General Relativistic Center-of-Mass Coordinates for Composite Quantum Particles

TL;DR

This paper develops a relativistic framework for the center-of-mass and relative coordinates of quantum particles in curved spacetime, enabling more accurate modeling of atom interferometry experiments testing fundamental physics.

Contribution

It generalizes special-relativistic COM and relative coordinates to curved spacetime, deriving a Hamiltonian for quantum atoms in gravitational fields.

Findings

Derived gravitational correction terms for Poincaré symmetry generators.

Formulated a Hamiltonian incorporating relativistic effects for quantum atoms in curved spacetime.

Provided a foundation for improved quantum tests of gravity and equivalence principle.

Abstract

Recent proposals suggested quantum clock interferometry for tests of the Einstein equivalence principle. However, atom interferometric models often include relativistic effects only in an ad hoc fashion. Here, instead, we start from the multi-particle nature of quantum-delocalizable atoms in curved spacetime and generalize the special-relativistic center of mass (COM) 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 Poincar\'e symmetry generators and use them to derive general relativistic COM 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.