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We present a systematic approach to determine all relativistic phases up to$\mathcal{O}(c^{-2})$ in light-pulse atom interferometers in weakly curvedspacetime that are based on elastic scattering, namely Bragg diffraction andBloch oscillations. Our analysis is derived from first principles using theparameterized post-Newtonian formalism. In the treatment developed here, wederive algebraic expressions for relativistic phases for arbitraryinterferometer geometries in an automated manner. As case studies, we considersymmetric and antisymmetric Ramsey-Bord\'e interferometers, as well as asymmetric double diffraction interferometer with baseline lengths of 10 m and100 m. We compare our results to previous calculations conducted for aMach-Zehnder interferometer.

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