Engineering transient spectrum for a two-level system interacting with two-mode intelligent states

The problem of a single two-level atom in its excited state, placed in a bimodal cavity in which an arbitrary form of the intensity-dependent atom-field coupling is present, is solved exactly. Expressions for the energy eigenvalues and eigenvectors are derived, and an exact representation for the time-dependent unitary evolution operator of the system is given, by means of which we analyze the analytic form of the fluorescence spectrum using the transitions among the dressed states of the system. The influence of parameter misfits on the quantum system is discussed. An interesting relation between the fluorescence spectrum and the dynamical evolution is found when the initial field states are prepared in properly intelligent states. By comparison with exact numerical results, we demonstrate that features of the fluorescence spectrum are influenced significantly by the different kinds of the nonlinearity of the intensity-dependent atom-field coupling. We provide numerous examples to illustrate this correspondence, and provide evidence of its usefulness. The present work considerably extends earlier results for two-level systems.