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The dynamics of a three-level atom in a cascade configuration with bothtransitions coupled to a single structured reservoir of quantized field modesis treated using Laplace transform methods applied to the coupled amplitudeequations. Results are also obtained from master equations by two differentapproaches, that is, involving either pseudomodes or quasimodes. Two differenttypes of reservoir are considered, namely a high-Q cavity and a photonicband-gap system, in which the respective reservoir structure functions involveLorentzians. Non-resonant transitions are included in the model. In all casesnon-Markovian behaviour for the atomic system can be found, such as oscillatorydecay for the high-Q cavity case and population trapping for the photonicband-gap case. In the master equation approaches, the atomic system isaugmented by a small number of pseudomodes or quasimodes, which in thequasimode approach themselves undergo Markovian relaxation into a flatreservoir of continuum quasimodes. Results from these methods are found to beidentical to those from the Laplace transform method including two-photonexcitation of the reservoir with both emitting sequences. This shows thatcomplicated non-Markovian decays of an atomic system into structured EM fieldreservoirs can be described by Markovian models for the atomic system coupledto a small number of pseudomodes or quasimodes

Theory of non-Markovian decay of a cascade atom in high-Q cavities and photonic band gap materials