Cavity-assisted squeezing of a mechanical oscillator

We investigate the creation of squeezed states of a vibrating membrane or a movable mirror in an optomechanical system. An optical cavity is driven by the squeezed light and couples via the radiation pressure to the membrane or mirror, effectively providing a squeezed heat bath for the mechanical oscillator. Under the conditions of laser cooling to the ground state, we find an efficient transfer of squeezing with roughly 60% of light squeezing conveyed to the membrane or mirror (on a dB scale). We determine the requirements on the carrier frequency and the bandwidth of squeezed light. Beyond the conditions of ground-state cooling, we predict mechanical squashing to be observable in current systems.