Geometric phases and the Sagnac effect: Foundational aspects and sensing applications

Abstract

Geometric phase is a key player in many areas of quantum science and technology. In this review article, several foundational aspects of quantum geometric phases and their relations to classical geometric phases are outlined. How the Aharonov--Bohm and Sagnac effects fit into this context is then discussed. Moreover, a concise overview of technological applications of the latter, with special emphasis on gravitational sensing, like in gyroscopes and gravitational wave detectors is presented.

Author's accepted version

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• Quantum circuits for measuring weak values, Kirkwood--Dirac quasiprobability distributions, and state spectra
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• Interferometry and higher-dimensional phase measurements using directionally unbiased linear optics
• The Aharonov-Bohm effect in a closed flux line
• Aharonov-Bohm effect with an effective complex-valued vector potential
• Dynamical Casimir effects with atoms: from the emission of photon pairs to geometric phases
• Time-symmetry and topology of the Aharonov-Bohm effect