Atom interferometry in the presence of an external test mass

TL;DR

This paper provides a theoretical analysis of how an external test mass influences the phase of an atom interferometer signal, highlighting quantum corrections and methods to enhance sensitivity for detecting external masses.

Contribution

It introduces a detailed theoretical framework using density matrix and Wigner representation techniques to analyze quantum and classical phase contributions in atom interferometry with external test masses.

Findings

Quantum corrections to atomic motion can be measured with increased effective wave vector.

Derived expressions allow numerical evaluation of test mass contributions.

Validity regions for the theoretical expressions are established.

Abstract

The influence of an external test mass on the phase of the signal of an atom interferometer is studied theoretically. Using traditional techniques in atom optics based on the density matrix equations in the Wigner representation, we are able to extract the various contributions to the phase of the signal associated with the classical motion of the atoms, the quantum correction to this motion resulting from atomic recoil that is produced when the atoms interact with Raman field pulses, and quantum corrections to the atomic motion that occur in the time between the Raman field pulses. By increasing the effective wave vector associated with the Raman field pulses using modified field parameters, we can increase the sensitivity of the signal to the point where the quantum corrections can be measured. The expressions that are derived can be evaluated numerically to isolate the contribution to the signal from an external test mass. The regions of validity of the exact and approximate expressions are determined.