Modal approach to the coupling strength of quantum emitters in electromagnetic resonators

We present a modal analysis of a popular modeling framework for studying light-matter interaction between quantum emitters and general electromagnetic resonators, in which the active materials are modeled via Lorentzian material responses. The method relies on the Lippmann-Schwinger equation to calculate the complex resonance frequencies of the coupled system based only on a single calculation for the electromagnetic resonator without the active material and without fitting to calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anticrossing of the emitter and cavity resonance frequencies, and comparing with independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. To connect with the Jaynes-Cummings model, we relate the classical description of the emitter to the dipole moment in the corresponding quantum optical model. The combined framework therefore enables classical calculations to be used for evaluating the coupling strength entering quantum optical theories in a transparent way. The methodology is expected to be useful in the design and interpretation of ongoing and future experiments and devices involving single-photon sources for quantum information and quantum communication technology.