Theory of pseudomodes in quantum optical processes

B.J. Dalton, S. M. Barnett, B.M. Garraway

Research output: Contribution to journalArticle

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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 languageEnglish
Pages (from-to)053813/1-053813/21
Number of pages21
JournalPhysical Review A
Volume64
Issue number5
DOIs
Publication statusPublished - 12 Oct 2001

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photonics
continuums
excitation
atoms
cavities
coupled modes
Q factors
electromagnetic fields

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
Dalton, B.J. ; Barnett, S. M. ; Garraway, B.M. / Theory of pseudomodes in quantum optical processes. In: Physical Review A. 2001 ; Vol. 64, No. 5. pp. 053813/1-053813/21.
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Dalton, BJ, Barnett, SM & Garraway, BM 2001, 'Theory of pseudomodes in quantum optical processes', Physical Review A, vol. 64, no. 5, pp. 053813/1-053813/21. https://doi.org/10.1103/PhysRevA.64.053813

Theory of pseudomodes in quantum optical processes. / Dalton, B.J.; Barnett, S. M.; Garraway, B.M.

In: Physical Review A, Vol. 64, No. 5, 12.10.2001, p. 053813/1-053813/21.

Research output: Contribution to journalArticle

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AB - 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.

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Dalton BJ, Barnett SM, Garraway BM. Theory of pseudomodes in quantum optical processes. Physical Review A. 2001 Oct 12;64(5):053813/1-053813/21. https://doi.org/10.1103/PhysRevA.64.053813