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We employ a recently developed quantization scheme for quasinormal modes(QNMs) to study a nonperturbative open cavity-QED system consisting of a hybridmetal-dielectric resonator coupled to a quantum emitter. This hybrid cavitysystem allows one to explore the complex coupling between a low $Q$ (qualityfactor) resonance and a high $Q$ resonance, manifesting in a striking Fanoresonance, an effect that is not captured by traditional quantization schemesusing normal modes or a Jaynes-Cummings (JC) type model. The QNM quantizationapproach rigorously includes dissipative coupling between the QNMs, and issupplemented with generalized input-output relations for the output electricfield operator for multiple modes in the system, and correlation functionsoutside the system. The role of the dissipation-induced mode coupling isexplored in the strong coupling regime between the photons and emitter beyondthe first rung of the JC dressed-state ladder. Important differences in thequantum master equation and input-output relations between the QNM quantummodel and phenomenological dissipative JC models are found. In a second step,numerical results for the Fock distributions and system as well as outputcorrelation functions obtained from the quantized QNM model for the hybridstructure are compared with results from a phenomenological approach. Wedemonstrate explicitly how the quantized QNM model manifests in multiphotonquantum correlations beyond what is predicted by the usual JC models.

Quantized quasinormal mode description of non-linear cavity QED effects from coupled resonators with a Fano-like resonance