Interaction of a Λ-type three-level atom with a two-mode field and a two-mode Raman-coupled model

Abstract

The Hamiltonian is derived for the interaction of a Λ-type three-level atom with a two-mode quantum cavity field from the general interaction Hamiltonian between a multi-level atom and a multi-mode radiation field, and it is reduced to an effective two-mode Raman-coupled model under a large detuning condition. We propose a modified effective Hamiltonian for the two-mode Raman-coupled model, find the time-dependent state vectors, and present the validity conditions for the involved interaction Hamiltonians. It is shown that in the study of the two-mode Raman-coupled model it is not enough to retain only the usually used effective Hamiltonian, one must also take into account the ac Stark shift of the atomic levels (at least one of the levels). Finally, we study the atomic dynamics in the interaction of a Λ-type three-level atom with a two-mode quantum cavity field and in the two-mode Raman-coupled model. We find that the number of collapse-revivals, the collapse time and the revival time show new characteristics.