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We present a comprehensive review on the state-of-the-art of the approximate analytic approaches describing the finite-temperature thermodynamic quantities of the Lieb-Liniger model of the one-dimensional (1D) Bose gas with contact repulsive interactions. This paradigmatic model of quantum many-body-theory plays an important role in many areas of physics -- thanks to its integrability and possible experimental realization using, e.g., ensembles of ultracold bosonic atoms confined to quasi-1D geometries. The thermodynamics of the uniform Lieb-Liniger gas can be obtained numerically using the exact thermal Bethe ansatz (TBA) method, first derived in 1969 by Yang and Yang. However, the TBA numerical calculations do not allow for the in-depth understanding of the underlying physical mechanisms that govern the thermodynamic behavior of the Lieb-Liniger gas at finite temperature. Our work is then motivated by the insights that emerge naturally from the transparency of closed-form analytic results, which are derived here in six different regimes of the gas and which exhibit an excellent agreement with the TBA numerics. Our findings can be further adopted for characterising the equilibrium properties of inhomogeneous (e.g., harmonically trapped) 1D Bose gases within the local density approximation and for the development of improved hydrodynamic theories, allowing for the calculation of breathing mode frequencies which depend on the underlying thermodynamic equation of state. Our analytic approaches can be applied to other systems including impurities in a quantum bath, liquid helium-4, and ultracold Bose gas mixtures., Comment: 55 pages, 9 figures; minor revisions in v2 in response to referee's comments

Positronium (Ps) has emerged as a promising test particle within the QUPLAS collaboration for investigating the gravitational effect. In this work, we present a novel approach to generate a monoenergetic and highly coherent Ps beam by creating a negative Ps ion (Ps$^-$, consisting of two electrons and one positron). The necessary positron beam is formed by using a high flux electron LINAC. Subsequently, we utilize a Fabry-Perot IR laser cavity operating at a wavelength of 1560 nm to selectively remove the extra electron. An alternative pulsed laser operating at a 3600 nm wavelength was studied to reduce broadening due to recoil and excitation. Here, we provide a Monte Carlo simulation to estimate the characteristics of the Ps beam, including its energy distribution and intensity profiles. The results obtained from this study will provide essential groundwork for future advancements in fundamental studies as Ps gravity measurements by using a Mach-Zehnder interferometer., Comment: 16 pages, 4 figures

This paper reports the study of a new interferometric configuration to measure the effect of gravity on positronium. A Mach-Zehnder matter-wave interferometer has been designed to operate with single-photon transitions and to transfer high momentum to a 200 eV positronium beam. The work shows the results and methods used to simulate the interferometer and estimate the operating parameters and the time needed to perform the experiment. It has been estimated that within less than one year, the acquisition time is sufficient to achieve a 10\% accuracy level in measuring positronium gravitational acceleration, even with a poorly collimated beam, which is significant for theoretical models describing matter-antimatter symmetry. These results pave the way for single photon transition large momentum transfer interferometry with fast atomic beams, which is particularly useful for studies with antimatter and unstable atoms., Comment: 24 pages, 11 figures

We demonstrate a novel scheme for Raman-pulse and Bragg-pulse atom interferometry based on the $5\mathrm{S} - 6\mathrm{P}$ blue transitions of $^{87}$Rb that provides an increase by a factor $\sim 2$ of the interferometer phase due to accelerations with respect to the commonly used infrared transition at 780 nm. A narrow-linewidth laser system generating more than 1 W of light in the 420-422 nm range was developed for this purpose. Used as a cold-atom gravity gradiometer, our Raman interferometer attains a stability to differential acceleration measurements of $1\times10^{-8}$ $g$ at 1 s and $2\times 10^{-10}$ $g$ after 2000 s of integration time. When operated on first-order Bragg transitions, the interferometer shows a stability of $6\times10^{-8}$ g at 1 s, averaging to $1\times10^{-9}$ g after 2000 s of integration time. The instrument sensitivity, currently limited by the noise due to spontaneous emission, can be further improved by increasing the laser power and the detuning from the atomic resonance. The present scheme is attractive for high-precision experiments as, in particular, for the determination of the Newtonian gravitational constant.

We propose a new scheme for an improved determination of the Newtonian gravitational constant G and evaluate it by numerical simulations. Cold atoms in free fall are probed by atom interferometry measurements to characterize the gravitational field generated by external source masses. Two source mass configurations having different geometry and using different materials are compared to identify an optimized experimental setup for the G measurement. The effects of the magnetic fields used to manipulate the atoms and to control the interferometer phase are also characterized.

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

One of the major limitations of atomic gravimeters is represented by the vibration noise of the measurement platform, which cannot be distinguished from the relevant acceleration signal. We demonstrate a new method to perform an atom interferometry measurement of the gravitational acceleration without any need for a vibration isolation system or post-corrections based on seismometer data monitoring the residual accelerations at the sensor head. With two subsequent Ramsey interferometers, we measure the velocity variation of freely falling cold atom samples, thus determining the gravitational acceleration experienced by them. Our instrument has a fractional stability of $ 9 \times 10^{-6}$ at 1 s of integration time, one order of magnitude better than a standard Mach-Zehnder interferometer when operated without any vibration isolation or applied post-correction. Using this technique, we measure the gravitational acceleration in our laboratory, which is found in good agreement with a previous determination obtained with a FG5 mechanical gravimeter.

The Einstein Equivalence Principle (EEP) has a central role in the understanding of gravity and space-time. In its weak form, or Weak Equivalence Principle (WEP), it directly implies equivalence between inertial and gravitational mass. Verifying this principle in a regime where the relevant properties of the test body must be described by quantum theory has profound implications. Here we report on a novel WEP test for atoms. A Bragg atom interferometer in a gravity gradiometer configuration compares the free fall of rubidium atoms prepared in two hyperfine states and in their coherent superposition. The use of the superposition state allows testing genuine quantum aspects of EEP with no classical analogue, which have remained completely unexplored so far. In addition, we measure the Eotvos ratio of atoms in two hyperfine levels with relative uncertainty in the low $10^{-9}$, improving previous results by almost two orders of magnitude., Comment: Accepted for publication in Nature Communication

In precision metrology the determination of the Newtonian gravity constant $G$ represents a real problem, since its history is plagued by huge unknown discrepancies between a large number of independent experiments. In this paper we propose a novel experimental setup for measuring $G$ with a relative accuracy of $10^{-5}$ using a standard cold atomic fountain and matter wave interferometry. We discuss in details the major sources of systematic errors, providing also the expected statistical uncertainty. Feasibility of determining $G$ at a level of $10^{-6}$ level is also discussed., Comment: Accepted for publication in Metrologia

We present the first direct measurement of the gravity-field curvature based on three conjugated atom interferometers. Three atomic clouds launched in the vertical direction are simultaneously interrogated by the same atom interferometry sequence and used to probe the gravity field at three equally spaced positions. The vertical component of the gravity-field curvature generated by nearby source masses is measured from the difference between adjacent gravity gradient values. Curvature measurements are of interest in geodesy studies and for the validation of gravitational models of the surrounding environment. The possibility of using such a scheme for a new determination of the Newtonian constant of gravity is also discussed., Comment: 5 pages, 3 figures

About 300 experiments have tried to determine the value of the Newtonian gravitational constant, G, so far, but large discrepancies in the results have made it impossible to know its value precisely. The weakness of the gravitational interaction and the impossibility of shielding the effects of gravity make it very difficult to measure G while keeping systematic effects under control. Most previous experiments performed were based on the torsion pendulum or torsion balance scheme as in the experiment by Cavendish in 1798, and in all cases macroscopic masses were used. Here we report the precise determination of G using laser-cooled atoms and quantum interferometry. We obtain the value G=6.67191(99) x 10^(-11) m^3 kg^(-1) s^(-2) with a relative uncertainty of 150 parts per million (the combined standard uncertainty is given in parentheses). Our value differs by 1.5 combined standard deviations from the current recommended value of the Committee on Data for Science and Technology. A conceptually different experiment such as ours helps to identify the systematic errors that have proved elusive in previous experiments, thus improving the confidence in the value of G. There is no definitive relationship between G and the other fundamental constants, and there is no theoretical prediction for its value, against which to test experimental results. Improving the precision with which we know G has not only a pure metrological interest, but is also important because of the key role that G has in theories of gravitation, cosmology, particle physics and astrophysics and in geophysical models., Comment: 3 figures, 1 table

In this note we show that the relaxed linear micromorphic model recently proposed by the authors can be suitably used to describe the presence of band-gaps in metamaterials with microstructures in which strong contrasts of the mechanical properties are present (e.g. phononic crystals and lattice structures). This relaxed micromorphic model only has 6 constitutive parameters instead of 18 parameters needed in Mindlin- and Eringen-type classical micromorphic models. We show that the onset of band-gaps is related to a unique constitutive parameter, the Cosserat couple modulus $\mu_{c}$ which starts to account for band-gaps when reaching a suitable threshold value. The limited number of parameters of our model, as well as the specific effect of some of them on wave propagation can be seen as an important step towards indirect measurement campaigns.

We evaluate the sensitivity of a dual cloud atom interferometer to the measurement of vertical gravity gradient. We study the influence of most relevant experimental parameters on noise and long-term drifts. Results are also applied to the case of doubly differential measurements of the gravitational signal from local source masses. We achieve a short term sensitivity of 3*10^(-9) g/Hz^(-1/2) to differential gravity acceleration, limited by the quantum projection noise of the instrument. Active control of the most critical parameters allows to reach a resolution of 5*10^(-11) g after 8000 s on the measurement of differential gravity acceleration. The long term stability is compatible with a measurement of the gravitational constant G at the level of 10^(-4) after an integration time of about 100 hours., Comment: 19 pages, 20 figures

In this paper a stationary action principle is proven to hold for capillary fluids, i.e. fluids for which the deformation energy has the form suggested, starting from molecular arguments, for instance by Cahn and Hilliard. Remark that these fluids are sometimes also called Korteweg-de Vries or Cahn-Allen. In general continua whose deformation energy depend on the second gradient of placement are called second gradient (or Piola-Toupin or Mindlin or Green-Rivlin or Germain or second gradient) continua. In the present paper, a material description for second gradient continua is formulated. A Lagrangian action is introduced in both material and spatial description and the corresponding Euler-Lagrange bulk and boundary conditions are found. These conditions are formulated in terms of an objective deformation energy volume density in two cases: when this energy is assumed to depend on either C and grad C or on C^-1 and grad C^-1 ; where C is the Cauchy-Green deformation tensor. When particularized to energies which characterize fluid materials, the capillary fluid evolution conditions (see e.g. Casal or Seppecher for an alternative deduction based on thermodynamic arguments) are recovered. A version of Bernoulli law valid for capillary fluids is found and, in the Appendix B, useful kinematic formulas for the present variational formulation are proposed. Historical comments about Gabrio Piola's contribution to continuum analytical mechanics are also presented. In this context the reader is also referred to Capecchi and Ruta., Comment: 52 pages

We here present a high sensitivity gravity-gradiometer based on atom interferometry. In our apparatus, two clouds of laser-cooled rubidium atoms are launched in fountain configuration and interrogated by a Raman interferometry sequence to probe the gradient of gravity field. We recently implemented a high-flux atomic source and a newly designed Raman lasers system in the instrument set-up. We discuss the applications towards a precise determination of the Newtonian gravitational constant G. The long-term stability of the instrument and the signal-to-noise ratio demonstrated here open interesting perspectives for pushing the measurement precision below the 100 ppm level.