Quantum optics in a dielectric: Macroscopic electromagnetic-field and medium operators for a linear dispersive lossy medium-a microscopic derivation of the operators and their commutation relations

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Abstract

We derive the macroscopic electromagnetic-field and medium operators for a linear dispersive medium with a microscopic model. As an alternative to the previous treatments in the literature, we show that the canonical momentum for the macroscopic field can be chosen to be -εoE instead of −D with the standard minimalcoupling Hamiltonian. We find that, despite the change in the field operator normalization constants, the equal-time commutators among the macroscopic electric-field, magnetic-field, and medium operators have the same values as their microscopic counterparts under a coarse-grained approximation. This preservation of the equal-time commutator is important from a fundamental standpoint, such as the preservation of microcausality for macroscopic quantities. The existence of more than one normal frequency mode at each k vector in a realistic causal-response medium is shown to be responsible for the commutator preservation. The process of macroscopic averaging is discussed in our derivation. The macroscopic field operators we derive are valid for a wide range of frequencies below, above, and around resonances. Our derivation covers the lossless, slightly lossy, and dispersionless as well as dispersive regimes of the medium. The local-field correction is also included in the formalism by inclusion of dipole-dipole interactions. Comparisons are made with other derivations of the macroscopic field operators. Using our theory, we discuss the questions of field propagation across a dielectric boundary and the decay rate of an atom embedded in a dielectric medium. We also discuss the question of squeezing in a linear dielectric medium and the extension of our theory to the case of a nonuniform medium.

Original languageEnglish (US)
Pages (from-to)1620-1638
Number of pages19
JournalJournal of the Optical Society of America B: Optical Physics
Volume10
Issue number9
DOIs
StatePublished - Jan 1 1993

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Atomic and Molecular Physics, and Optics

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