Resonance fluorescence in Markovian stochastic fields

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Abstract
A systematic method is presented for averaging the integral equations of motion for the atomic density matrix operator and its quantum correlation functions over the fluctuations of Markovian exciting fields with arbitrary bandwidth. The theory takes into account the statistics of the field to all orders. The method is applied to the investigation of resonance fluorescence in the presence of three different Markovian fields: (i) a phase-diffusion field, (ii) a chaotic field, and (iii) a Gaussian-amplitude field. It is shown that in the case of a resonant, intense phase-diffusion field a center line dip develops in the spectrum of resonance fluorescence when the Rabi frequency is approximately equal to the bandwidth of the field. In the case of amplitude fluctuations the sidebands of the on-resonance spectrum tend to reproduce the probability distribution for the amplitude of the exciting field.