Abstract
We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment. The field quantization requires only the fitting of the spectral density, obtained through classical electromagnetic simulations, to a model system involving a small number of lossy and interacting modes. We illustrate the power and validity of our approach by describing the population and electric field spatial dynamics in the spontaneous decay of an emitter placed in a complex hybrid plasmonic-photonic structure.
Highlights
Motivated by the desire to use nanophotonic devices for quantum optics and quantum technology applications, there is large interest in developing strategies for quantizing electromagnetic (EM) modes in open, dispersive, and absorbing photonic environments, where standard ways of obtaining quantized modes are not valid [1,2]
We develop a framework that provides a few-mode master equation description of the interaction between a single quantum emitter and an arbitrary electromagnetic environment
While macroscopic quantum electrodynamics (QED) provides a framework for such quantization in material structures described by EM constitutive relations [3,4,5,6,7,8,9], it describes electromagnetic fields by a continuum of harmonic oscillators, restricting its applicability to cases where they can be treated perturbatively or eliminated by Laplace transform or similar techniques
Summary
EM modes at frequency ω [34] and correspond to the “true modes” of Refs. [11,12]. The light-matter coupling is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi gðωÞ 1⁄4. The system of N interacting modes and continua can be diagonalized by adapting Fano diagonalization, originally developed for autoionizing states of atomic systems [29], and related to quasimode and pseudomode theory [11,12] in this context This strategy allows us to obtain a simple, closed expression for JmodðωÞ. This is achieved by solving the Lippmann-Schwinger equations to obtain the N eigenmodes of the model at each frequency ω Forming their unique linear superposition (the “bright” or “emitter-centered” mode) coupling to the emitter leads to a compact expression for the model spectral density (for details, see the Supplemental Material [40]): JmodðωÞ μ2 π
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