  In this paper, we theoretically investigate the displacement and momentum
fluctuations spectra of the movable mirror in a standard optomechanical system
driven by a finite bandwidth squeezed vacuum light accompanying a coherent
laser field. Two cases in which the squeezed vacuum is generated by degenerated
and non-degenerate parametric oscillators (DPO and NDPO) are considered. We
find that for the case of finite bandwidth squeezed vacuum injection, the two
spectra exhibit unique features, which strongly differ from those of broadband
squeezing excitation. In particular, the spectra exhibit a three-peaked and a
four-peaked structure, respectively, for the squeezing injection from DPO and
NDPO. Besides, some anomalous characteristics of the spectra such as
squeezing-induced pimple, hole burning, and dispersive profile are found to be
highly sensitive to the squeezing parameters and the temperature of the mirror.
We also evaluate the mean-square fluctuations in position and momentum
quadratures of the movable mirror and analyze the influence of the squeezing
parameters of the input field on the mechanical squeezing. It will be shown
that the parameters of driven squeezed vacuum affects the squeezing. We find
the optimal mechanical squeezing is achievable via finite bandwidth squeezed
vacuum injection which is affected by the intensity of squeezed vacuum. We also
show that the phase of incident squeezed vacuum determines whether position or
momentum squeezing occurs. Our proposed scheme not only provides a feasible
experimental method to detect and characterize squeezed light by optomechanical
systems, but also suggests a way for controllable transfer of squeezing from an
optical field to a mechanical oscillator.
