A quantum nonlinear resonance with account of relaxation processes

The dynamics of a quantum nonlinear resonance taking place at the interaction of radiation with a multi-level quantum system is considered with allowance for relaxation processes. Dissipation is taken into account phenomenologically, namely, by the introduction of additional terms in the equations for the dynamic variables. It is shown that under certain conditions, the influence of dissipation can be reduced to two effects with essentially different time scales: the “external field” effect and the “trajectory torsion” one. The former is determining. In the quantum case, the “external field” effect generates tunnelling processes in the system that eventually lead to the finite lifetime of the nonlinear resonance. The lifetime of the nonlinear resonance due to the tunnelling effects is estimated as a function of the system parameters.