Approximate analytical results on the cavity dynamical Casimir effect in   the presence of a two-level atom
  We study analytically the photon generation from vacuum due to the Dynamical Casimir effect in a cavity with a two-level atom, prepared initially in an arbitrary pure state. Performing small unitary transformations we obtain closed analytical expressions for the probability amplitudes and other important quantities in the resonant/dispersive regimes. 
A. V. Dodonov and V. V. Dodonov
quant-ph