Vacuum-fluctuation-mediated phonon heat transfer in a coupled optomechanical system

Vacuum is usually regarded as a thermally insulating medium, and heat transfer across vacuum is commonly associated with thermal radiation. In conventional vacuum heat transfer, energy exchange is mainly achieved through electromagnetic fluctuations between matter. In this paper, we investigate a new, to the best of our knowledge, structure: a pair of coupled optomechanical systems in which heat transfer channels are constructed using optical vacuum fluctuations. We find that even when both cavities are in an optical vacuum state, radiation pressure interaction combined with inter-cavity photon tunneling can induce effective coupling between two spatially separated mechanical oscillators via virtual photons, thereby achieving steady-state phonon heat transfer between their heat reservoirs. We further find that effective detuning and induced coupling can be controlled by cavity length and photon tunneling intensity, and that in the degenerate state, heat flux and dissipation exhibit a non-monotonic relationship, reaching a maximum at γ=2|ξ|. These results elucidate the role of vacuum fluctuations in optomechanical heat transfer and provide a feasible pathway for tunable quantum thermal devices.