  We investigate the dynamics of an optomechanical system where a cavity with a
movable mirror involves a degenerate optical parametric amplifier and is driven
by a periodically modulated laser field. Our results show that the cooperation
between the parametric driving and periodically modulated cavity driving
results in a two-fold squeezing on the movable cavity mirror that acts as a
mechanical oscillator. This allows the fluctuation of the mechanical oscillator
in one quadrature (momentum or position) to be reduced to a level that cannot
be reached by solely applying either of these two drivings. In addition to the
fundamental interests, e.g., study of quantum effects at the macroscopic level
and exploration of the quantum-to-classical transition, our results have
potential applications in ultrasensitive sensing of force and motion.
