Cooperative interaction of dressed atoms with a quantised mode of the electromagnetic field

The nonlinear dynamics of an open quantum system containing an arbitrary number of two-level atoms coupled with a classical polychromatic electromagnetic field and a quantised mode of the electromagnetic field is studied. Two particular cases of the elastic and inelastic interactions are considered. In the first case, the quantised mode is resonant with the transition between the quasi-energy levels corresponding to the same quasi-energy state, while in the second case, the levels involved in the interaction correspond to different quasi-energy states. For the elastic interaction, which can appear only in open quantum systems, an analytic solution of the Heisenberg equations is obtained. The time dependences of the population of quasi-energy states, the number of photons in the quantised mode, and photon statistics are numerically analysed for the inelastic interaction and at the crossing point of quasi-levels, when both types of the interaction are simultaneously present.