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The INTENTAS project aims to develop an atomic sensor utilizing entangled Bose-Einstein condensates (BECs) in a microgravity environment. This key achievement is necessary to advance the capability for measurements that benefit from both entanglement-enhanced sensitivities and extended interrogation times. The project addresses significant challenges related to size, weight, and power management (SWaP) specific to the experimental platform at the Einstein-Elevator in Hannover. The design ensures a low-noise environment essential for the creation and detection of entanglement. Additionally, the apparatus features an innovative approach to the all-optical creation of BECs, providing a flexible system for various configurations and meeting the requirements for rapid turnaround times. Successful demonstration of this technology in the Einstein-Elevator will pave the way for a future deployment in space, where its potential applications will unlock high-precision quantum sensing.

Compared to light interferometers, the flux in cold-atom interferometers is low and the associated shot noise large. Sensitivities beyond these limitations require the preparation of entangled atoms in different momentum modes. Here, we demonstrate a source of entangled atoms that is compatible with state-of-the-art interferometers. Entanglement is transferred from the spin degree of freedom of a Bose-Einstein condensate to well-separated momentum modes, witnessed by a squeezing parameter of -3.1(8) dB. Entanglement-enhanced atom interferometers open up unprecedented sensitivities for quantum gradiometers or gravitational wave detectors., Comment: 9 pages, 5 figures

We proposed the European Laboratory for Gravitation and Atom-interferometric Research (ELGAR), an array of atom gradiometers aimed at studying space-time and gravitation with the primary goal of observing gravitational waves (GWs) in the infrasound band with a peak strain sensitivity of $3.3 \times 10^{-22}/\sqrt{\text{Hz}}$ at 1.7 Hz. In this paper we detail the main technological bricks of this large scale detector and emphasis the research pathways to be conducted for its realization. We discuss the site options, atom optics, and source requirements needed to reach the target sensitivity. We then discuss required seismic isolation techniques, Gravity Gradient Noise reduction strategies, and the metrology of various noise couplings to the detector., Comment: This paper contains the technical aspects of the ELGAR facility. This content was originally included in arXiv:1911.03701 and will finally be published separately

The analysis of entangled atomic ensembles and their application for interferometry beyond the standard quantum limit requires an accurate determination of the number of atoms. We present an accurate fluorescence detection technique for atoms that is fully integrated into an experimental apparatus for the production of many-particle entangled quantum states. Single-particle resolving fluorescence measurements for $1$ up to $30$ atoms are presented. According to our noise analysis, we extrapolate that the single-atom resolution extends to a limiting atom number of $390(20)$ atoms. We utilize the accurate atom number detection for a number stabilization of the laser-cooled atomic ensemble. For a target ensemble size of $7$ atoms prepared on demand, we achieve a $92(2)\,\%$ preparation fidelity and reach number fluctuations $18(1)\,\mathrm{dB}$ below the shot noise level using real-time feedback on the magneto-optical trap., Comment: 10 pages, 4 figures

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 towards multi-band GW astronomy, but will leave the infrasound (0.1 Hz to 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 $4.1 \times 10^{-22}/\sqrt{\text{Hz}}$ 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.

The proposed mission "Space Atomic Gravity Explorer" (SAGE) has the scientific objective to investigate gravitational waves, dark matter, and other fundamental aspects of gravity as well as the connection between gravitational physics and quantum physics using new quantum sensors, namely, optical atomic clocks and atom interferometers based on ultracold strontium atoms., Comment: Published in Eur. Phys. J. D 73 (2019) 228 in the Topical Issue Quantum Technologies for Gravitational Physics, Guest editors Tanja Mehlstaubler, Yanbei Chen, Guglielmo M. Tino and Hsien-Chi Yeh

Fluctuations are a key property of both classical and quantum systems. While the fluctuations are well understood for many quantum systems at zero temperature, the case of an interacting quantum system at finite temperature still poses numerous challenges. Despite intense theoretical investigations of atom number fluctuations in Bose-Einstein condensates (BECs), their amplitude in experimentally relevant interacting systems is still poorly understood. Moreover, technical limitations have prevented their experimental observation to date. Here we report the first observation of these fluctuations. Our experiments are based on a stabilization technique, which allows for the preparation of ultracold thermal clouds at the shot noise level, thereby eliminating numerous technical noise sources. Furthermore, we make use of the correlations established by the evaporative cooling process to precisely determine the fluctuations and the sample temperature. This allows us to observe a telltale signature: the sudden increase in fluctuations of the condensate atom number close to the critical temperature., Comment: Main text: 5 pages, 4 figures. Supplemental Information: 3 figures, 1 pages

If the boundary conditions of the quantum vacuum are changed in time, quantum field theory predicts that real, observable particles can be created in the initially empty modes. Here, we realize this effect by changing the boundary conditions of a spinor Bose-Einstein condensate, which yields a population of initially unoccupied spatial and spin excitations. We prove that the excitations are created as entangled excitation pairs by certifying continuous-variable entanglement within the many-particle output state.

We propose to generate macroscopic superposition states of a large number of atoms in the ground state of a three-mode spinor Bose-Einstein condensate. The ground state is protected by a finite energy gap, is immune to phase noise, and the measurement of the number of particles in one mode heralds the coherent preparation of the two other modes simultaneously empty and filled. Highly entangled macroscopic superposition states are generated with large probability also taking into account quasi-adiabatic preparation of the ground state. All the key ingredients necessary to realize our proposal are experimentally available., Comment: 6 pages, 3 figures

Recent experiments have demonstrated the generation of entanglement by quasi-adiabatically driving through quantum phase transitions of a ferromagnetic spin-1 Bose-Einstein condensate in the presence of a tunable quadratic Zeeman shift. We analyze, in terms of the Fisher information, the interferometric value of the entanglement accessible by this approach. In addition to the Twin-Fock phase studied experimentally, we unveil a second regime, in the broken axisymmetry phase, which provides Heisenberg scaling of the quantum Fisher information and can be reached on shorter time scales. We identify optimal unitary transformations and an experimentally feasible optimal measurement prescription that maximize the interferometric sensitivity. We further ascertain that the Fisher information is robust with respect to non-adiabaticity and measurement noise. Finally, we show that the quasi-adiabatic entanglement preparation schemes admit higher sensitivities than dynamical methods based on fast quenches., Comment: 11 pages, 6 figures

Since the pioneering work of Ramsey, atom interferometers are employed for precision metrology, in particular to measure time and to realize the second. In a classical interferometer, an ensemble of atoms is prepared in one of the two input states, whereas the second one is left empty. In this case, the vacuum noise restricts the precision of the interferometer to the standard quantum limit (SQL). Here, we propose and experimentally demonstrate a novel clock configuration that surpasses the SQL by squeezing the vacuum in the empty input state. We create a squeezed vacuum state containing an average of 0.75 atoms to improve the clock sensitivity of 10,000 atoms by 2.05 dB. The SQL poses a significant limitation for today's microwave fountain clocks, which serve as the main time reference. We evaluate the major technical limitations and challenges for devising a next generation of fountain clocks based on atomic squeezed vacuum., Comment: 9 pages, 6 figures

In 1935, Einstein, Podolsky and Rosen (EPR) questioned the completeness of quantum mechanics by devising a quantum state of two massive particles with maximally correlated space and momentum coordinates. The EPR criterion qualifies such continuous-variable entangled states, where a measurement of one subsystem seemingly allows for a prediction of the second subsystem beyond the Heisenberg uncertainty relation. Up to now, continuous-variable EPR correlations have only been created with photons, while the demonstration of such strongly correlated states with massive particles is still outstanding. Here, we report on the creation of an EPR-correlated two-mode squeezed state in an ultracold atomic ensemble. The state shows an EPR entanglement parameter of 0.18(3), which is 2.4 standard deviations below the threshold 1/4 of the EPR criterion. We also present a full tomographic reconstruction of the underlying many-particle quantum state. The state presents a resource for tests of quantum nonlocality and a wide variety of applications in the field of continuous-variable quantum information and metrology., Comment: 8 pages, 7 figures

Quantum mechanics predicts that our physical reality is influenced by events that can potentially happen but factually do not occur. Interaction-free measurements (IFMs) exploit this counterintuitive influence to detect the presence of an object without requiring any interaction with it. Here we propose and realize an IFM concept based on an unstable many-particle system. In our experiments, we employ an ultracold gas in an unstable spin configuration which can undergo a rapid decay. The object - realized by a laser beam - prevents this decay due to the indirect quantum Zeno effect and thus, its presence can be detected without interacting with a single atom. Contrary to existing proposals, our IFM does not require single-particle sources and is only weakly affected by losses and decoherence. We demonstrate confidence levels of 90%, well beyond previous optical experiments., Comment: manuscript with 5 figures, 3 supplementary figure, 1 supplementary note

Typical sources of ultracold atoms operate with a considerable delay between the delivery of ensembles due to sequential trapping and cooling schemes. Therefore, alternative schemes for the continuous generation of ultracold atoms are highly desirable. Here, we demonstrate the continuous loading of a magnetic trap from a quasi-continuous atom beam. We achieve a steady state with $3.8 \times 10^7$ magnetically trapped atoms and a temperature of $102 \mu$K. The ensemble is protected from laser light sources, a requirement for its application for metrological tasks or sympathetic cooling. The continuous scheme is robust and applicable to a wide range of particles and trapping potentials., Comment: 5 pages, 6 figures

We present the production of dual-species Bose-Einstein condensates of $^{39}\mathrm{K}$ and $^{87}\mathrm{Rb}$. Preparation of both species in the $\left| F=1,m_F=-1 \right\rangle$ state enabled us to exploit a total of three Fesh\-bach resonances which allows for simultaneous Feshbach tuning of the $^{39}\mathrm{K}$ intraspecies and the $^{39}\mathrm{K}$-$^{87}\mathrm{Rb}$ interspecies scattering length. Thus dual-species Bose-Einstein condensates were produced by sympathetic cooling of $^{39}\mathrm{K}$ with $^{87}\mathrm{Rb}$. A dark spontaneous force optical trap was used for $^{87}\mathrm{Rb}$, to reduce the losses in $^{39}\mathrm{K}$ due to light-assisted collisions in the optical trapping phase, which can be of benefit for other dual-species experiments. The tunability of the scattering length was used to perform precision spectroscopy of the interspecies Feshbach resonance located at $117.56(2)\,\mathrm{G}$ and to determine the width of the resonance to $1.21(5)\,\mathrm{G}$ by rethermalization measurements. The transition region from miscible to immiscible dual-species condensates was investigated and the interspecies background scattering length was determined to $28.5\,a_\mathrm{0}$ using an empirical model. This paves the way for dual-species experiments with $^{39}\mathrm{K}$ and $^{87}\mathrm{Rb}$ BECs ranging from molecular physics to precision metrology., Comment: 9 pages, 9 figures

Contemporary understanding of correlations in quantum many-body systems and in quantum phase transitions is based to a large extent on the recent intensive studies of entanglement in many-body systems. In contrast, much less is known about the role of quantum nonlocality in these systems, mostly because the available multipartite Bell inequalities involve high-order correlations among many particles, which are hard to access theoretically, and even harder experimentally. Standard, "theorist- and experimentalist-friendly" many-body observables involve correlations among only few (one, two, rarely three...) particles. Typically, there is no multipartite Bell inequality for this scenario based on such low-order correlations. Recently, however, we have succeeded in constructing multipartite Bell inequalities that involve two- and one-body correlations only, and showed how they revealed the nonlocality in many-body systems relevant for nuclear and atomic physics [Science 344, 1256 (2014)]. With the present contribution we continue our work on this problem. On the one hand, we present a detailed derivation of the above Bell inequalities, pertaining to permutation symmetry among the involved parties. On the other hand, we present a couple of new results concerning such Bell inequalities. First, we characterize their tightness. We then discuss maximal quantum violations of these inequalities in the general case, and their scaling with the number of parties. Moreover, we provide new classes of two-body Bell inequalities which reveal nonlocality of the Dicke states---ground states of physically relevant and experimentally realizable Hamiltonians. Finally, we shortly discuss various scenarios for nonlocality detection in mesoscopic systems of trapped ions or atoms, and by atoms trapped in the vicinity of designed nanostructures., Comment: 46 pages (25.2 + appendices), 7 figures

We present an analytical model for the theoretical analysis of spin dynamics and spontaneous symmetry breaking in a spinor Bose-Einstein condensate (BEC). This allows for an excellent intuitive understanding of the processes and provides good quantitative agreement with experimental results in Phys. Rev. Lett. 105, 135302 (2010). It is shown that the dynamics of a spinor BEC initially prepared in an unstable Zeeman state mF=0 (|0>) can be understood by approximating the effective trapping potential for the state |+-1> with a cylindrical box potential. The resonances in the creation efficiency of these atom pairs can be traced back to excitation modes of this confinement. The understanding of these excitation modes allows for a detailed characterization of the symmetry breaking mechanism, showing how a twofold spontaneous breaking of spatial and spin symmetry can occur. In addition a detailed account of the experimental methods for the preparation and analysis of spinor quantum gases is given., Comment: 12 pages, 14 figures

In recent decades, cold atom experiments have become increasingly complex. While computers control most parameters, optimization is mostly done manually. This is a time-consuming task for a high-dimensional parameter space with unknown correlations. Here we automate this process using a genetic algorithm based on Differential Evolution. We demonstrate that this algorithm optimizes 21 correlated parameters and that it is robust against local maxima and experimental noise. The algorithm is flexible and easy to implement. Thus, the presented scheme can be applied to a wide range of experimental optimization tasks., Comment: minor revision

Optically trapped ensembles are of crucial importance for frequency measurements and quantum memories, but generally suffer from strong dephasing due to inhomogeneous density and light shifts. We demonstrate a drastic increase of the coherence time to 21 s on the magnetic field insensitive clock transition of Rb-87 by applying the recently discovered spin self-rephasing. This result confirms the general nature of this new mechanism and thus shows its applicability in atom clocks and quantum memories. A systematic investigation of all relevant frequency shifts and noise contributions yields a stability of 2.4E-11 x tau^(-1/2), where tau is the integration time in seconds. Based on a set of technical improvements, the presented frequency standard is predicted to rival the stability of microwave fountain clocks in a potentially much more compact setup., Comment: 5 pages, 4 figures

Spatial entropy redistribution plays a key role in adiabatic cooling of ultra-cold lattice gases. We show that high-spin fermions with a spatially variable quadratic Zeeman coupling may allow for the creation of an inner spin-1/2 core surrounded by high-spin wings. The latter are always more entropic than the core at high temperatures and, remarkably, at all temperatures in the presence of frustration. Combining thermodynamic Bethe Ansatz with local density approximation, we study the spatial entropy distribution for the particular case of one-dimensional spin-3/2 lattice fermions in the Mott phase. Interestingly, this spatially dependent entropy opens a possible path for an adiabatic cooling technique that, in contrast to previous proposals, would specifically target the spin degree of freedom. We discuss a possible realization of this adiabatic cooling, which may allow for a highly efficient entropy decrease in the spin-1/2 core and help access antiferromagnetic order in experiments on ultracold spinor fermions., Comment: 9 pages, 5 figures

Parametric amplification of quantum fluctuations constitutes a fundamental mechanism for spontaneous symmetry breaking. In our experiments, a spinor condensate acts as a parametric amplifier of spin modes, resulting in a twofold spontaneous breaking of spatial and spin symmetry in the amplified clouds. Our experiments permit a precise analysis of the amplification in specific spatial Bessel-like modes, allowing for the detailed understanding of the double symmetry breaking. On resonances that create vortex-antivortex superpositions, we show that the cylindrical spatial symmetry is spontaneously broken, but phase squeezing prevents spin-symmetry breaking. If, however, nondegenerate spin modes contribute to the amplification, quantum interferences lead to spin-dependent density profiles and hence spontaneously-formed patterns in the longitudinal magnetization., Comment: 5 pages, 4 figures

We report on a slow guided atom laser beam outcoupled from a Bose-Einstein condensate of 87Rb atoms in a hybrid trap. The acceleration of the atom laser beam can be controlled by compensating the gravitational acceleration and we reach residual accelerations as low as 0.0027 g. The outcoupling mechanism allows for the production of a constant flux of 4.5x10^6 atoms per second and due to transverse guiding we obtain an upper limit for the mean beam width of 4.6 \mu\m. The transverse velocity spread is only 0.2 mm/s and thus an upper limit for the beam quality parameter is M^2=2.5. We demonstrate the potential of the long interrogation times available with this atom laser beam by measuring the trap frequency in a single measurement. The small beam width together with the long evolution and interrogation time makes this atom laser beam a promising tool for continuous interferometric measurements., Comment: 7 pages, 8 figures, to be published in Applied Physics B

Spin-changing collisions may lead under proper conditions to the parametric amplification of matter waves in spinor Bose-Einstein condensates. Magnetic dipole-dipole interactions, although typically very weak in alkaline atoms, are shown to play a very relevant role in the amplification process. We show that these interactions may lead to a strong dependence of the amplification dynamics on the angle between the trap axis and the magnetic-field orientation. We analyze as well the important role played by magnetic-field gradients, which modify also strongly the amplification process. Magnetic-field gradients must be hence carefully controlled in future experiments, in order to observe clearly the effects of the dipolar interactions in the amplification dynamics.

Parametric amplification of vacuum fluctuations is crucial in modern quantum optics, enabling the creation of squeezing and entanglement. We demonstrate the parametric amplification of vacuum fluctuations for matter waves using a spinor F=2 Rb-87 condensate. Interatomic interactions lead to correlated pair creation in the m_F= +/- 1 states from an initial unstable m_F=0 condensate, which acts as a vacuum for m_F unequal 0. Although this pair creation from a pure m_F=0 condensate is ideally triggered by vacuum fluctuations, unavoidable spurious initial m_F= +/- 1 atoms induce a classical seed which may become the dominant triggering mechanism. We show that pair creation is insensitive to a classical seed for sufficiently large magnetic fields, demonstrating the dominant role of vacuum fluctuations. The presented system thus provides a direct path towards the generation of non-classical states of matter on the basis of spinor condensates., Comment: 5 pages, 4 figures

We analyze the spinor dynamics of a Rb-87 F=2 condensate initially prepared in the m_F=0 Zeeman sublevel. We show that this dynamics, characterized by the creation of correlated atomic pairs in m_F=+/-1, presents an intriguing multi-resonant magnetic field dependence induced by the trap inhomogeneity. This dependence is directly linked to the most unstable Bogoliubov spin excitations of the initial m_F = 0 condensate, showing that, in general, even a qualitative understanding of the pair creation efficiency in a spinor condensate requires a careful consideration of the confinement., Comment: 5 pages, 4 figures

We present a detailed analysis of the production efficiency of weakly bound heteronuclear KRb-Feshbach molecules using radio frequency association in a harmonic trap. The efficiency was measured in a wide range of temperatures, binding energies and radio frequencies. A comprehensive analytical model is presented, explaining the observed asymmetric spectra and achieving good quantitative agreement with the measured production rates. This model provides a deep understanding of the molecule association process and paves the way for future experiments which rely on Feshbach molecules e.g. for the production of deeply bound molecules., Comment: 5 pages, 4 figures

We report on the transport of mixed quantum degenerate gases of bosonic 87Rb and fermionic 40K in a harmonic potential provided by a modified QUIC trap. The samples are transported over a distance of 6 mm to the geometric center of the anti-Helmholtz coils of the QUIC trap. This transport mechanism was implemented by a small modification of the QUIC trap and is free of losses and heating. It allows all experiments using QUIC traps to use the highly homogeneous magnetic fields that can be created in the center of a QUIC trap and improves the optical access to the atoms, e.g., for experiments with optical lattices. This mechanism may be cascaded to cover even larger distances for applications with quantum degenerate samples., Comment: 7 pages, 8 figures

We have observed 28 heteronuclear Feshbach resonances in 10 spin combinations of the hyperfine ground states of a 40K 87Rb mixture. The measurements were performed by observing the loss rates from an atomic mixture at magnetic fields between 0 and 700 G. This data was used to significantly refine an interatomic potential derived from molecular spectroscopy, yielding a highly consistent model of the KRb interaction. Thus, the measured resonances can be assigned to the corresponding molecular states. In addition, this potential allows for an accurate calculation of the energy differences between highly excited levels and the rovibrational ground level. This information is of particular relevance for the formation of deeply bound heteronuclear molecules. Finally, the model is used to predict Feshbach resonances in mixtures of 87Rb combined with 39K or 41K., Comment: 4 pages, 3 figures

We show that light-induced atom desorption (LIAD) can be used as a flexible atomic source for large Rb-87 and K-40 magneto-optical traps. The use of LIAD at short wavelengths allows for fast switching of the desired vapor pressure and permits experiments with long trapping and coherence times. The wavelength dependence of the LIAD effect for both species was explored in a range from 630 nm to 253 nm in an uncoated quartz cell and a stainless steel chamber. Only a few mW/cm^2 of near-UV light produce partial pressures that are high enough to saturate a magneto-optical trap at 3.5 x 10^9 Rb atoms or 7 x 10^7 K atoms. Loading rates as high as 1.2 x 10^9 Rb atoms/s and 8 x 10^7 K atoms/s were achieved without the use of a secondary atom source. After the desorption light is turned off, the pressure quickly decays back to equilibrium with a time constant as short as 200 us, allowing for long trapping lifetimes after the MOT loading phase., Comment: 8 pages, 9 figures