Connecting classical and quantum mode theories for coupled lossy cavity resonators using quasinormal modes

TL;DR

This paper introduces a quantized quasinormal mode approach to accurately describe coupled lossy cavity resonators, revealing new interference effects and limitations of traditional models, with implications for quantum and classical cavity physics.

Contribution

It develops a rigorous quantized quasinormal mode framework connecting classical and quantum descriptions, improving modeling of coupled lossy resonators and addressing limitations of existing master equations.

Findings

Interference effects depend on quasinormal mode phase

Traditional master equations are often inadequate

Enhanced models accurately capture high-Q mode interference

Abstract

We present a quantized quasinormal approach to rigorously describe coupled lossy resonators, and quantify the quantum coupling parameters as a function of distance between the resonators. We also make a direct connection between classical and quantum quasinormal modes parameters and theories, offering new and unique insights into coupled open cavity resonators. We present detailed calculations for coupled microdisk resonators and show striking interference effects that depend on the phase of the quasinormal modes, an effect that is also significant for high quality factor modes. Our results demonstrate that commonly adopted master equations for such systems are generally not applicable and we discuss the new physics that is captured using the quantized quasinormal mode coupling parameters and show how these relate to the classical mode parameters. Using these new insights, we also present several models to fix the failures of the dissipative Jaynes-Cummings type models for coupled cavity resonators. Additionally, we show how to improve the classical and quantum lossless mode models (i.e., using normal modes) by employing a non-diagonal mode expansion based on the knowledge of the quasinormal mode eigenfrequencies, and analytical coupled mode theory, to accurately capture the mode interference effects for high quality factors.