Atom Interferometer Phase Shear and Spacetime Sectional Curvature
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914013354393600 |
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| author | Swan, Hunter Hogan, Jason M. |
| author_facet | Swan, Hunter Hogan, Jason M. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_21331 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Atom Interferometer Phase Shear and Spacetime Sectional Curvature Swan, Hunter Hogan, Jason M. Atomic Physics General Relativity and Quantum Cosmology 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. |
| title | Atom Interferometer Phase Shear and Spacetime Sectional Curvature |
| topic | Atomic Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2508.21331 |