Jaynes–Cummings model in a weak gravitational wave background

Abstract

Working in the framework of the linearized theory, we analyze the influence of a weak gravitational wave on the dynamics of the Jaynes–Cummings model, describing the interaction between a two-level quantum system and the electromagnetic field in a cavity. We show that the gravitational wave induces a small, time-dependent modulation in the generalized Rabi frequency Ω of the system. Such a modulation has the same frequency as the incoming gravitational wave. We also find that the atomic inversion acquires a similar time-dependent modulation. After a π / 2 − pulse of the electromagnetic driving field in the cavity, an atomic population N 0, previously prepared in its excited state, ends showing a small unbalance Δ N = N e − N g between the excited and the de-excited atoms. The unbalance amplitude is proportional to HN 0, with H being the gravitational strain. We briefly comment about possible astrophysical implications.