The renewed interest in lunar exploration and the development of future lunar communication and navigation services highlight the need for a precise, stable, and interoperable geodetic and timing infrastructure on the Moon. NovaMoon, proposed as a scientific and navigation payload for ESA's Argonaut lander, is designed as a lunar-based local differential, geodetic, and timing station supporting both operational needs in the Moon's south polar region and a broad range of scientific investigations. The payload integrates a lunar laser retroreflector, a Very Long Baseline Interferometry transmitter, a receiver for navigation signals compatible with LunaNet standards, high-stability atomic clocks, and direct-to-Earth radio links – making it the first lunar station to co-locate multiple ranging, tracking, and timing techniques. NovaMoon will enable sub-metre to decimetre positioning, provide local differential corrections for lunar users, and ensure an accurate and stable realisation of position and time. Preliminary simulation studies show that this multi-technique dataset improves the lunar reference frame, orientation and ephemerides, and estimates of interior parameters like tidal response and core properties. NovaMoon will also provide the first long-duration physical realisation of a lunar time reference. Beyond its primary goals, it supports improved cartography, precise surface geolocation, and higher-resolution topography, contributing to safer landings and operations. It also enables new tests of fundamental physics, including constraints on relativity and possible deviations from classical gravity.

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.

Atomic Clock Ensemble in Space (ACES) is a mission in fundamental physics that will operate a new generation of atomic clocks in the microgravity environment of the International Space Station. Fractional frequency stability and accuracy of a few parts in 10 16 will be achieved. The on-board time base, distributed on the Earth via a microwave link, will be used to perform space-to-ground as well as ground-to-ground comparisons of atomic frequency standards. Based on these comparisons, ACES will perform fundamental physics tests (Einstein's theories of special and general relativity, the search for drift of fundamental constants, the Standard Model extension and tests of string theories) and develop applications in time and frequency metrology, time scales, geodesy, global positioning and navigation. After an overview of the mission concept and its scientific objectives, the present status of ACES instruments and subsystems will be discussed.

We present the Space active H-Maser (SHM) qualification status for ACES based on the latest results of the SHM Proto Fight Model (PFM) test campaign performed after the refurbishment. They include the environmental tests (vibration, thermal vacuum cycle, EMC) for the verification of proper workmanship and the validation of the refurbishment, the full performance test under thermal vacuum, as well as the final SHM tuning performed after integration in the ACES payload to optimize SHM performances. The characterization of frequency sensitivities to the environment (e.g. temperature, magnetic field, voltage) and frequency stability is reported as well.

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.

A new era of lunar exploration has begun bringing immense opportunities for science as well. It has been proposed to deploy a new generation of observatories on the lunar surface for deep studies of our Universe. This includes radio antennas, which would be protected on the far side of the Moon from terrestrial radio interference, and gravitational-wave (GW) detectors, which would profit from the extremely low level of seismic disturbances on the Moon. In recent years, novel concepts have been proposed for lunar GW detectors based on long-baseline laser interferometry or on compact sensors measuring the lunar surface vibrations caused by GWs. In this article, we review the concepts and science opportunities for such instruments on the Moon. In addition to promising breakthrough discoveries in astrophysics and cosmology, lunar GW detectors would also be formidable probes of the lunar internal structure and improve our understanding of the lunar geophysical environment.

We summarise 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 the European Space Agency (ESA) and national space and research funding agencies.

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.

The space segment of the Global Navigation Satellite System (GNSS) is equipped with highly stable atomic clocks. In order to use these clocks as references, their time offsets must be estimated from ground measurements as accurately as possible. This work presents a multi-frequency and multi-constellation method for estimating satellite and receiver clock corrections, starting from unambiguous, uncombined, and undifferenced carrier-phase measurements. A byproduct of the estimation process is phase biases (i.e., the hardware delays of the carrier-phase measurements occurring at receivers and satellites). The stability and predictability of our clock estimates for receivers and satellites (GPS and Galileo) are compared with those obtained by the International GNSS Service (IGS), whereas the phase biases are assessed against two independent determinations involving combinations of carrier-phase measurements. We conclude that the method reduces day boundary discontinuities in the clock corrections, and that the estimated phase biases reproduce variabilities already observed by other authors.

Global navigation satellite system (GNSS) satellites are equipped with very stable atomic clocks that can be used for assessing the models and strategies involved in the estimation processes, where the clock estimates should present high stability. For instance, GNSS products (including satellite and receiver clocks) are computed on daily basis, i.e., with the data of each day being processed independently from other days. This choice produces the well-known day-boundary discontinuities (DBDs) on clock estimates that stem from the estimation process, rather than to the nature of the atomic clock itself. The aim of the present contribution is to propose a strategy to estimate the satellite and receiver clock offsets that is capable to reduce the DBDs observed in the products of different analysis centers (ACs) within the International GNSS Service (IGS), ultimately improving the accuracy of clock estimates. Our approach relies on the use of unambiguous, undifferenced and uncombined carrier phase measurements collected by a network of permanent receivers on ground. The strategy considers the carrier phase hardware delays and assumes their possible variations along time. Our daily data processing aims to maintaining the natural continuity over days of the carrier phase measurements after integer ambiguity resolution (IAR), even if IAR is performed on daily batches. We compare our clock estimations with those computed by different IGS ACs, evaluating the linear behavior of the satellite atomic clocks on the day change. The results show the removal of DBD on clock estimates computed with the continuous and unambiguous carrier phase measurements. This DBD improvement may benefit the statistical characterization of long-term phenomena correlated with the on-board clocks.

It is shown that even in the case of a negligibly small change in the gradient of the gravitational field of the mass source in the axial direction, the dependence of this gradient in the radial direction leads to a systematic error in Newton gravitational constant value. The magnitude of this error is calculated for two configurations of the field. For both configurations it was found that this error is larger than the inaccuracy predicted in the article by Jain et al. (Eur Phys J D 75:197, 2021). In addition, we found the geometry of the source mass, for which this systematic error disappears.

Atomic Clock Ensemble in Space (ACES) is a mission designed to test Einstein’s theory of General Relativity from the International Space Station (ISS). A primary frequency standard based on laser cooled caesium atoms (PHARAO) and an active H-maser (SHM) generate a clock signal that is distributed to a network of clocks on the ground to perform space-to-ground comparison. With a fractional frequency stability of 1 × 10−16 after 10 days of integration time and an accuracy of 1 – 2 × 10−16, ACES will provide an absolute measurement of the gravitational redshift, it will search for time variations of fundamental constant, and perform Standard Model Extension (SME) tests. The ACES payload is currently completing its qualification tests before flying. The mission status, the latest test results, and the ACES performance for testing General Relativity are discussed.

Time synchronization is one of the main applications of Global Navigation Satellite System (GNSS). Indeed, GNSS satellites are equipped with highly stable atomic clocks, which can be used as clock references. In particular, Galileo constellation satellites are equipped with Rubidium and Hydrogen-maser frequency standards that have a long-term (1-day) stability at the level of 10(-14) for intervals of 10(4) s. However, in order to use these clocks as references, their time offsets must be estimated from measurements collected on ground. In this sense, the effectiveness of these references depends on the accuracy and stability of such estimates. For that reason, the International GNSS Service (IGS) is providing satellite solutions with a nominal accuracy of 75 ps (i.e. better than 3 cm). The clock accuracy is assessed by evaluating the discontinuities over consecutive days, computed independently. These discontinuities appear because of the correlations between the different parameters, which are estimated jointly with the satellite clocks (e.g. receiver clocks or carrier phase ambiguities). Therefore, satellite clocks depend on the robustness of the different models used in the estimation process. For the Galileo satellites, the inter-day discontinuities are at the level of 0.5 ns. These large jumps are due to the minor number of Galileo satellites available than in GPS, which results in a reduced number of fixed carrier phase ambiguities (other solutions from other IGS analysis centers present similar features). In this work we present a refinement of the method for estimating satellite and receiver clocks, which is able to reduce these discontinuities and, consequently, to improve the accuracy of the satellite clock estimations (according to the above-mentioned IGS metric applied). Some of the main characteristics of this new approach are 1) the use of unambiguous carrier phases, 2) processing several constellations and several frequencies and 3) considering the temperature dependency of the phase biases.

General Relativity is today the best theory of gravity addressing a wide range of phenomena. Our understanding of physical laws, from cosmology to local scales, cannot be properly formulated without taking into account it. It is based on one of the most fundamental principles of Nature, the Equivalence Principle, which represents the core of the Einstein theory of gravity. The confirmation of its validity at different scales and in different contexts represents one of the main challenges of modern physics both from the theoretical and the experimental points of view. A major issue related to this principle is the fact that we actually do not know if it is valid at quantum level. Furthermore, recent progress on relativistic theories of gravity have to take into account new issues like Dark Matter and Dark Energy, as well as the validity of fundamental principles like local Lorentz and position invariance. Experiments allow to set stringent constraints on well established symmetry laws, on the physics beyond the Standard Model of particles and interactions, and on General Relativity and its possible extensions. In this review, we discuss precision tests of gravity in General Relativity and alternative theories and their relation with the Equivalence Principle. In the first part, we discuss the Einstein Equivalence Principle according to its weak and strong formulation. We recall some basic topics of General Relativity and the necessity of its extension. Some models of modified gravity are presented in some details. The second part of the paper is devoted to the experimental tests of the Equivalence Principle in its weak formulation. We present the results and methods used in high-precision experiments, and discuss the potential and prospects for future experimental tests.

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.

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. In this paper we perform atom interferometry measurements of the gravitational acceleration with high resolution without any need for a vibration isolation system or post-corrections based on seismometer data monitoring the residual accelerations at the sensor head. Using two different schemes, a Ramsey and a Ramsey–Bordé interferometer, 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 2.7 × 10−6 at 1 s of integration time, more than one order of magnitude better than a standard Mach–Zehnder interferometer when operated without any vibration isolation or applied post-correction.

In this article, we illustrate a series of experiments performed in our group in the field of atom interferometry for precision gravity measurements. We show that instruments measuring and testing gravity can be built both with rubidium and with strontium atoms, while keeping the sources of systematic error under control. The application of these devices in the test of the Weak Equivalence Principle with quantum objects, in the measurement of the Newtonian gravitational constant G and in the development of a new type atom interferometer for the detection of gravitational waves is discussed.

Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum correlations, such as entanglement, may exhibit different behavior to purely classical correlations in curved space. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph et al [5] and Ralph and Pienaar [1], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's Space QUEST (Space-Quantum Entanglement Space Test) mission, and study the feasibility of the mission scheme.