Exact Semiclassical Phase Shifts for Relativistic Atom Interferometers in Flat Spacetime

Abstract

Atom interferometry is a sensitive tool for measuring relativistic effects, but there are no known non-trivial exact solutions for relativistic atom interferometer phase shifts. Here we derive relativistically exact expressions within the usual semiclassical approximation for a wide range of experimentally interesting atom interferometer pulse sequences in flat spacetime, including Mach-Zehnder, resonant, and large momentum transfer interferometer geometries. As an example, the leading order phase shift $\ddot{I}{‰}_{a}g{T}^2/c$ for a Mach-Zehnder clock atom interferometer is found to become $\ddot{I}{‰}_a\left(1+\frac{\ddot{I}{‰}_a}{2m}\right)(e^{-gT/c}-1{)}^{2}c/g$ when all relativistic kinematics are included. We calculate exact phase shifts for both clock (single-photon) interferometers and Raman or Bragg (two-photon) interferometers.

15 pages, 6 figures