Quantized quasinormal mode theory of coupled lossy and amplifying resonators

TL;DR

This paper develops a comprehensive quantum theory for coupled lossy and amplifying resonators using quasinormal modes, providing new methods for quantization and insights into gain-loss interactions affecting quantum emitter dynamics.

Contribution

It introduces a novel electromagnetic quantization scheme for QNMs in media with both loss and gain, including two different operator basis constructions and their impact on quantum dynamics.

Findings

Two distinct QNM photon Fock space constructions are proposed.

Loss and gain induce intermode coupling affecting quantum emitter behavior.

Numerical analysis validates the quantization methods in gain-loss microdisk resonators.

Abstract

In the presence of arbitrary three-dimensional linear media with material loss and amplification, we present an electromagnetic field quantization scheme for quasinormal modes (QNMs), extending previous work for lossy media [Franke et al., Phys. Rev. Lett. 122, 213901 (2019)]. Applying a symmetrization transformation, we show two fundamentally different ways for constructing a QNM photon Fock space, including (i) where there is a separate operator basis for both gain and loss, and (ii) where the loss and gain degrees of freedom are combined into a single basis. These QNM operator bases are subsequently used to derive the associated QNM master equations, including the interaction with a quantum emitter, modelled as a quantized two-level system (TLS). We then compare the two different quantization approaches, and also show how commonly used phenomenological methods to quantize light in gain-loss resonators are corrected by several important aspects, such as a loss-induced and gain-induced intermode coupling, which appears through the rigorous treatment of loss and amplification on a dissipative mode level. For specific resonator designs, modelled in a fully consistent way with the classical Maxwell equations with open boundary conditions, we then present numerical results for the quantum parameters and observables of a TLS weakly interacting with the medium-assisted field in a gain-loss microdisk resonator system, and discuss the validity of the different quantization approaches for several gain-loss parameter regimes.