### Abstract

This paper deals with non-Markovian behavior in atomic systems coupled to a structured reservoir of quantum electromagnetic field modes, with particular relevance to atoms interacting with the field in high-Q cavities or photonic band-gap materials. In cases such as the former, we show that the pseudomode theory for single-quantum reservoir excitations can be obtained by applying the Fano diagonalization method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two, and many discrete quasimodes are made. For a simple photonic band-gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.

Original language | English |
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Pages (from-to) | 053813/1-053813/21 |

Number of pages | 21 |

Journal | Physical Review A |

Volume | 64 |

Issue number | 5 |

DOIs | |

Publication status | Published - 12 Oct 2001 |

### Keywords

- non-Markovian behavior
- atomic systems
- cavities
- pseudomode theory
- quantum
- photonic band-gap
- quasimodes

## Cite this

Dalton, B. J., Barnett, S. M., & Garraway, B. M. (2001). Theory of pseudomodes in quantum optical processes.

*Physical Review A*,*64*(5), 053813/1-053813/21. https://doi.org/10.1103/PhysRevA.64.053813