General relativistic center-of-mass coordinates for composite quantum particles

Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an fashion. Here, instead, we start from the multiparticle nature of quantum-delocalizable atoms in curved spacetime and generalize the special-relativistic center of mass (c.m.) and relative coordinates that have previously been studied for Minkowski spacetime to obtain the light-matter dynamics in curved spacetime. In particular, for a local Schwarzschild observer located at the surface of the Earth using Fermi-Walker coordinates, we find gravitational correction terms for the Poincaré symmetry generators and use them to derive general relativistic c.m. and relative coordinates. In these coordinates we obtain the Hamiltonian of a fully first-quantized two-particle atom interacting with the electromagnetic field in curved spacetime that naturally incorporates special and general relativistic effects. Published by the American Physical Society 2025