This summary of the second Terrestrial Very-Long-Baseline Atom Interferometry (TVLBAI) Workshop provides a comprehensive overview of our meeting held in London in April 2024 (Second Terrestrial Very-Long-Baseline Atom Interferometry Workshop, Imperial College, April 2024), building on the initial discussions during the inaugural workshop held at CERN in March 2023 (First Terrestrial Very-Long-Baseline Atom Interferometry Workshop, CERN, March 2023). Like the summary of the first workshop (Abend et al. in AVS Quantum Sci. 6:024701, 2024), this document records a critical milestone for the international atom interferometry community. It documents our concerted efforts to evaluate progress, address emerging challenges, and refine strategic directions for future large-scale atom interferometry projects. Our commitment to collaboration is manifested by the integration of diverse expertise and the coordination of international resources, all aimed at advancing the frontiers of atom interferometry physics and technology, as set out in a Memorandum of Understanding signed by over 50 institutions (Memorandum of Understanding for the Terrestrial Very Long Baseline Atom Interferometer Study).

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.

Quantum-optical experiments situated in a gravitationally bound experimental setup are fundamentally limited in numerous ways, such as the gravitational sag experienced by the trapped atoms or the limited free-evolution times of an atomic interferometer.These constraints can be overcome by deploying the experiment in a microgravity platform, such as the International Space Station (ISS).The Bose-Einstein Condensate and Cold Atom Laboratory (BECCAL), a collaboration between NASA and DLR and successor to NASA's CAL mission, aims to achieve just that.Planned as a multi-user experimental facility, it will enable numerous quantum-optical experiments with ultracold atomic clouds of different isotopes of rubidium and potassium in the microgravity environment of the ISS.The optical capabilities of this experiment will be manifold: Atoms can be cooled and trapped using a 2D-and 3D-magneto optical trap (MOT).They can then be loaded into a red-detuned crossed optical dipole trap.Using blue-detuned light, arbitrary painted optical potentials can be applied.Atom interferometry along two separate interferometry axes is also possible.Fluorescence and absorption detection are available for imaging of the atomic ensemble.In this paper, we present a compact and robust optical distribution system which is required to enable this functionality.To this end, we use a combination of fiber-to-fiber coupled optical benches, and fiber-based components.This distribution system needs to withstand the vibrational loads during launch to the ISS, and needs to retain a good fiber-to-fiber coupling efficiency under varying environmental conditions, such as temperature fluctuations, without maintenance, through the multi-year mission time.We have designed a total of ten optical benches, eight for light distribution and two as spectroscopic units.The optical benches make use of our micro-optical bench toolkit based on the glass-ceramic Zerodur, which has mechanical properties akin to aluminium and a negligible coefficient of thermal expansion.The toolkit has been

We report on the design and the construction of a sounding rocket payload capable of performing atom interferometry with Bose-Einstein condensates of 41K and 87Rb. The apparatus is designed to be launched in two consecutive missions with a VSB-30 sounding rocket and is qualified to withstand the expected vibrational loads of 1.8 g root-mean-square in a frequency range between 20-2000 Hz and the expected static loads during ascent and re-entry of 25 g. We present a modular design of the scientific payload comprising a physics package, a laser system, an electronics system and a battery module. A dedicated on-board software provides a largely automated process of predefined experiments. To operate the payload safely in laboratory and flight mode, a thermal control system and ground support equipment has been implemented and will be presented. The payload presented here represents a cornerstone for future applications of matter wave interferometry with ultracold atoms on satellites.

Bose-Einstein condensates (BECs) in free fall constitute a promising source for space-borne interferometry. Indeed, BECs enjoy a slowly expanding wave function, display a large spatial coherence and can be engineered and probed by optical techniques. Here we explore matter-wave fringes of multiple spinor components of a BEC released in free fall employing light-pulses to drive Bragg processes and induce phase imprinting on a sounding rocket. The prevailing microgravity played a crucial role in the observation of these interferences which not only reveal the spatial coherence of the condensates but also allow us to measure differential forces. Our work marks the beginning of matter-wave interferometry in space with future applications in fundamental physics, navigation and earth observation.

In contrast to light, matter-wave optics of quantum gases deals with interactions even in free space and for ensembles comprising millions of atoms. We exploit these interactions in a quantum degenerate gas as an adjustable lens for coherent atom optics. By combining an interaction-driven quadrupole-mode excitation of a Bose-Einstein condensate (BEC) with a magnetic lens, we form a time-domain matter-wave lens system. The focus is tuned by the strength of the lensing potential and the oscillatory phase of the quadrupole mode. By placing the focus at infinity, we lower the total internal kinetic energy of a BEC comprising 101(37) thousand atoms in three dimensions to 3/2 k_{B}·38_{-7}^{+6}  pK. Our method paves the way for free-fall experiments lasting ten or more seconds as envisioned for tests of fundamental physics and high-precision BEC interferometry, as well as opens up a new kinetic energy regime.

Microgravity eases several constraints limiting experiments with ultracold and condensed atoms on ground. It enables extended times of flight without suspension and eliminates the gravitational sag for trapped atoms. These advantages motivated numerous initiatives to adapt and operate experimental setups on microgravity platforms. We describe the design of the payload, motivations for design choices, and capabilities of the Bose-Einstein Condensate and Cold Atom Laboratory (BECCAL), a NASA-DLR collaboration. BECCAL builds on the heritage of previous devices operated in microgravity, features rubidium and potassium, multiple options for magnetic and optical trapping, different methods for coherent manipulation, and will offer new perspectives for experiments on quantum optics, atom optics, and atom interferometry in the unique microgravity environment on board the International Space Station.

Fiber-coupled optical benches are an integral part of many laser systems. The base of such an optical bench is usually a slab of solid material, onto which optical components are fixed. In many environments, the ability to retain high fiber coupling efficiency under mechanical loads is essential. In this article, we study the fiber-to-fiber coupling efficiency under the application of static mechanical loads experimentally and theoretically: We constructed a simple three-point bending setup to interferometrically measure the deformation of an optical bench under load. Using the same setup, we further recorded the resulting coupling efficiency variations. The examined optical benches are based on Zerodur optical benches used in sounding rockets and International Space Station missions. We also developed an analytical model that incorporates an Euler-Bernoulli beam deformation model and a simple model for calculating the coupling efficiency, to which the experimentally obtained data are compared. Furthermore, we use a finite element method simulation to compare to the recorded deformation data. Recorded data, the analytical model, and simulations show good agreement. We also show how the presented analytical model can easily be expanded to contain more complex beam paths and, thus, be used to estimate coupling losses for experimentally relevant optical benches under load.

We present an optical element for the separation of superimposed beams that only differ in angle. The beams are angularly resolved and separated by total internal reflection at an air gap between two prisms. As a showcase application, we demonstrate the separation of superimposed beams of different diffraction orders directly behind acousto-optic modulators for an operating wavelength of 800 nm. The wavelength as well as the component size can easily be adapted to meet the requirements of a wide variety of applications. The presented optical element allows one to reduce the lengths of beam paths and thus to decrease laser system size and complexity.

Numerous quantum technologies make use of a microgravity environment e.g. in space. Operating in this extreme environment makes high demands on the experiment and especially the laser system regarding miniaturization and power consumption as well as mechanical and thermal stability. In our systems, optical modules consisting of ZERODUR based optical benches with free-space optics are combined with fiber components. Suitability of the technology has been demonstrated in the successful sounding rocket missions FOKUS, KALEXUS and MAIUS-1. Here, we report on our toolkit for stable optical benches including mounts, fixed and adjustable mirrors as well as polarization maintaining fiber collimators and couplers made from ZERODUR. As an example, we present the optical modules for the scientific rocket payload of MAIUS-2, a quantum gas experiment performing dual-species atom interferometry with Bose-Einstein condensates. The modules are used on the one hand to stabilize the laser frequencies and on the other hand to distribute, overlap and switch the laser beams. This includes the overlap and joint fiber coupling of beams at 767nm and 780nm in the same polarization state to cool and manipulate atoms of both species simultaneously. Future projects include the development of a platform for experiments with cold atoms onboard the International Space Station. The laser system again involves ZERODUR based optical benches in conjunction with fiber optical components. The experiment is planned as multi-user facility and currently in the design phase. The next step is to build the training, test and flight hardware.

Owing to the low-gravity conditions in space, space-borne laboratories enable experiments with extended free-fall times. Because Bose-Einstein condensates have an extremely low expansion energy, space-borne atom interferometers based on Bose-Einstein condensation have the potential to have much greater sensitivity to inertial forces than do similar ground-based interferometers. On 23 January 2017, as part of the sounding-rocket mission MAIUS-1, we created Bose-Einstein condensates in space and conducted 110 experiments central to matter-wave interferometry, including laser cooling and trapping of atoms in the presence of the large accelerations experienced during launch. Here we report on experiments conducted during the six minutes of in-space flight in which we studied the phase transition from a thermal ensemble to a Bose-Einstein condensate and the collective dynamics of the resulting condensate. Our results provide insights into conducting cold-atom experiments in space, such as precision interferometry, and pave the way to miniaturizing cold-atom and photon-based quantum information concepts for satellite-based implementation. In addition, space-borne Bose-Einstein condensation opens up the possibility of quantum gas experiments in low-gravity conditions1,2.

A number of cold atom experiments are restrained by the impeding effects of gravity. While efforts have been made to overcome these limitations in a gravitational environment, another approach is placing the experiment in a microgravity environment, as can be found aboard sounding rockets, satellites or a space station. The cornerstone of such experiments is a robust laser system. The adverse conditions during a rocket launch impose stringent requirements on thermal stability and resilience against mechanical stress on this part of the experimental setup. Furthermore, the very limited space found on any of the aforementioned microgravity platforms necessitates maximal miniaturization. In order to meet these requirements, we have developed a technology based on miniaturized free-space optics, mounted onto optical benches made from Zerodur, a glass-ceramic which exhibits a vanishing first order coefficient of thermal expansion. The technology has already been successfully implemented in the sounding rocket missions FOKUS, KALEXUS and MAIUS-1. It will also be used in the upcoming MAIUS-2/3 sounding rocket missions. To meet the even more restrictive size and mass constraints of the NASA-DLR Bose-Einstein Condensate and Cold Atom Laboratory (BECCAL) mission, a quantum optics multi-user facility aboard the International Space Station, we are currently investigating a new and improved design concept. While being motivated by these missions, our technology can be expanded to any other experimental field where a small and robust laser system is needed.

We present a technique for simultaneous laser frequency stabilization on transitions of multiple atomic species with a single optical setup. The method is based on modulation transfer spectroscopy, and the signals are separated by modulating at different frequencies and electronically filtered. As a proof of concept, we demonstrate simultaneous spectroscopy of the potassium D1, D2 and rubidium D2 transitions. The technique can be extended in principle to other atomic species given the availability of optics and cells and allows the development of versatile and compact frequency reference modules.

We have developed, assembled, and flight-proven a stable, compact, and autonomous extended-cavity diode laser (ECDL) system designed for atomic physics experiments in space. To that end, two microintegrated ECDLs at 766.7 nm were frequency stabilized during a sounding rocket flight by means of frequency modulation spectroscopy of 39K and offset locking techniques based on the beat note of the two ECDLs. The frequency stabilization as well as additional hardware and software to test hot redundancy mechanisms were implemented as part of a state machine, which controlled the experiment completely autonomously throughout the entire flight mission. (C) 2017 Optical Society of America

We report on a micro-integrated high power diode laser based system for the MAIUS II/III missions. The laser system features fiber coupled and frequency stabilized external cavity diode lasers (ECDL) for laser cooling, Bose-Einstein condensate (BEC) generation and dual species atom interferometry with rubidium and potassium on board a sounding rocket.

We employ light-induced double Bragg diffraction of delta-kick collimated Bose-Einstein condensates to create three symmetric Mach-Zehnder interferometers. They rely on (i) first-order, (ii) two successive first-order, and (iii) second-order processes which demonstrate the scalability of the corresponding momentum transfer. With respect to devices based on conventional Bragg scattering, these symmetric interferometers double the scale factor and feature a better suppression of noise and systematic uncertainties intrinsic to the diffraction process. Moreover, we utilize these interferometers as tiltmeters for monitoring their inclination with respect to gravity.

We present a diode laser system optimized for laser cooling and atom interferometry with ultra-cold rubidium atoms aboard sounding rockets as an important milestone toward space-borne quantum sensors. Design, assembly and qualification of the system, combing micro-integrated distributed feedback (DFB) diode laser modules and free space optical bench technology, is presented in the context of the MAIUS (Matter-wave Interferometry in Microgravity) mission. This laser system, with a volume of 21 l and total mass of 27 kg, passed all qualification tests for operation on sounding rockets and is currently used in the integrated MAIUS flight system producing Bose–Einstein condensates and performing atom interferometry based on Bragg diffraction. The MAIUS payload is being prepared for launch in fall 2016. We further report on a reference laser system, comprising a rubidium stabilized DFB laser, which was operated successfully on the TEXUS 51 mission in April 2015. The system demonstrated a high level of technological maturity by remaining frequency stabilized throughout the mission including the rocket’s boost phase.