  We create squeezed light by exploiting the quantum nature of the mechanical
interaction between laser light and a membrane mechanical resonator embedded in
an optical cavity. The radiation pressure shot noise (fluctuating optical force
from quantum laser amplitude noise) induces resonator motion well above that of
thermally driven motion. This motion imprints a phase shift on the laser light,
hence correlating the amplitude and phase noise, a consequence of which is
optical squeezing. We experimentally demonstrate strong and continuous
optomechanical squeezing of 1.7 +/- 0.2 dB below the shot noise level. The peak
level of squeezing measured near the mechanical resonance is well described by
a model whose parameters are independently calibrated and that includes thermal
motion of the membrane with no other classical noise sources.
