The Hamiltonian for an atom interacting with gravitational waves

TL;DR

This paper derives a Hamiltonian describing how weak gravitational waves influence atomic systems, revealing curvature-dependent effects on internal energy and center-of-mass motion, which could be detectable with future sensitive experiments.

Contribution

It extends the relativistic Hamiltonian framework to include curvature effects on atoms in gravitational waves, highlighting new force contributions beyond mass renormalization.

Findings

Curvature-dependent corrections modify atomic Hamiltonians.

Internal energy variations can induce genuine forces.

Potential detectability of gravitational wave effects in future experiments.

Abstract

Building on the relativistic Hamiltonian of Sonnleitner and Barnett arXiv:1806.00234 and its post-Newtonian extensions by Schwartz and Giuilini arXiv:1908.06929, we investigate composite atomic systems in dynamical gravitational backgrounds. Using a local inertial frame and a perturbed Minkowski metric, we derive curvature-dependent corrections to both center-of-mass and internal Hamiltonians for atoms interacting with weak gravitational waves. The resulting Hamiltonian contains distinct curvature couplings modifying the internal potential and affecting the center-of-mass dynamics. These contributions imply that internal-energy variations do not always reduce to mass renormalization and can induce genuine forces due to changes in momentum. The initial research was motivated by anomalous friction-like forces emerging in quantum optics, and clarified that the anomalous forces are mere relativistic corrections from mass-energy equivalence. Our results suggest that, with increasingly sensitive detectors, additional forces from gravitational wave interactions may become visible in future experiments.