  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.
