Stationary and Nonstationary Processes in Pumped Resonant Media

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Abstract
The response of a system of coherently pumped atoms to weak electromagnetic perturbing fields is discussed in general terms. The pump field is prescribed, and is assumed to propagate unattenuated through the medium which the (identical) atoms comprise, exciting a particular transition through either electric or magnetic dipole coupling. The perturbing field, which is assumed to act through electric dipole coupling, is allowed to be the (resonant) field emitted by the atoms, a weak external field absorbed by the atoms under resonant conditions, or a resonant or nonresonant wave propagating through the pumped medium. All of these cases are conveniently described within the same general framework, based on an analysis of the (single-atom) two-time dipole-moment correlation function. This function contains nonstationary components as well as stationary ones, owing to the time dependence imposed by the pump field. We are accordingly led to introduce a time-dependent linear susceptibility, which is inhomogeneous and anisotropic, due, respectively, to the variation of the pump phase within the medium and the preferred direction established by the pump-field polarization. Such disparate effects as parametric frequency conversion, emission- and absorption-line splitting, and time-dependent modulation of resonant emission and absorption functions in optical-pumping experiments emerge naturally from a single unified formalism.