Atom interferometers in weakly curved spacetimes using Bragg diffraction and Bloch oscillations

TL;DR

This paper systematically derives relativistic phase corrections up to order c^{-2} for light-pulse atom interferometers in weakly curved spacetime, using first principles and the parameterized post-Newtonian formalism.

Contribution

It provides a general algebraic framework for calculating relativistic phases in atom interferometers with arbitrary geometries, including new case studies and comparisons.

Findings

Derived algebraic expressions for relativistic phases.

Analyzed symmetric and antisymmetric Ramsey-Bordé interferometers.

Compared results with previous Mach-Zehnder calculations.

Abstract

We present a systematic approach to determine all relativistic phases up to $\mathcal{O}(c^{-2})$ in light-pulse atom interferometers in weakly curved spacetime that are based on elastic scattering, namely Bragg diffraction and Bloch oscillations. Our analysis is derived from first principles using the parameterized post-Newtonian formalism. In the treatment developed here, we derive algebraic expressions for relativistic phases for arbitrary interferometer geometries in an automated manner. As case studies, we consider symmetric and antisymmetric Ramsey-Bord\'e interferometers, as well as a symmetric double diffraction interferometer with baseline lengths of 10 m and 100 m. We compare our results to previous calculations conducted for a Mach-Zehnder interferometer.