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

9 pages, 4 figures