  The dynamics of a three-level atom in a cascade configuration with both
transitions coupled to a single structured reservoir of quantized field modes
is treated using Laplace transform methods applied to the coupled amplitude
equations. Results are also obtained from master equations by two different
approaches, that is, involving either pseudomodes or quasimodes. Two different
types of reservoir are considered, namely a high-Q cavity and a photonic
band-gap system, in which the respective reservoir structure functions involve
Lorentzians. Non-resonant transitions are included in the model. In all cases
non-Markovian behaviour for the atomic system can be found, such as oscillatory
decay for the high-Q cavity case and population trapping for the photonic
band-gap case. In the master equation approaches, the atomic system is
augmented by a small number of pseudomodes or quasimodes, which in the
quasimode approach themselves undergo Markovian relaxation into a flat
reservoir of continuum quasimodes. Results from these methods are found to be
identical to those from the Laplace transform method including two-photon
excitation of the reservoir with both emitting sequences. This shows that
complicated non-Markovian decays of an atomic system into structured EM field
reservoirs can be described by Markovian models for the atomic system coupled
to a small number of pseudomodes or quasimodes.
