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arXiv · 2508.21331

Atom Interferometer Phase Shear and Spacetime Sectional Curvature

Hunter Swan·Jason M. Hogan
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Abstract

Atom interferometry is a natural laboratory for precision tests of general relativity, but there is no simple relationship between atom interferometer phase and geometric properties of spacetime. Here we show that a different atom interferometer observable, the phase shear, can be expressed directly as the integrated sectional curvature over a spacetime surface enclosed by the interferometer arms and final beamsplitter. This is a consequence of a generalized Gauss-Bonnet theorem, which also explicitly computes small correction terms arising from gravitational redshift of atom optics pulses. This synthesis of quantum mechanics, relativity, and differential geometry affords a manifestly coordinate-free and representation-free means of measuring spacetime properties. Additionally, it provides a convenient computational tool for predicting atom interferometer properties in arbitrary background spacetimes.

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Hunter Swan, Jason M. Hogan. 2025-08-29. Atom Interferometer Phase Shear and Spacetime Sectional Curvature. https://arxiv.org/abs/2508.21331

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