Time-delay interferometry (TDI) suppresses laser frequency noise by forming linear combinations of time-shifted interferometric measurements. The time-shift operation is implemented by interpolating discretely sampled data. To enable in-band laser noise reduction by eight to nine orders of magnitude, interpolation has to be performed with high accuracy. Interpolation can be understood as the convolution of an interpolation kernel with the data to be shifted. Optimizing the design of this interpolation kernel is the focus of this work. Previous research that studied constant time-shifts suggested Lagrange interpolation as the interpolation method for TDI. Its transfer function is maximally flat at DC and therefore performs well at low frequency. However, to be accurate at high frequencies, Lagrange interpolation requires a high number of coefficients. Furthermore, when applied in TDI we observed prominent time-domain features when a time-varying shift scanned over a pure integer sample shift. To limit this effect we identify an additional requirement for the interpolation kernel: when considering time-varying shifts the interpolation kernel must be sufficiently smooth to avoid unwanted time-domain transitions that produce glitch-like features in power spectral density estimates. The Lagrange interpolation kernel exhibits a discontinuous first derivative by construction, which is insufficient for the application to LISA or other space-based gravitational-wave observatories. As a solution we propose a novel design method for interpolation kernels that respect a predefined requirement on in-band interpolation residuals and that possess continuous derivatives up to a prescribed order. Using this method we show that an interpolation kernel with 22 coefficients is sufficient to respect LISA's picometre-requirement and to allow for a continuous first derivative which suppresses the magnitude of the time-domain transition adequately. The reduction from 42 (Lagrange interpolation) to 22 coefficients enables us to increase robustness against artifacts in the data and, as a side effect, save computational cost.

We propose a simple modification of space-based gravitational wave (GW) detector optical benches which would enable the measurement of vacuum birefringence of light induced by axion dark matter through its coupling to electromagnetism. Specifically, we propose to change a half-wave plate by a circular polarizer. While marginally affecting the sensitivity to GW by a factor 2, we show that such an adjustment would make future detectors such as LISA, TianQin, Taiji and Big-Bang Observer the most sensitive experiments at low axion masses.

Axion dark matter coupled via QCD induces a non-zero differential acceleration between test masses of different composition. Tests of the equivalence principle, like the recent MICROSCOPE space mission, are sensitive to such a signal. We use the final released data of the MICROSCOPE experiment, to search for this effect. We find no positive signal consistent with the dark matter model, and set upper limits on the axion-gluon coupling that improve existing laboratory bounds by up to two orders of magnitude for axion masses in the 10^-17 eV to 10^-13 eV range.

A scalar ultralight dark matter (ULDM) candidate would induce oscillatory motion of freely falling test masses via its coupling to Standard Model fields. Such oscillations would create an observable Doppler shift of light exchanged between the test masses, and in particular would be visible in space-based gravitational waves (GW) detectors, such as LISA. While this kind of detection has been proposed multiple times in the recent years, we numerically investigate if it is possible to extract a scalar ULDM signal in a space-based GW detector, and in particular how to differentiate such a signal from a GW signal. Using one year of realistic orbits for the LISA spacecrafts and Bayesian methods, we find that LISA will indeed be able to discriminate between the two signals.

We present the results of an optical link to a corner cube on board a tethered balloon at 300 m altitude including a Tip/Tilt compensation for the balloon tracking. Our experiment measures the carrier phase of a 1542 nm laser, which is the useful signal for frequency comparison of distant clocks. An active phase noise compensation of the carrier is implemented, demonstrating a fractional frequency stability of 8x10-19 after 16 s averaging, which slightly (factor ~3) improves on best previous links via an airborne platform. This state-of-the-art result is obtained with a transportable set-up that enables a fast field deployment.

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.

The Space Time Explorer and QUantum Equivalence principle Space Test (STE-QUEST) recently proposed, aims at performing a precision test of the weak equivalence principle (WEP), a fundamental cornerstone of General Relativity. Taking advantage of the ideal operation conditions for high-precision quantum sensing on board of a satellite, it aims to detect possible violations of WEP down to the $10^{-17}$ level. This level of performance leads to stringent environmental requirements on the control of the spacecraft. We assume an operation of a dual-species atom interferometer of rubidium and potassium isotopes in a double-diffraction configuration and derive the constraints to achieve an Eötvös parameter $η=10^{-17}$ in statistical and systematic uncertainties. We show that technical heritage of previous satellite missions, such as MICROSCOPE, satisfies the platform requirements to achieve the proposed objectives underlying the technical readiness of the STE-QUEST mission proposal.

We present a theoretical investigation of the expected experimental signals produced by freely falling atoms with time oscillating mass and transition frequency. These oscillations could be produced in a variety of models, in particular, models of scalar dark matter nonuniversally coupled to the standard matter such as axionlike particles and dilatons. Performing complete and rigorous calculations, we show that, on one hand, two different atomic species would accelerate at a different rate, and, on the other hand, they would produce a nonzero differential phase shift in atom interferometers (AI). The former would produce observable signals in equivalence principle tests like the recent MICROSCOPE mission, and we provide a corresponding sensitivity estimate, showing that MICROSCOPE can reach beyond the best existing searches in the axionlike particle case. We also compare the expected sensitivity of two future AI experiments, namely the AION-10 gradiometer and an isotope differential AI considered for MAGIS-100, that we will refer to as SPID. We show that the SPID setup would be more sensitive to these dark matter fields compared to the gradiometer one, assuming equivalent experimental parameters.

A vector dark matter candidate, also known as dark photon, would induce an oscillating electric field through kinetic mixing. One detection strategy uses a spherical reflector to focus the induced emission at its center of curvature. On one hand, we investigate the effects of diffraction in this type of experiment from an analytical standpoint, making use of the Kirchhoff integral theorem in the low-curvature dish limit. On the other hand, we estimate the impact of mode-matching, in the case of detection by a pyramidal horn antenna. We show that the expected signal intensity can be significantly reduced compared to usual estimates. Our method is applied to the re-interpretation of the SHUKET experiment data, the results of which are shown to be degraded by a factor of $\sim$~50 due to both diffraction and mode-matching. The analytical method allows optimizing some experimental parameters to gain sensitivity in future runs. Our results can be applied to any dish antenna experiment using a low curvature reflector.

The data produced by the future space-based millihertz gravitational-wave detector LISA will require nontrivial pre-processing, which might affect the science results. It is crucial to demonstrate the feasibility of such processing algorithms and assess their performance and impact on the science. We are building an end-to-end pipeline that includes state-of-the-art simulations and noise reduction algorithms. The simulations must include a detailed model of the full measurement chain, capturing the main features that affect the instrument performance and processing algorithms. In particular, we include in these simulations, for the first time, proper relativistic treatment of reference frames with realistic numerically-optimized orbits; a model for onboard clocks and clock synchronization measurements; proper modeling of total laser frequencies, including laser locking, frequency planning and Doppler shifts; and a better treatment of onboard processing. Using these simulated data, we show that our pipeline is able to reduce the most critical noises and form synchronized observables. By injecting signals from a verification binary, we demonstrate that good parameter estimation can be obtained on this more realistic setup, extending existing results from previous LISA Data Challenges.

Quantum sensors based on the interference of matter waves provide an exceptional performance to test the postulates of General Relativity by comparing the free-fall acceleration of matter waves of different composition. Space-borne quantum tests of the universality of free fall (UFF) promise to exploit the full potential of these sensors due to long free-fall times, and to reach unprecedented sensitivity beyond current limits. In this contribution, we present a simulator for satellite-based atom interferometry and demonstrate its functionality in designing the STE-QUEST mission scenario, a satellite test of the UFF with ultra-cold atoms to 10^-17 as proposed to the ESA Medium mission frame [https://arxiv.org/abs/2211.15412]. Moreover, we will highlight the possibility of this simulator to design Earth Observation missions going beyond state of the art such as the CARIOQA concept [https://arxiv.org/abs/2211.01215]. This work is supported by DLR funds from the BMWi (50WM2263A-CARIOQA-GE and 50WM2253A-(AI)^2).

We propose a novel experiment to search for dark matter, based on the application of an electric field inside a microwave cavity and electrometry using Rydberg atoms. We show that this kind of experiment could be extremely useful for detecting specific dark matter candidates, namely massive vector fields coupled to the photon field, more commonly known as dark photons. Such a massive vector field is a good candidate for dark matter. Using realistic experimental parameters we show that such an experiment could improve the current constraint on the coupling constant of the dark photons to Standard Model photons in the 1 mu eV to 10 mu eV mass range, with the possibility of tuning the maximum sensitivity via the cavity size. The main limiting factors on the sensitivity of the experiment are the amplitude stability of the applied field and the measurement uncertainty of the electric field by the atoms.

Space-borne quantum technologies, particularly those based on atom interferometry, are heralding a new era of strategic and robust space exploration. The unique conditions of space, characterized by low noise and low gravity environments, open up diverse possibilities for applications ranging from precise time and frequency transfer to Earth Observation and the search of new Physics. In this paper, we summarise the M-class mission proposal in response to the 2022 call in ESA's science program: Space-Time Explorer and Quantum Equivalence Principle Space Test (STE-QUEST). It consists in a satellite mission featuring a dual-species atom interferometer operating over extended durations. This mission aims to tackle three of the most fundamental questions in Physics: (i) testing the universality of free fall with an accuracy better than one part in 10^-17, (ii) exploring various forms of Ultra-Light Dark Matter, and (iii) scrutinizing the foundations of Quantum Mechanics.

Time-delay interferometry (TDI) is a data processing technique for LISA designed to suppress the otherwise overwhelming laser noise by several orders of magnitude. It is widely believed that TDI can only be applied once all phase or frequency measurements from each spacecraft have been synchronized to a common time frame. We demonstrate analytically, using as an example the commonly-used Michelson combination X, that TDI can be computed using the raw, unsynchronized data, thereby avoiding the need for an initial synchronization processing step and significantly simplifying the initial noise reduction pipeline. Furthermore, the raw data is free of any potential artifacts introduced by clock synchronization and reference frame transformation algorithms, which allows to operate directly on the MHz beatnotes. As a consequence, in-band clock noise is directly suppressed as part of TDI, in contrast to the approach previously proposed in the literature (in which large trends in the beatnotes are removed before the main laser-noise reduction step, and clock noise is suppressed in an extra processing step). We validate our algorithm with full-scale numerical simulations that use LISA Instrument and PyTDI and show that we reach the same performance levels as the previously proposed methods, ultimately limited by the clock sideband stability.

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.

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.

We propose a new type of experiment that compares the frequency of a clock (an ultrastable optical cavity in this case) at time t to its own frequency some time t-T earlier, by "storing" the output signal (photons) in a fiber delay line. In ultralight oscillating dark matter (DM) models, such an experiment is sensitive to coupling of DM to the standard model fields, through oscillations of the cavity and fiber lengths and of the fiber refractive index. Additionally, the sensitivity is significantly enhanced around the mechanical resonances of the cavity. We present experimental results of such an experiment and report no evidence of DM for masses in the [4.1×10^{-11}, 8.3×10^{-10}] eV region. In addition, we improve constraints on the involved coupling constants by one order of magnitude in a standard galactic DM model, at the mass corresponding to the resonant frequency of our cavity. Furthermore, in the model of relaxion DM, we improve on existing constraints over the whole DM mass range by about one order of magnitude, and up to 6 orders of magnitude at resonance.

Some models for Dark Matter (DM) suggest possible encounters with a period τ of macroscopic dark structures with the Earth, implying transient signatures on clocks onboard GNSS satellites. In this paper we first introduce the GASTON project, an original study dedicated to the search for such ‘DM transients’ using the network of passive H-Maser onboard Galileo satellites. This project is based on a 3-months measurements campaign carried out in the early 2021 where precise satellite clock measurements are supplemented by an intensive laser ranging (SLR) campaign on Galileo satellites. Then, we present preliminary results based on single satellite frequency jumps between consecutive 30s epochs over the 3 months campaign. In particular, we already bring strong constraints on the parameter space for transient DM objects from 10 5 to 10 9 km, a region which was never explored previously with GNSS clocks.

Timescale comparison between optical atomic clocks over ground-to-space and terrestrial free-space laser links will have enormous benefits for fundamental and applied sciences. However, atmospheric turbulence creates phase noise and beam wander that degrade the measurement precision. Here we report on phase-stabilized optical frequency transfer over a 265 m horizontal point-to-point free-space link between optical terminals with active tip-tilt mirrors to suppress beam wander, in a compact, human-portable set-up. A phase-stabilized 715 m underground optical fiber link between the two terminals is used to measure the performance of the free-space link. The active optical terminals enable continuous, cycle-slip free, coherent transmission over periods longer than an hour. In this work, we achieve residual instabilities of 2.7 × 10-6 rad2 Hz-1 at 1 Hz in phase, and 1.6 × 10-19 at 40 s of integration in fractional frequency; this performance surpasses the best optical atomic clocks, ensuring clock-limited frequency comparison over turbulent free-space links.

The Atomic Clock Ensemble in Space is a fundamental physics mission of the European Space Agency to be launched in August 2021. It relies on a high-performance clock onboard the International Space Station (ISS), a network of high-performance clocks on ground, a dedicated 2-way microwave link (MWL) enabling space-to-ground and ground-to-ground clock comparisons, as well as an optical link (ELT). PHARAO/SHM (Projet d’Horloge Atomique par Refroidissement d’Atomes en Orbite/Space Hydrogen Maser), the clock onboard the ISS, has a relative frequency accuracy at the $${10}^{-16}$$ level, a relative frequency stability (Allan deviation) equal to $${10}^{-13}/\sqrt{\tau }$$ ( $$\tau$$ being the integration time in seconds) and a time deviation of 12 picoseconds after one day of integration. The MWL is designed to reach a time deviation below 7 ps after one day of integration. While space-to-ground clock comparisons will enable precise tests of the gravitational redshift, tests of deviations from General Relativity at the $${10}^{-6}$$ level, and tests of local Lorentz invariance at the $${10}^{-10}$$ level, ground-to-ground clock comparisons will enable a search of the time variation of fundamental constants with uncertainty at the $${10}^{-17}$$ level after one year. In this contribution, we review the mission setup with a particular emphasis on the MWL, discuss the simulation and data analysis software developed to investigate mission performance, focusing on its primary scientific objective: the test of the gravitational redshift.