Phases and relativity in atomic gravimetry

TL;DR

This paper analyzes the phase measurement in atomic gravimeters within a relativistic framework, emphasizing gauge invariance and conservation laws, and compares techniques for Doppler shift compensation.

Contribution

It provides a fully relativistic formulation of phase in atomic gravimetry, connecting laser phases to gauge invariance and conservation laws, and discusses Doppler compensation methods.

Findings

Relativistic gauge-invariant expression for phase

Connection between light and atomic contributions via conservation laws

Comparison of chirped and ramped frequency techniques

Abstract

The phase observable measured by an atomic gravimeter built up on stimulated Raman transitions is discussed in a fully relativistic context. It is written in terms of laser phases which are invariant under relativistic gauge transformations. The dephasing is the sum of light and atomic contributions which are connected to one another through their interplay with conservation laws at the interaction vertices. In the case of a closed geometry, a compact form of the dephasing is written in terms of a Legendre transform of the laser phases. These general expressions are illustrated by discussing two techniques used for compensating the Doppler shift, one corresponding to chirped frequencies and the other one to ramped variations.