Dressed states and exact dynamics of intensity-dependent two-mode two-photon Jaynes-Cummings models

Abstract

We study the two-photon interaction of a two-level atom with a quantized bimodal field of a loss-free cavity. We assume that both the coupling strength and the atom-field detuning may depend on the populations of the two modes. We show that this general nonlinear model is exactly solvable in terms of a dressing unitary operator. Exact expressions for the eigenstates as well as for the Rabi frequencies of the coupled system are given as explicit functions of the nonlinearity terms present in the model. Exploiting the flexibility of these results, we investigate the atomic inversion supposing that at t=0 one mode is coherent, the other is in a Fock state and the atom is excited. We compare the dynamical behaviour of various particular nonlinear models. A common feature is the presence of collapses and revivals of the Rabi oscillations. We find that the atomic inversion manifests exact periodicity when only one specific type of intensity-dependent term (coupling strength or detuning) is present. Such behaviour is physically interpreted in the framework of the dressed atom representation. The simulataneous presence of both nonlinear contributions in the model breaks such regular behaviour in the long-time atomic evolution, in which case competition effects occur which qualitatively modify the quantum dynamics of the system. Other quantum manifestations are brought to light. Their relevance, in connection with the possibility of preparing a cavity mode in an arbitrary Fock state, is briefly discussed.