  We investigate the nonlinear interaction between a squeezed cavity mode and a
mechanical mode in an optomechanical system (OMS) that allows us to selectively
obtain either a radiation-pressure coupling or a parametric-amplification
process. The squeezing of the cavity mode can enhance the interaction strength
into the single-photon strong-coupling regime, even when the OMS is originally
in the weak-coupling regime. Moreover, the noise of the squeezed mode can be
suppressed completely by introducing a broadband-squeezed vacuum that is
phase-matched with the parametric amplification that squeezes the cavity mode.
This proposal offers an alternative approach to control OMS using a squeezed
cavity mode, which should allow single-photon quantum processes to be
implemented with currently available optomechanical technology. Potential
applications range from engineering single-photon sources to nonclassical
phonon states.
