Analytical and numerical analysis of the atom-field dynamics in non-stationary cavity QED

We study analytically and numerically the dynamics of the quantum non-stationary system composed of a two-level atom interacting with a single mode cavity field whose frequency is rapidly modulated in time (with a small amplitude). We identify modulation laws resulting in qualitatively different dynamical regimes and we present analytical solutions in some simple cases. In particular, we analyse minutely the influence of the field-atom coupling on the photon generation from vacuum via the dynamical Casimir effect.