Non-Markovian decay of a three-level cascade atom in a structured reservoir

The dynamics of a three-level atom in a cascade (or ladder) configuration with both transitions coupled to a single structured reservoir of quantized electromagnetic field modes is treated using Laplace transform methods applied to the coupled amplitude equations. In this system two-photon excitation of the reservoir occurs, and both sequences for emitting the two photons are allowed and included in the theory. An integral equation is found to govern the complex amplitudes of interest. It is shown that the dynamics of the atomic system is completely determined in terms of reservoir structure functions, which are products of the mode density with the coupling constant squared. This dependence on reservoir structure functions rather than on the mode density or coupling constants alone, shows that it may be possible to extend pseudomode theory to treat multiphoton excitation of a structured reservoir