Semi-analytical Framework for Modeling Strong Coupling of Quantum Emitters in Electromagnetic Resonators

TL;DR

This paper introduces a semi-analytical method to accurately model the interaction between quantum emitters and electromagnetic resonators, avoiding fitting parameters and enabling direct quantum-classical correspondence.

Contribution

The authors develop a novel semi-analytical framework using the Lippmann-Schwinger equation that predicts strong coupling phenomena without fitting, and explicitly connects classical and quantum descriptions.

Findings

Achieves quantitative agreement with reference calculations below 0.01% error.

Successfully demonstrates anti-crossing in a dielectric cavity with deep subwavelength confinement.

Provides explicit relation between classical and quantum emitter models.

Abstract

We present a semi-analytical framework for studying interactions between quantum emitters and general electromagnetic resonators. 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 quantum emitter and with no fitting parameters. This is in stark contrast to standard approaches in the literature, in which the properties of the coupled system are fitted from calculated spectra. As an application example, we consider a recent dielectric cavity design featuring deep subwavelength confinement of light. We find the expected anti-crossing of the emitter and cavity resonance frequencies, and comparing to independent reference calculations, we find an extraordinary quantitative agreement with a relative error below one part in ten thousand. In order to unambiguously connect with the Jaynes-Cummings model, we derive an explicit expression relating the classical description of the emitter, as modeled by a spherical inclusion with a Lorentzian material response, to the dipole moment of 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.