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Interacting quantum plasmons in metal-dielectric structures

We develop a consistent quantum description of surface plasmons interacting with quantum emitters and external electromagnetic field. Within the framework of macroscopic electrodynamics in dispersive and absorptive medium, we derive, in the Markov approximation, the canonical Hamiltonian, commutation relations, and coupling parameters for the plasmon modes in metal-dielectric structures of an arbitrary shape whose characteristic size is well below the diffraction limit. We then develop a new quantum approach bridging the macroscopic and canonical schemes which describes the interacting plasmons in terms of bosonic modes with linear dispersion whose coupling to the electromagnetic field and quantum emitters is mediated by the classical plasmons. By accurately accounting for medium optical dispersion and losses in the interactions of surface plasmons with light and localized electron excitations, this approach can serve as a framework for studying non-Markovian effects in plasmonics.