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Effective Raman Theory for a Three-Level Atom in the V-Configuration

It is shown that the system of a three-level atom coupled with two modes of quantized cavity fields in the V-configuration with arbitrary detunings can be exactly reduced to a two-level system with a nonsingular effective coupling which depends nonlinearly on the intensity of the two cavity fields. By performing a unitary transformation, we obtain an exact transformed Hamiltonian in which one of the three levels is decoupled for all values of the detunings including the zero-detuning. We also present the analytical expressions of energy eigenvdues and eigenvectors, evolution operator, time-varying atomic inversion operator and photon number operators of the two modes for the effective two-level model.