Parametric approximation as an open-quantum-system problem

In this work we develop an open quantum system view of the parametric approximation, which allows us to obtain systematic perturbative corrections to it. We consider the Jaynes-Cummings model with dissipation, assuming that the field is in the regime close to the parametric approximation with depletion. We obtain non-unitary corrections to the parametric approximation and additional dynamical Lamb-shift contributions to it. For high detuning, these nonunitary corrections appear to be non-Markovian before depletion. We also show that even after depletion, initial non-Markovian behavior contributes to the dynamics via laser-induced polishing of the density matrix.