  Two close parallel mirrors attract due to a small force (Casimir effect)
originating from the electromagnetic quantum vacuum uctuations of the
electromagnetic field. These vacuum uctuations can also induce motional forces
exerted upon one mirror when the other one moves. Here we consider an
optomechanical system consisting of two vibrating mirrors coupled to an optical
resonator. We find that motional forces can determine noticeable coupling rates
between the two spatially separated vibrating mirrors. We show that, by tuning
the two mechanical oscillators into resonance, energy is exchanged between them
at the quantum level. This coherent motional coupling is enabled by the
exchange of virtual photon pairs, originating from the dynamical Casimir
effect. The process proposed here shows that the electromagnetic quantum vacuum
is able to transfer mechanical energy somewhat like an ordinary uid. We show
that this system can also operate as a mechanical parametric down-converter
even at very weak excitations. These results demonstrate that vacuuminduced
motional forces open up new possibilities for the development of optomechanical
quantum technologies.
