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

We present a systematic approach to determine all relativistic phases up to Ooc-2 thorn 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 parametrized 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-Borde 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.