Stochastic Theory of the Resonant Scattering of Photons

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Abstract
The resonant scattering of photons from a perturbed two-level system is studied in detail. Adiabatic perturbations are approximated by a randomly fluctuating term in the level splitting. Off-diagonal perturbations are accounted for in the linewidth and the time dependence of the correlation functions. Explicit expressions for the cross section are obtained in the statistical and motional-narrowing limits. The detailed-balancing symmetry of the scattering is established. Minor modifications of the approximate expressions for the cross sections are proposed in order to preserve this symmetry. The effects of off-diagonal perturbations, which couple the atom to a thermal bath, are investigated at length for a model interaction.

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