Semiclassical phases of charged spin-$1/2$ matter-wave interferometers in gravitational wave backgrounds

TL;DR

This paper develops a semiclassical framework for charged spin-1/2 matter-wave interferometers in gravitational wave backgrounds, analyzing how curvature influences quantum phases through dynamical, spin, and electromagnetic effects.

Contribution

It introduces a unified semiclassical approach to understand how gravitational waves affect matter-wave interferometry via multiple physical pathways.

Findings

All three phase contributions are governed by local tidal fields.

The responses are determined by the same tidal scale and filtered by a common geometric kernel.

The Aharonov-Bohm phase depends on spatial variations and traversal time, showing frequency dependence.

Abstract

A matter wave propagating through curved spacetime accumulates phase that encodes both geometry and gauge structure. We develop a semiclassical framework for charged spin-$1/2$ matter-wave interferometers based on a WKB expansion of the covariant Dirac equation, in which the phase decomposes into dynamical, spin, and electromagnetic Aharonov-Bohm (AB) contributions. In a freely falling detector frame, all three channels are governed by local tidal fields. In a weak gravitational-wave (GW) background, the dynamical and spin phases probe the gravitoelectric and gravitomagnetic sectors of curvature, while the AB phase arises from curvature-induced electromagnetic fields obtained from Maxwell's equations in curved spacetime. For a Mach-Zehnder interferometer (MZI), all three responses are determined by the same tidal scale, $\ddot{h}_A \sim \Omega^2_{gw}h_0$, and filtered by a common geometric kernel, while entering through distinct physical couplings. In particular, the AB contribution depends not only on the enclosed flux but also on spatial variations of the induced fields and exhibits an intrinsic frequency dependence set by the traversal time. These results provide a unified description of matter-wave interferometric phases in time-dependent GW backgrounds and identify complementary dynamical, spin, and electromagnetic pathways through which spacetime curvature imprints itself on quantum interference.