Explanation of the Observed Energy Exchange through the vacuum in Optomechanics

In cavity optomechanics, the standard large-detuning regime is commonly described by retaining only the radiation-pressure interaction, while higher-order mirror--field interactions are assumed to be negligible. This approximation, however, fails to provide a microscopic explanation for the vacuum-mediated heat transfer observed between the mechanical membranes in the experiment of Fong, et.al.,[Nature 576, 243 (2019)], whose physical origin has remained under active debate. Here, using a fully quantum model, we show that the neglected higher-order optomechanical interactions naturally generate phonon-phonon coupling and quantitatively account for the observed energy exchange within the standard optomechanical framework. Building on this microscopic description, we further propose a protocol in which phonon-phonon interaction drives a cyclic process enabling net work extraction. Our results establish the fundamental role of higher-order optomechanical interactions and provide a microscopic framework for describing next-generation optomechanical experiments beyond the linear approximation.