Correlation-function analysis of coherent optical transients and fluorescence from a quasi-two-level system

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Abstract
A quasi-two-level system is a generalization of a two-level system where each of the single levels is replaced by a nearly degenerate multiplet. We develop the theory of the photon echo, the stimulated echo, and fluorescence emission for such systems when they are subjected to pulses of electromagnetic radiation that are short compared to the reciprocal (in frequency units) of the widths of the multiplets. The observable in each of these experiments is related to equilibrium time-correlation functions of the system in the absence of the radiation field. The correlation functions associated with these experiments involve more than two dynamical operators and more than two times, unlike the correlation functions for such processes as low-power optical absorption and neutron scattering. We introduce an exactly solvable factorization model for the transition moments, which includes as special cases the situation where either of the multiplets is a single state. We also consider the unitary model, which was introduced by Mims, and which leads to considerable simplification of the correlation functions. Several examples of these models are discussed to investigate the features of time-dependent fluorescence experiments and coherent optical transient experiments. In general, there is no simple connection between the time dependence of the decay of a photon echo and the Fourier transform of the low-power homogeneous absorption spectrum.