Non-adiabatic effects induced by strong light-matter coupling in cavity QED.

We present a systematic study of the diagonal Born-Oppenheimer correction (DBOC) for atoms and molecules embedded in optical cavities and interacting with a quantized electromagnetic field. By explicitly evaluating the nuclear kinetic energy operator, we analyze cavity-induced modifications of DBOC within a quantum electrodynamics configuration-interaction framework built on quantum electrodynamics Hartree-Fock (QED-HF) and strong-coupling quantum electrodynamics Hartree-Fock (SC-QED-HF) reference states. The analysis covers a diverse set of atomic and molecular systems, including He, H-, Be, H2, LiH, HF, ammonia (NH3), and formaldehyde (CH2O). We show that the presence of the cavity leads to shifts in molecular dissociation energies on the order of a few inverse centimeters. For several atomic systems, the inclusion of the DBOC yields a pronounced effect, with the correction magnitude reaching the experimental resolution. These findings reveal finite nuclear mass effects as an essential component of nuclear dynamics in cavity QED and suggest their relevance for precision analysis in strongly coupled light-matter systems.