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

TL;DR

This work derives an exact AI phase for an atom interferometer in a non‑inertial platform relative to a rotating gravity source by employing the density matrix in the Wigner representation. It analyzes the full phase‑space dynamics, yielding propagators that capture platform motion, rotation, and gravity gradients, and produces an exact phase expression for arbitrary trajectories and orientations. In the small‑rotation, short‑time limit, it reveals three new cross‑coupling terms arising from platform rotation and translation that are absent in inertial or purely classical treatments. The results enhance the accuracy and reliability of AI‑based sensing and navigation, and they provide a foundation for modeling vibrational and rotational noise, differential measurements, and potential measurements of the gravity source rotation rate.

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.