Quantum transient heat transport in the hyperparametric oscillator

We explore nonequilibrium quantum heat transport in nonlinear bosonic systems in the presence of a nonKerr-type interaction governed by hyperparametric oscillation due to two-photon hopping between the two cavities. We estimate the thermodynamic response analytically by constructing the su(2) algebra of the nonlinear Hamiltonian and predict that the system exhibits a negative excitation mode. Consequently, this specific form of interaction enables the cooling of the system by inducing a ground-state transition when the number of particles increases, even though the interaction strength is small. We demonstrate a transition of the heat current numerically in the presence of symmetric coupling between the system and the bath and show long relaxation times in the cooling phase. We compare with the Kerr-type Bose-Hubbard form of interaction induced via cross-phase modulation, which does not exhibit any such transition. We further compute the nonequilibrium heat current in the presence of two baths at different temperatures and observe that the cooling effect for the non-Kerr-type interaction persists. Our findings may help in the manipulation of quantum states using the system's interactions to induce cooling.