  We investigate the creation of squeezed states of a vibrating membrane or a
movable mirror in an opto-mechanical system. An optical cavity is driven by
squeezed light and couples via radiation pressure to the membrane/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/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.
