Optomechanical two-photon hopping

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 we quantize the system and show this purely quantum feature. This opens the possibility to investigate a new mechanism of photon-pair propagation in optomechanical lattices.