  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.
