The universal model of strong coupling at the nonlinear parametric resonance in open cavity-QED systems

Many molecular, quantum-dot, and optomechanical nanocavity-QED systems demonstrate strong nonlinear interactions between electrons, photons, and phonon (vibrational) modes. We show that such systems can be described by a universal model in the vicinity of the nonlinear parametric resonance involving all three degrees of freedom. We solve the nonperturbative quantum dynamics in the strong coupling regime of the nonlinear resonance, taking into account quantization, dissipation, and fluctuations of all fields. We find analytic solutions for quantum states in the rotating wave approximation which demonstrate tripartite quantum entanglement once the strong coupling regime is reached. We show how the strong coupling at the nonlinear resonance modifies photon emission and vibrational spectra, and how the observed spectra can be used to extract information about relaxation rates and the nonlinear coupling strength in specific systems.