RESPONSE OF A 2-LEVEL ATOM TO A CLASSICAL FIELD AND A QUANTIZED CAVITY FIELD OF DIFFERENT FREQUENCIES

We consider a two-level atom interacting simultaneously with a classically described cw laser field and a quantized cavity field. The classical field is assumed strong, and the cavity field is regarded as a quantum probe of its dressed states. The two fields have different frequencies and amplitudes, but we show that an effective time-independent Hamiltonian can be obtained via two rotating-frame transformations. There is a different effective Hamiltonian in each of an infinite sequence of "probe resonance zones" associated with the subharmonic Rabi sidebands of the dressed states. In the mth zone, the Hamiltonian has the same form as the m-photon Jaynes-Cummings Hamiltonian. We consider both time-dependent and time-averaged atomic response and make comparisons with recent findings in the case that both fields are fully classical.