Optomechanical two-photon hopping

The hopping mechanism plays a key role in collective phenomena emerging many-body physics. ability to create and control systems that display this feature is important for next generation quantum technologies. Here we study two cavities separated by vibrating two-sided perfect mirror show that, within currently available experimental parameters, system displays photon-pair between the electromagnetic resonators. In particular, two-photon not due tunneling, but rather higher-order resonant processes. Starting from classical problem quantize purely feature. This opens possibility investigate new of propagation optomechanical lattices.