Cooling and thermophonon transports in nonlinear optomechanical systems

We propose theoretically a nonlinear optomechanical system with a suspended graphene sheet, a single atom and a degenerate optical parametric amplifier to explore the ground-state cooling of the graphene oscillator and the steady-state thermophonon flux flowing from the thermal bath of the graphene oscillator into the optomechanical system. We find that the cooling properties of the graphene oscillator and the magnitude of thermophonon flux can be controlled flexibly by changing the vacuum coupling strength between the trapped atom and the nearby graphene sheet. In particular, the maximum thermophonon flux always corresponds to the minimum effective phonon number of the graphene sheet, which attributes to the optimal transfer of thermal noise energy at the optimal cavity field detuning. We also investigate in detail the influence of the parametric gain, the pump phase, the oscillating frequency, the position of the atom and the temperature on the cooling and the thermophonon flux. The results obtained here have potential applications in evaluating thermal noise energy transport and preparation of functional thermal devices. •A nonlinear optomechanical system with vacuum-induced atom–graphene coupling is proposed.•The vacuum effect of single atom mediates the coupling between a graphene sheet and the atomic mechanical motion.•A degenerate optical parametric amplifier enhances the nonlinearity of the hybrid system.•Optimal cooling characteristics of the graphene sheet and the corresponding thermophonon flux are obtained.