Year: 2025
Abstract: This work is a theoretical investigation of atom interferometers in complex gravitational fields. The underlying gravitational models include non-trivial corrections in the gravitational potential within the framework of classical Newtonian mechanics, which go beyond the assumption of an idealised or even completely homogeneous gravitational field. On the other hand, the theory of general relativity is used to enable a post-Newtonian description, particularly in the area of weak gravitational fields. This approach makes it possible to systematically investigate the main effects of spacetime curvature. The quantum optical systems discussed in this work are atom interferometers, highly accurate experiments that cause cold atoms or Bose-Einstein condensates to interfere. This description offers a potential approach to testing the boundaries of modern physics and explores regions where quantum gravity may emerge, distinct from the realm of high-energy physics.
We start with an introduction to the theory of (general) relativity and the theory of atomic interferometers in idealised Newtonian gravitational fields. In order to gradually extend the gravitational model and integrate additional effects such as spacetime curvature, we introduce a more compact and versatile notation. This allows us to systematically take into account the additional complexity due to relativistic effects. With this new notation, we present the current state of research in this field, enabling us to directly build upon it and seamlessly incorporate our own developments. Furthermore, we present a new interferometer geometry that is particularly well suited for the detection of gravitational curvature. We perform a detailed analysis to investigate how such an interferometer behaves in idealised gravitational fields and compare this with a numerical simulation of the same interferometer at the VLBAI facility in Hannover, which is the newest large scale atom interferometer experiment in Hannover. We use this example because this experiment provides us with a precise model of the gravitational field.
The corrections caused by non-trivial gravitational fields and the theory of relativity occur at many levels in the theoretical description. This means that the final results quickly become unwieldy, especially in the case of more complex interferometer geometries. To reduce the risk of overlooking terms and effects, an essential part of this work was to develop a computer algorithm that automates the calculation of this algebra. This enables us to reliably model results even for very complex experiments in a short time. The combination of a computer algorithm that provides us with algebraic results and a numerical model for an explicitly measured gravitational field enables us to compare theory and experiment in great detail. In addition, we can derive new results for future experiments in the VLBAI Hannover and in other atom interferometers worldwide.

Authors: Michael Werner, Ali Lezeik, Dennis Schlippert, Ernst Rasel, Naceur Gaaloul, Klemens Hammerer
Year: 2024
Journal: Accepted in Communication Physics
Abstract: Light pulse atom interferometers (AIFs) are exquisite quantum probes of spatial inhomogeneity and gravitational curvature. Moreover, detailed measurement and calibration are necessary prerequisites for very-long-baseline atom interferometry (VLBAI). Here we present a method in which the differential signal of two co-located interferometers singles out a phase shift proportional to the curvature of the gravitational potential. The scale factor depends only on well controlled quantities, namely the photon wave number, the interferometer time and the atomic recoil, which allows the curvature to be accurately inferred from a measured phase. As a case study, we numerically simulate such a co-located gradiometric interferometer in the context of the Hannover VLBAI facility and prove the robustness of the phase shift in gravitational fields with complex spatial dependence. We define an estimator of the gravitational curvature for non-trivial gravitational fields and calculate the trade-off between signal strength and estimation accuracy with regard to spatial resolution. As a perspective, we discuss the case of a time-dependent gravitational field and corresponding measurement strategies.

Authors: Michael Werner, Philip K. Schwartz, Jan-Niclas Kirsten-Siemß, Naceur Gaaloul, Domenico Giulini, Klemens Hammerer
Year: 2024
Journal: Physical Review D
Abstract: We present a systematic approach to determine all relativistic phases up to c^-2 in light-pulse atom interferometers in weakly curved spacetime that are based on elastic scattering — namely, Bragg diffraction and Bloch oscillations. Our analysis is derived from first principles using the parametrized post-Newtonian formalism. In the treatment developed here, we derive algebraic expressions for relativistic phases for arbitrary interferometer geometries in an automated manner. As case studies, we consider symmetric and antisymmetric Ramsey-Bordé interferometers, as well as a symmetric double diffraction interferometer with baseline lengths of 10 m and 100 m. We compare our results to previous calculations conducted for a Mach-Zehnder interferometer.

Authors: Abdalla et al.
Year: 2025
Journal: EPJ Quantum Technology
Abstract: 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).

Authors: Sven Abend et al.
Year: 2024
Journal: AVS quantum science
Abstract: 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 kilometer–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.

Authors: Michael Werner, Klemens Hammerer
Year: 2024
Link to the DOI Repo: https://doi.org/10.25835/7d8kyoz3
Link to the GitLab Repo: https://gitlab.uni-hannover.de/michael.werner/vlbai-phase-shift-analysis/

Authors: Michael Werner, Klemens Hammerer
Year: 2023
Link to the DOI Repo: https://doi.org/10.25835/jnh3eryx
Link to the GitLab Repo: https://gitlab.uni-hannover.de/michael.werner/atom-interferometers-in-weakly-curved-spacetimes-using-bragg-diffraction-and-bloch-oscillations.git

Talk Title: “Systematic analysis of atom interferometric measurements in complex gravitational environments”

Co-Organizing the local event. See https://indico.cern.ch/event/1522217/.

Poster: “Atom interferometric sensing over large baselines”.

Talk Title: “Systematic analysis of atom interferometric measurements in complex gravitational environments”.

Talk Title: “Local Measurement Scheme of Gravitational Curvature using Atom Interferometers”.

Talk Title: “Systematic analysis of atom interferometric measurements in complex gravitational environments”.

Title: “Atom interferometric sensing over large baselines”

Poster Title: “Tidal Phase-Shifts in Atom Interferometry:
Case Study of the VLBAI Hannover”

Poster Title: “Local Measurement of Gravitational Curvature using Atom
Interferometers”

Poster Title: “Atom Interferometry: Tidal Phase-Shifts in the VLBAI and Gravitational Modeling”

Poster Title: “Phase-shifts Of Atom Interferometers in Weakly Curved Spacetime Using Elastic Scattering”

Poster Title: “Phase-shifts Of Atom Interferometers in Weakly Curved Spacetimes Using Elastic Scattering”

Participant.

Title: “Atom interferometers in weakly curved spacetimes using elastic scattering”

Poster Title: “Phase-shifts Of Atom Interferometers in Weakly Curved Spacetimes Using Elastic Scattering”

Poster Title: “Systematic description of matter wave interferometers using elastic scattering in weakly curved space-times”

Poster Title: “Systematic Approach To Phase-shifts Of Matter Wave Interferometers in Weakly Curved Spacetimes Using Elastic Scattering”

Online due to reasons. Poster: “Systematic Approach To Phase-shifts Of Matter Wave Interferometers in Weakly Curved Spacetimes”.

Online due to reasons. Poster: “Phase shifts of arbitrary matter wave interferometers in a PPN spacetime”.