  We propose a method to generate quadrature squeezed states of a moving mirror
in a Fabry-Perot cavity. This is achieved by exploiting the fact that when the
cavity is driven by an external field with a large detuning, the moving mirror
behaves as a parametric oscillator. We show that parametric resonance can be
reached approximately by modulating the driving field amplitude at a frequency
matching the frequency shift of the mirror. The parametric resonance leads to
an efficient generation of squeezing, which is limited by the thermal noise of
the environment.
