Theory of pseudomodes in quantum optical processes - art. no. 053813

This paper deals with non-Markovian behavior in atomic systems coupled to a structured reservoir of quantum electromagnetic field modes, with particul ar relevance to atoms interacting with the field in high-Q cavities or phot onic band-gap materials. In cases such as the former, we show that the pseu domode theory for single-quantum reservoir excitations can be obtained by a pplying the Fano diagonalization method to a system in which the atomic tra nsitions are coupled to a discrete set of (cavity) quasimodes, which in tur n are coupled to a continuum set of (external) quasimodes with slowly varyi ng coupling constants and continuum mode density. Each pseudomode can be id entified with a discrete quasimode, which gives structure to the actual res ervoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitati on of the reservoir to now be treated via Markovian master equations for th e atom-discrete quasimode system. Applications of the theory to one, two, a nd many discrete quasimodes are made. For a simple photonic band-gap model, where the reservoir structure is associated with the true mode density rat her than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.