Quantum transient heat transport in hyper-parametric oscillator

We explore the nonequilibrium quantum heat transport of a nonlinear bosonic system in the presence of hyper-parametric oscillation, using degenerate spontaneous four-wave mixing (SFWM) occurring in two cavities. We estimate thermodynamic response analytically by constructing su(2) algebra of nonlinear Hamiltonian and predict that the system exhibits the negative energy gap mode. Excitation mode including a non-uniform energy gap with the ground-state transition in this specific form of the interaction causes the transition of transient heat current enabling the system to cool down, and mode mixing effect unlike pure linear coupling in the presence of symmetric coupling between the system and the bath. We then show this numerically for single and two baths cases by considering the non-equilibrium situation and obtain the notion of mode mixing effect in the appearance of the metastable state by comparing the thermodynamic response of a generic nonlinear interactions, e.g., Bose-Hubbard type interaction induced via cross-phase modulation (XPM). We believe that SFWM in the strong-coupling regime can be applicable to initialize of the quantum state exhibiting quantum coherence by the cooling process.