Researchers Link Atom Interferometry Phase Shear to Spacetime Curvature Via Generalized Gauss-Bonnet Theorem

Atom interferometry offers a powerful means of testing the fundamental principles of general relativity, yet linking the observed phase shifts to specific geometric features of spacetime remains a complex challenge. Hunter Swan and Jason M. Hogan now demonstrate a direct connection between an alternative measurement from atom interferometers, known as phase shear, and the integrated sectional curvature of spacetime. Their work reveals that phase shear accurately reflects the curvature enclosed by the interferometer’s beams, a result stemming from a generalized Gauss-Bonnet theorem that also accounts for subtle effects of gravitational redshift. This synthesis of quantum mechanics, relativity, and differential geometry provides a uniquely clear and coordinate-independent method for measuring spacetime properties, and offers a valuable tool for predicting interferometer behaviour in diverse gravitational environments.

Spacetime Curvature Measurement via Atom Interferometry

Researchers have established a new connection between atom interferometry and the curvature of spacetime, refining the theoretical framework for measuring this curvature with greater precision and robustness. This work builds upon existing techniques for probing fundamental physics and testing general relativity, aiming to develop methods capable of resolving subtle features within gravitational fields. Atom interferometry utilizes the wave-like properties of atoms to create incredibly sensitive measurements of acceleration, rotation, and potentially, gravitational effects. This research connects these measurements to the geometry of spacetime, leveraging the tools of differential geometry to precisely calculate how curvature influences the interference patterns observed in these devices.

Atom Interferometry and Spacetime Curvature Calculations

This research provides a rigorous theoretical framework for understanding how spacetime curvature, or gravity, affects atom interferometers, connecting atom interferometry to the principles of general relativity. A key element is the application of differential geometry, extending the Gauss-Bonnet theorem to correctly handle light-like paths, allowing for accurate calculations of the effects of spacetime curvature on the interferometer and providing a method for interpreting experimental results. Standard formulations of the Gauss-Bonnet theorem often assume non-light-like paths, so the team extended the theorem to correctly handle these null paths, ensuring the reliability of the calculations. The research provides a comprehensive approach to understanding the interplay between quantum mechanics, gravity, and the geometry of spacetime.

Phase Shear Directly Measures Spacetime Curvature

Researchers have discovered a direct relationship between phase shear, a specific measurement in atom interferometry, and the curvature of spacetime. This breakthrough reveals that phase shear can be understood as the integrated curvature over the area enclosed by the interferometer’s arms, offering a new geometric interpretation of measurements made with these devices and enhancing robustness against noise. Experiments demonstrate that this method allows for the calculation of phase shear in complex gravitational environments, such as near massive objects. Calculations predict that a phase shear wavelength of approximately 1.

5 millimeters could be observed for an atom cloud of a few millimeters in size near Earth’s surface, a readily measurable effect, and that phase shear from a spherical test mass, like Tungsten, could also be detectable. For future long baseline terrestrial gradiometers, researchers calculate a measurable differential phase shear of approximately 3. 2 millimeters between two interferometers separated by one kilometer, significantly enhancing the sensitivity of these detectors. Importantly, the team determined that gravitational waves are unlikely to produce a measurable phase shear signal, and laser frequency noise is shown to be safely unobservable for proposed experiments. This work establishes a powerful theoretical tool for understanding the connection between gravitation and atom interferometry, paving the way for more precise measurements of spacetime geometry and gravitational phenomena.

Phase Shear Quantifies Spacetime Curvature Directly

This research establishes a direct relationship between phase shear, a specific measurement in atom interferometry, and the sectional curvature of spacetime. By extending the Gauss-Bonnet theorem, the team demonstrates that phase shear precisely quantifies the integrated curvature enclosed by the interferometer’s arms, providing a new, coordinate-free method for measuring spacetime properties using quantum mechanical systems and offering a powerful tool for testing general relativity. The authors acknowledge that applying this approach in higher dimensions or with complex interferometer geometries may require careful consideration of the connecting paths between interferometer arms. Future work could explore the practical implications of this new formulation for designing and interpreting atom interferometry experiments aimed at detecting subtle gravitational effects or probing the nature of spacetime itself.