Vacuum-Fluctuation-Mediated Phonon Heat Transfer in a Coupled Optomechanical System

We theoretically investigate a quantum heat transfer mechanism mediated by vacuum fluctuations in a pair of optomechanical systems. By combining radiation-pressure interaction and photon tunneling coupling, effective coupling between two mechanical oscillators can be established even when both cavities remain in the vacuum state. Under nonequilibrium steady-state conditions, a persistent heat flux arises. The cavity architecture allows simultaneous control over the detuning and the effective optomechanical coupling via adjustments in cavity length and coupling strength. In the degenerate regime, the system exhibits a non-monotonic dependence of heat flux on dissipation parameter: the thermal current reaches maximum intensity at $\gamma=2|\xi|$ with $\xi$ the vacuum-fluctuation-mediated effective coupling, marking an optimal balance between coherent energy transfer and damping effects. This work provides a new strategy for realizing quantum thermal devices and highlights the crucial role of vacuum fluctuations as a quantum mediator in thermal transport.