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This document presents a summary of the 2023 Terrestrial Very-Long-Baseline Atom Interferometry Workshop hosted by CERN. The workshop brought together experts from around the world to discuss the exciting developments in large-scale atom interferometer (AI) prototypes and their potential for detecting ultralight dark matter and gravitational waves. The primary objective of the workshop was to lay the groundwork for an international TVLBAI proto-collaboration. This collaboration aims to unite researchers from different institutions to strategize and secure funding for terrestrial large-scale AI projects. The ultimate goal is to create a roadmap detailing the design and technology choices for one or more km-scale detectors, which will be operational in the mid-2030s. The key sections of this report present the physics case and technical challenges, together with a comprehensive overview of the discussions at the workshop together with the main conclusions., Comment: Summary of the Terrestrial Very-Long-Baseline Atom Interferometry Workshop held at CERN: https://indico.cern.ch/event/1208783/

An M-class mission proposal in response to the 2021 call in ESA's science programme with a broad range of objectives in fundamental physics, which include testing the Equivalence Principle and Lorentz Invariance, searching for Ultralight Dark Matter and probing Quantum Mechanics., Comment: As submitted to the M7 call in July 2022, except updated for the recent (Sept. 2022) MICROSCOPE results, and new section 2.5 summarizing the information provided to ESA during the September 2022 audition

We summarize the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with ESA and national space and research funding agencies., Comment: Summary of the Community Workshop on Cold Atoms in Space and corresponding Road-map: https://indico.cern.ch/event/1064855/

Based on fundamental symmetries, molecules cannot have a permanent electric dipole moment although it is commonly used in the literature to explain the different molecular spectra for heteronuclear and homonuclear molecules. Electric-dipole rotational and vibrational spectra can indeed be observed in heteronuclear molecules while they are missing in molecules with identical nuclei. I show that the missing spectral features can be explained as an effect of the exchange symmetry for identical particles., Comment: Revised argument, results unchanged. Corrected typos. Added references

Atom interferometers have been developed in the last three decades as new powerful tools to investigate gravity. They were used for measuring the gravity acceleration, the gravity gradient, and the gravity-field curvature, for the determination of the gravitational constant, for the investigation of gravity at microscopic distances, to test the equivalence principle of general relativity and the theories of modified gravity, to probe the interplay between gravitational and quantum physics and to test quantum gravity models, to search for dark matter and dark energy, and they were proposed as new detectors for the observation of gravitational waves. Here I describe past and ongoing experiments with an outlook on what I think are the main prospects in this field and the potential to search for new physics.

We present the scientific motivation for future space tests of the equivalence principle, and in particular the universality of free fall, at the $10^{-17}$ level or better. Two possible mission scenarios, one based on quantum technologies, the other on electrostatic accelerometers, that could reach that goal are briefly discussed., Comment: White paper submitted to the ESA Voyage 2050 long term plan. Partly derived from Altschul et al., Advances in Space Research, 2015, 55, 501 - 524, arXiv:1404.4307

We characterize the performance of a gravimeter and a gravity gradiometer based on the $^{1}$S$_{0}$-$^3$P$_0$ clock transition of strontium atoms. We use this new quantum sensor to measure the gravitational acceleration with a relative sensitivity of $1.7\times10^{-5}$, representing the first realisation of an atomic interferometry gravimeter based on a single-photon transition. Various noise contributions to the gravimeter are measured and characterized, with the current primary limitation to sensitivity seen to be the intrinsic noise of the interferometry laser itself. In a gravity gradiometer configuration, a differential phase sensitivity of 1.53~rad/$\sqrt{Hz}$ was achieved at an artificially introduced differential phase of $\pi/2$~rad. We experimentally investigated the effects of the contrast and visibility based on various parameters and achieve a total interferometry time of 30~ms, which is longer than previously reported for such interferometers. The characterization and determined limitations of the present apparatus employing $^{88}$Sr atoms provides a guidance for the future development of large-scale clock-transition gravimeters and gravity gradiometers with alkali-earth and alkali-earth-like atoms (e.g., $^{87}$Sr, Ca, Yb)., Comment: 32 pages, 14 figures

We present a gradiometer based on matter-wave interference of alkaline-earth-metal atoms, namely $^{88}$Sr. The coherent manipulation of the atomic external degrees of freedom is obtained by large-momentum-transfer Bragg diffraction, driven by laser fields detuned away from the narrow $^1$S$_0$-$^3$P$_1$ intercombination transition. We use a well-controlled artificial gradient, realized by changing the relative frequencies of the Bragg pulses during the interferometer sequence, in order to characterize the sensitivity of the gradiometer. The sensitivity reaches $1.5 \times 10^{-5}$ s$^{-2}$ for an interferometer time of 20 ms, limited only by geometrical constraints. We observed extremely low sensitivity of the gradiometric phase to magnetic field gradients, approaching a value 10$^{5}$ times lower than the sensitivity of alkali-atom based gradiometers. An efficient double-launch technique employing accelerated red vertical lattices from a single magneto-optical trap cloud is also demonstrated. These results highlight strontium as an ideal candidate for precision measurements of gravity gradients, with potential application in future precision tests of fundamental physics., Comment: 10 pages, 7 figures

We present results from deep and very spatially extended CTIO/DECam $g$ and $r$ photometry (reaching out to $\sim$ 2 mag below the oldest MSTO and covering $\sim$ 20 deg$^2$) around the Sextans dSph. We use this data-set to study the structural properties of Sextans overall stellar population and its different stellar evolutionary phases, as well as to search for signs of tidal disturbance from the MW, which would indicate departure from dynamical equilibrium. We perform the most accurate structural analysis to-date of Sextans' stellar components by applying Bayesian MCMC methods to the individual stars' positions. Surface density maps are built by decontaminating the sample through a matched filter analysis of the CMD, and then analysed for departures from axisymmetry. Sextans is found to be considerably less spatially extended than early studies suggested. No significant distortions or tidal disturbances are found down to a surface brightness of $\sim$ 31.8 mag/arcsec$^{-2}$ in V-band. We identify an overdensity in the central regions that may correspond to previously reported kinematic substructure(s). In agreement with previous findings, old $\&$ metal-poor stars such as BHB stars cover a much larger area than stars in other evolutionary phases, and bright BSs are less spatially extended than faint ones. However, the different spatial distribution of bright and faint BSs appears consistent with the general age/metallicity gradients found in Sextans' stellar component. This is compatible with BSs having formed by evolution of binaries and not necessarily due to the presence of a central disrupted globular cluster, as suggested in the literature. We provide structural parameters for the various populations analyzed and make publicly available the photometric catalogue of point-sources as well as a catalogue of literature spectroscopic measurements with updated membership probabilities., Comment: 21 pages, 14 figures, 9 tables, accepted for publication in Astronomy & Astrophysics (A&A), the associated photometric and spectroscopic catalogues will be available at CDS, abstract abridged for arXiv

We propose and analyse a method that allows for the production of squeezed states of the atomic center-of-mass motion that can be injected into an atom interferometer. Our scheme employs dispersive probing in a ring resonator on a narrow transition of strontium atoms in order to provide a collective measurement of the relative population of two momentum states. We show that this method is applicable to a Bragg diffraction-based atom interferometer with large diffraction orders. The applicability of this technique can be extended also to small diffraction orders and large atom numbers by inducing atomic transparency at the frequency of the probe field, reaching an interferometer phase resolution scaling $\Delta\phi\sim N^{-3/4}$, where $N$ is the atom number. We show that for realistic parameters it is possible to obtain a 20 dB gain in interferometer phase estimation compared to the Standard Quantum Limit., Comment: 5 pages, 4 figures

We report on the realization of a matter-wave interferometer based on single-photon interaction on the ultra-narrow optical clock transition of strontium atoms. We experimentally demonstrated its operation as a gravimeter and as a gravity gradiometer. No reduction of interferometric contrast was observed up to an interferometer time $2T=10$ ms, limited by geometric constraints of the apparatus. In the gradiometric configuration, the sensitivity approaches the shot noise limit. Single-photon interferometers represent a new class of high-precision sensors that could be used for the detection of gravitational waves in so far unexplored frequency ranges and to enlighten the boundary between Quantum Mechanics and General Relativity., Comment: 5 pages, 4 figures

We report on a trapped atom interferometer based on Bragg diffraction and Bloch oscillations with alkaline-earth-metal atoms. We use a Ramsey-Bord\'e Bragg interferometer with $^{88}$Sr atoms combined with Bloch oscillations to extend the interferometer time. Thanks to a long coherence time for Bloch oscillations of $^{88}$Sr atoms, we observed interference up to 1 s evolution time in the lattice. A detailed study of decoherence sources during the Bloch phase is also presented. While still limited in sensitivity by lattice lifetime and beam inhomogeneity this result opens the way to high contrast trapped interferometers with extended interrogation time., Comment: 9 pages, 8 figures, Accepted for publication in Phys. Rev. A

Do the laws of quantum physics still hold for macroscopic objects - this is at the heart of Schr\"odinger's cat paradox - or do gravitation or yet unknown effects set a limit for massive particles? What is the fundamental relation between quantum physics and gravity? Ground-based experiments addressing these questions may soon face limitations due to limited free-fall times and the quality of vacuum and microgravity. The proposed mission MAQRO may overcome these limitations and allow addressing those fundamental questions. MAQRO harnesses recent developments in quantum optomechanics, high-mass matter-wave interferometry as well as state-of-the-art space technology to push macroscopic quantum experiments towards their ultimate performance limits and to open new horizons for applying quantum technology in space. The main scientific goal of MAQRO is to probe the vastly unexplored "quantum-classical" transition for increasingly massive objects, testing the predictions of quantum theory for truly macroscopic objects in a size and mass regime unachievable in ground-based experiments. The hardware for the mission will largely be based on available space technology. Here, we present the MAQRO proposal submitted in response to the (M4) Cosmic Vision call of the European Space Agency for a medium-size mission opportunity with a possible launch in 2025., Comment: 38 pages, 10 tables, 23 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., Comment: 30 pages, 23 figures, accepted for publication in Experimental Astronomy

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