Population trapping in two-level models: Spectral and statistical properties

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Abstract
The interaction of a two-level atom with a single-mode radiation field through multiphoton transitions is studied in terms of the dressed-state formalism. It is shown that when only certain dressed states are initially excited, population trapping occurs. We particularize these results for some well-known models of one- and two-photon transitions. Photon statistics of the cavity mode is analyzed in terms of the quasiprobability distribution Q(α). It is shown that when population trapping occurs some two-time correlation functions become stationary, which allows one to obtain the resonance spectrum as the Fourier transform of the two-time dipole autocorrelation function.