists of 9 units with an overall mass of 221 kg, an average power consumption of 608 W (819 W peak), and a volume of 470 liters which would well fit on a satellite to be launched with a Soyuz rocket, as system studies have shown., 30 pages, 23 figures, accepted for publication in Experimental Astronomy

We propose a very long baseline atom interferometer test of Einstein's equivalence principle (EEP) with ytterbium and rubidium extending over 10m of free fall. In view of existing parametrizations of EEP violations, this choice of test masses significantly broadens the scope of atom interferometric EEP tests with respect to other performed or proposed tests by comparing two elements with high atomic numbfers. In the first step, our experimental scheme will allow us to reach an accuracy in the Eotvos ratio of 7 . 10(-13). This achievement will constrain violation scenarios beyond our present knowledge and will represent an important milestone for exploring a variety of schemes for further improvements of the tests as outlined in the paper. We will discuss the technical realisation in the new infrastructure of the Hanover Institute of Technology (HITec) and give a short overview of the requirements needed to reach this accuracy. The experiment will demonstrate a variety of techniques, which will be employed in future tests of EEP, high-accuracy gravimetry and gravity gradiometry. It includes operation of a force-sensitive atom interferometer with an alkaline earth-like element in free fall, beam splitting over macroscopic distances and novel source concepts. DFG/SFB/geo-Q BMWi/DLR/50WM1131.1137

The theory of general relativity describes macroscopic phenomena driven by the influence of gravity while quantum mechanics brilliantly accounts for microscopic effects. Despite their tremendous individual success, a complete unification of fundamental interactions is missing and remains one of the most challenging and important quests in modern theoretical physics. The STE-QUEST satellite mission, proposed as a medium-size mission within the Cosmic Vision program of the European Space Agency (ESA), aims for testing general relativity with high precision in two experiments by performing a measurement of the gravitational redshift of the Sun and the Moon by comparing terrestrial clocks, and by performing a test of the Universality of Free Fall of matter waves in the gravitational field of Earth comparing the trajectory of two Bose-Einstein condensates of Rb85 and Rb87. The two ultracold atom clouds are monitored very precisely thanks to techniques of atom interferometry. This allows to reach down to an uncertainty in the E\"otv\"os parameter of at least 2x10E-15. In this paper, we report about the results of the phase A mission study of the atom interferometer instrument covering the description of the main payload elements, the atomic source concept, and the systematic error sources., Comment: 21 pages, 5 figures

Long-baseline precision tests based on atom interferometry require drastic control over the initial external degrees of freedom of atomic ensembles to reduce systematic effects. The use of optical lattices (OLs) is a highly accurate method to manipulate atomic states in position and momentum allowing excellent control of the launch in atomic fountains. The simultaneous lattice launch of two atomic species, as required in a quantum test of the equivalence principle, is however problematic due to crosstalk effects. In this article, we propose to selectively address two species of alkalines by applying two OLs at or close to magic-zero wavelengths of the atoms. The proposed scheme applies in general for a pair of species with a vastly different ac Stark shift to a laser wavelength. We illustrate the principle by studying a fountain launch of condensed ensembles of 87Rb and 41K initially co-located. Numerical simulations confirm the fidelity of our scheme up to few nm and nm s−1 in inter-species differential position and velocity, respectively. This result is a pre-requisite for the next performance level in precision tests.

Matter-wave sensors are considered to be one of the most promising fields for progress in metrology and fundamental tests. We report on the development of a miniaturized and robust experiment within the QUANTUS collaboration using ultra cold atoms in a free fall environment as a test-bed for matter-wave interferometry on long timescales. Over 200 experiments in microgravity have been performed so far at the ZARM drop tower in Bremen and a BEC was observed after expansion times of up to 1s [1]. The combination of long expansion times and low density samples is beneficial for the application in interferometry. We present the recently implemented interferometer in our chip-based 87Rb BEC experiment including on-chip state preparation. Bragg diffraction is used for coherent manipulation, realizing different interferometer schemes. First results on ground and in microgravity are shown.

Building on a variant of the Jarzynski equation we propose a new method to numerically determine the prior-predictive value in a Bayesian inference problem. The method generalizes thermodynamic integration and is not hampered by equilibration problems. We demonstrate its operation by applying it to two simple examples and elucidate its performance. In the case of multi-modal posterior distributions the performance is superior to thermodynamic integration., Comment: 8 pages, 11 figures

Die Organoelementgruppen PhS–, PhSe–, Ph2P–, Ph2As–, Ph3Ge–, Ph2(O)P– und Ph2(O)As– ermoglichen die Cycloaddition von 2-Azaallyllithium-Verbindungen an die Ethen-Doppelbindung, wahrend die Gruppen PhTe–, Ph2Sb–, Ph3Sn– und Ph3Pbb– diesen Zweck nicht erfullen. 1,3-Anionic Cycloadditions, XVIII. Extension of the Scope of 1,3-Anionic Cycloadditions by Activating Organoelement Groups The organoelement groups PhS–, PhSe–, Ph2P–, Ph2As–, Ph3Ge–, Ph2(O)P–, and Ph2(O)As– make possible the cycloaddition of 2-azaallyllithium compounds to the double bond of ethene, whereas the groups PhTe–, Ph2Sb–, Ph3Sn–, and Ph3Pb– fail to do this.

Carbonyl olefination with a lithiomethane, having besides the group P(O)Ph 2 at the methane C-atom an organo-heavy-metal group, occurs at low temperatures to give exclusively diphenylphosphoryl substituted olefins.

Erstmals wurden (Phenyltelluro)ethen (2a; 78%) und -ethin (4; 51%) synthetisiert. 2a konnte durch sperrige Lithiumamide (Lithium-2,2,6,6-tetramethylpiperidid und Lithium-dicyclohexyl-amid) zu 1-Lithio-1-(phenyltelluro)ethen (2b) (≈50% Ausbeute) lithiiert werden, das mit Benzaldehyd und Chlortrimethylsilan zu den erwarteten Produkten 2c (88%) bzw. 2e (80%) reagiert. Mit 1-Iodpropan und Allylbromid erfolgte keine Reaktion. New Reagents, XXVI. (Phenyltelluro)ethene, 1-Lithio-1-(phenyltelluro)ethene, and (Phenyltelluro)ethyne, Synthesis and Reactions (Phenyltelluro)ethene (2a, 78%) and -ethyne (4, 51%) were synthesized for the first time. By lithiation with bulky lithium amides (lithium 2,2,6,6-tetramethylpiperidide and lithium dicyclohexylamide) 1-lithio-1-(phenyltelluro)ethene (2b) was obtained from 2a (≈50% yield). 2b reacts with benzaldehyde and chlorotrimethylsilane to give the expected products 2c (88%) and 2e (80%), respectively, but no reaction occurred with 1-iodopropane and allyl bromide.

Bose Einstein Condensates (BEC) opened the way for realization of atomic ensembles with Heisenberg limited uncertainty. In microgravity extremely dilute samples of BEC can be obtained and observed after a free evolution on timescales of seconds. Applications range from atom optics to matter wave interferometry. This has led us to realize a BEC of 10000 87Rb atoms in microgravity. The experimental results (to be published) establish the fact, that in a microgravity environment ultra-large condensates (≈1.5 mm) after a free evolution of 1 second can be observed. In particular, microgravity provides mass independent confining potential which is very important for the research on a mixture of quantum gases.We aim to realize a new setup for multispecies experiments, which can be used in catapult mode doubling the time for microgravity to 9 seconds. The experiment is planned to use 87Rb and 40K as degenerate Bose and Fermi gases respectively and can be used to carry out experiments on interferometry, Bose-Fermi mixtures and tests of the weak equivalence principle in quantum domain. Up to date progress and future prospects of this ambitious and technically challenging project will be presented.