Wigner representation enables the exact derivation of the atom interferometer phase, unlike the path integral approach

TL;DR

This paper derives an exact formula for the phase of an atomic interferometer in complex, non-inertial frames using the Wigner representation, surpassing the path integral approach in precision.

Contribution

It introduces a novel exact expression for interferometer phase accounting for arbitrary platform motion and orientation, using the Wigner representation.

Findings

Derived three new terms related to platform rotation and translation.

Provided an exact phase expression for non-inertial frames.

Enhanced understanding of gravitational and inertial effects in atom interferometry.

Abstract

An exact expression for the phase of an atomic interferometer located in a non-inertial reference frame (platform) moving along an arbitrary trajectory and with an orientation that changes arbitrarily over time is obtained. This expression takes into account precisely gravitational, Coriolis, centrifugal, and gravity-gradient forces, which arise during the rotation of the gravity source at a permanent rate. To achieve this result, we utilized the equations for the atomic density matrix in the Wigner representation. Starting from the exact formula, we derived three new terms in the well-known limit of small rotation angles and short interrogation time, which are attributed to the rotation and translational motion of the platform.