Connecting Classical and Quantum Mode Theories for Coupled Lossy Cavity Resonators Using Quasinormal Modes

We present a quantized quasinormal mode 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 mode parameters and theories, offering new insights into coupled open cavities. 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 quasinormal mode insights, we also present several models to fix the failures of the dissipative Jaynes–Cummings-type models for coupled cavities. Additionally, we show how to improve the classical and quantum lossless mode models (i.e., using normal modes) by employing a nondiagonal 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.