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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/

We investigate the intra-waveguide statistics manipulation of broadband light by combining semiconductor quantum dot physics with quantum optics. By cooling a quantum dot superluminescent diode to liquid nitrogen temperature of $77K$, Blazek et al. [Phys. Rev. A 84, 63840 (2011)] have demonstrated a temperature-dependent reduction of the second-order intensity correlation coefficient from two for thermal amplified spontaneous emission light to $g^{(2)}(T=190 K)\approx 1.33$. Here, we model the broadband photon statistics assuming amplified spontaneous emission radiation in a pumped, saturable quantum dot gain medium. We demonstrate that, by an intensity increase due to the quantum dot occupation dynamics via the temperature-tuned quasi Fermi levels, together with the saturation nonlinearity, a statistics manipulation from thermal Bose-Einstein statistics towards Poissonian statistics can be realized, thus producing "silent white light". Such intensity-noise reduced broadband radiation is relevant for many applications like optical coherence tomography, optical communication or optical tweezers.

A physical artificial complex-valued neuron is formed by four-wave mixing in a homogeneous three-dimensional Bose-Einstein condensate. Bragg beamsplitter pulses prepare superpositions of three plane-waves states as an input- and the fourth wave as an output signal. The nonlinear dynamics of the non-degenerate four-wave mixing process leads to Josephson-like oscillations within the closed four-dimensional subspace and defines the activation function of a neuron. Due to the high number of symmetries, closed form solutions can be found by quadrature and agree with numerical simulation. The ideal behaviour of an isolated four-wave mixing setup is compared to a situation with additional population of rogue states. We observe a robust persistence of the main oscillation. As an application for neural learning of this physical system, we train it on the XOR problem. After $100$ training epochs, the neuron responds to input data correctly at the $10^{-5}$ error level.

Technical optics with matter waves requires a universal description of three-dimensional traps, lenses, and complex matter-wave fields. In analogy to the two-dimensional Zernike expansion in beam optics, we present a three-dimensional multipole expansion for Bose-condensed matter waves and optical devices. We characterize real magnetic chip traps, optical dipole traps, and the complex matter-wave field in terms of spherical harmonics and radial Stringari polynomials. We illustrate this procedure for typical harmonic model potentials as well as real magnetic and optical dipole traps. Eventually, we use the multipole expansion to characterize the aberrations of a ballistically interacting expanding Bose-Einstein condensate in (3+1)-dimensions. In particular, we find deviations from the quadratic phase ansatz in the popular scaling approximation. This universal multipole description of aberrations can be used to optimize matter-wave optics setups, for example in matter-wave interferometers.

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/

Doppler-free three-photon coherence effects at a wavelength of 253.7 nm have been observed in thermal mercury vapor. The experimental results are compared to simulations based on a detailed theoretical model reproducing the measured effects. Based on these results, we show by simulations that amplification without inversion in our setup is feasible, paving the way towards lasing without inversion in mercury., Comment: 11 pages, 12 figures

We analyze the transfer function of a three-dimensional atomic Bragg beamsplitter formed by two counterpropagating pulsed Gaussian laser beams. Even for ultracold atomic ensembles, the transfer efficiency depends significantly on the residual velocity of the particles as well as on losses into higher diffraction orders. Additional aberrations are caused by the spatial intensity variation and wavefront curvature of the Gaussian beam envelope, studied with (3+1)D numerical simulations. The temporal pulse shape also affects the transfer efficiency significantly. Thus, we consider the practically important rectangular-, Gaussian-, Blackman- and hyperbolic secant pulses. For the latter, we can describe the time-dependent response analytically with the Demkov-Kunike method. The experimentally observed stretching of the $\pi$-pulse time is explained from a renormalization of the simple Pendell\"osung frequency. Finally, we compare the analytical predictions for the velocity-dependent transfer function with effective (1+1)D numerical simulations for pulsed Gaussian beams, as well as experimental data and find very good agreement, considering a mixture of Bose-Einstein condensate and thermal cloud., Comment: 20 pages, 15 figures

We present a stochastic procedure to investigate the correlation spectra of quantum dot superluminescent diodes. The classical electric field of a diode is formed by a polychromatic superposition of many independent stochastic oscillators. Assuming fields with individual carrier frequencies, Lorentzian linewidths and amplitudes we can form any relevant experimental spectrum using a least square fit. This is illustrated for Gaussian and Lorentzian spectra, Voigt profiles and box shapes. Eventually, the procedure is applied to an experimental spectrum of a quantum dot superluminescent diode which determines the first- and second-order temporal correlation functions of the emission. We find good agreement with the experimental data and a quantized treatment. Thus, a stochastic field represents broadband light emitted by quantum dot superluminescent diodes., Comment: 10 pages, 5 figures

The velocity distribution of a hot ionic beam can be filtered with a narrow stimulated Raman process to prepare a colder subensemble, as substantiated in this theoretical analysis. Using two counter-propagating, far-detuned lasers, we can define a $\pi$-pulse for the resonant velocity to transfer atoms within the linewidth of the Raman resonance between the ground-states of a $\Lambda$-system. Spontaneous emission from the two single-photon resonances, as well as the ground-state decoherence induced by laser noise, diminishes the efficiency of the filter. From a comprehensive master equation, we obtain conditions for the optimal frequency pair of the lasers and evaluate the filter performance numerically, as well as analytically. If we apply this analysis to current $^{40}$Ca$^+$ ion experiments, we obtain a sensitivity for measuring high ion acceleration voltages on the ppm level or below., Comment: Corrected typos. Corrected: Missing minus in Eq. 35. Improved readability by including a few repetitions of quantity definitions and improved display of relevant quantities in Table II of the Appendix

We present a microscopic theory of the amplified spontaneous emission of a spectrally broadband quantum dot superluminescent diode within the quantum white noise limit. From this multimode quantum theory, we have the ability to obtain all orders of temporal correlation functions. In particular, we derive rate equations for the optical power densities, the level occupation of inhomogeneous ensemble of quantum dots within the diode, as well as the emitted optical spectra. As the main result, we find the external power spectrum as a convolution of the intra-diode photon spectrum with a Lorentzian response. Assuming a Gaussian light-matter coupling results in a similar shaped Gaussian output spectrum, which agrees very well with available experimental data.

We study optical pulse propagation through a hollow-core fiber filled with a radially inhomogeneous cloud of cold atoms. A co-propagating control field establishes electromagnetically induced transparency. In analogy to a graded index fiber, the pulse experiences micro-lensing and the transmission spectrum becomes distorted. Based on a two-layer model of the complex index of refraction, we can analytically understand the cause of the aberration, which is corroborated by numerical simulations for a radial Gaussian-shaped function. With these insights, we show that the spectral distortions can be rectified by choosing an optimal detuning from one-photon resonance., Comment: 15 pages, 8 figures, typos corrected, references added, figure style slightly modified, Comment on Faraday rotation added between Eq. (21) and (22)

Space offers virtually unlimited free-fall in gravity. Bose-Einstein condensation (BEC) enables ineffable low kinetic energies corresponding to pico- or even femtokelvins. The combination of both features makes atom interferometers with unprecedented sensitivity for inertial forces possible and opens a new era for quantum gas experiments. On January 23, 2017, we created Bose-Einstein condensates in space on the sounding rocket mission MAIUS-1 and conducted 110 experiments central to matter-wave interferometry. In particular, we have explored laser cooling and trapping in the presence of large accelerations as experienced during launch, and have studied the evolution, manipulation and interferometry employing Bragg scattering of BECs during the six-minute space flight. In this letter, we focus on the phase transition and the collective dynamics of BECs, whose impact is magnified by the extended free-fall time. Our experiments demonstrate a high reproducibility of the manipulation of BECs on the atom chip reflecting the exquisite control features and the robustness of our experiment. These properties are crucial to novel protocols for creating quantum matter with designed collective excitations at the lowest kinetic energy scales close to femtokelvins., Comment: 6 pages, 4 figures

We theoretically analyze a scheme for a fast adiabatic transfer of cold atoms from the atomic limit of isolated traps to a Mott-insulator close to the superfluid phase. This gives access to the Bose-Hubbard physics without the need of a prior Bose-Einstein condensate. The initial state can be prepared by combining the deterministic assembly of atomic arrays with resolved Raman sideband cooling. In the subsequent transfer the trap depth is reduced significantly. We derive conditions for the adiabaticity of this process and calculate optimal adiabatic ramp shapes. Using available experimental parameters, we estimate the impact of heating due to photon scattering and compute the fidelity of the transfer scheme. Finally, we discuss the particle number scaling behavior of the method for preparing low-entropy states. Our findings demonstrate the feasibility of the proposed scheme with state-of-the-art technology., Comment: Minor changes based on referee reports

We present an effective two-channel model for reactive collisions of cold atoms. It augments elastic molecular channels with an irreversible, inelastic loss channel. Scattering is studied with the distorted-wave Born approximation and yields general expressions for angular momentum resolved cross sections as well as two-body loss rates. Explicit expressions are obtained for piece-wise constant potentials. A pole expansion reveals simple universal shape functions for cross sections and two-body loss rates in agreement with the Wigner threshold laws. This is applied to collisions of metastable ${^{20}}$Ne -- ${^{21}}$Ne atoms, which decay primarily through exothermic Penning-, or Associative- ionization processes. From a numerical solution of the multichannel Schr\"odinger equation using the best currently available molecular potentials, we have obtained synthetic scattering data. Using the two-body loss shape functions derived in this paper, we can match these scattering data very well., Comment: 12 pages, 11 color figures, to be published in Phys. Rev. A in 2018

We present a novel platform for the bottom-up construction of itinerant many-body systems: ultracold atoms transferred from a Bose-Einstein condensate into freely configurable arrays of micro-lens generated focused-beam dipole traps. This complements traditional optical lattices and gives a new quality to the field of two-dimensional quantum simulators. The ultimate control of topology, well depth, atom number, and interaction strength is matched by sufficient tunneling. We characterize the required light fields, derive the Bose-Hubbard parameters for several alkali species, investigate the loading procedures and heating mechanisms. To demonstrate the potential of this approach, we analyze coupled annular Josephson contacts exhibiting many-body resonances., Comment: 8 pages, 6 figures

Quantum sensors based on matter-wave interferometry are promising candidates for high-precision gravimetry and inertial sensing in space. The favorable source for the coherent matter waves in these devices are Bose-Einstein condensates. A reliable prediction of their dynamics, which is governed by the Gross-Pitaevskii equation, requires suitable analytical and numerical methods which take into account the center-of-mass motion of the condensate, its rotation and its spatial expansion by many orders of magnitude. In this chapter, we present an efficient way to study their dynamics in time-dependent rotating traps that meet this objective. Both, an approximate analytical solution for condensates in the Thomas-Fermi regime and dedicated numerical simulations on a variable adapted grid are discussed. We contrast and relate our approach to previous alternative methods and provide further results, such as analytical expressions for the one- and two-dimensional spatial density distributions and the momentum distribution in the long-time limit that are of immediate interest to experimentalists working in this field of research., Comment: 49 pages, 7 figures, preprint submitted to Advances in Atomic, Molecular, and Optical Physics Volume 66

We investigate the feasibility of UV lasing without inversion at a wavelength of $253.7$ nm utilizing interacting dark resonances in mercury vapor. Our theoretical analysis starts with radiation damped optical Bloch equations for all relevant 13 atomic levels. These master equations are generalized by considering technical phase noise of the driving lasers. From the Doppler broadened complex susceptibility we obtain the stationary output power from semiclassical laser theory. The finite overlap of the driving Gaussian laser beams defines an ellipsoidal inhomogeneous gain distribution. Therefore, we evaluate the intra-cavity field inside a ring laser self-consistently with Fourier optics. This analysis confirms the feasibility of UV lasing and reveals its dependence on experimental parameters., Comment: changes were made according to reviewer comments (accepted for publication in JOSA B)

Atom interferometry represents a quantum leap in the technology for the ultra-precise monitoring of accelerations and rotations and, therefore, for all the science that relies on the latter quantities. These sensors evolved from a new kind of optics based on matter-waves rather than light-waves and might result in an advancement of the fundamental detection limits by several orders of magnitude. Matter-wave optics is still a young, but rapidly progressing science. The Space Atom Interferometer project (SAI), funded by the European Space Agency, in a multi-pronged approach aims to investigate both experimentally and theoretically the various aspects of placing atom interferometers in space: the equipment needs, the realistically expected performance limits and potential scientific applications in a micro-gravity environment considering all aspects of quantum, relativistic and metrological sciences. A drop-tower compatible prototype of a single-axis atom interferometry accelerometer is under construction. At the same time the team is studying new schemes, e.g. based on degenerate quantum gases as source for the interferometer. A drop-tower compatible atom interferometry acceleration sensor prototype has been designed, and the manufacturing of its subsystems has been started. A compact modular laser system for cooling and trapping rubidium atoms has been assembled. A compact Raman laser module, featuring outstandingly low phase noise, has been realized. Possible schemes to implement coherent atomic sources in the atom interferometer have been experimentally demonstrated.