  Squeezing of quantum fluctuation plays an important role in fundamental
quantum physics and has marked influence on ultrasensitive detection. We
propose a scheme to generate and enhance the squeezing of mechanical mode by
exposing the optomechanical system to a non-Markovian environment. It is shown
that the effective parametric resonance term of mechanical mode can be induced
due to the interaction with cavity and non-Markovian reservoir, thus resulting
in quadrature squeezing of the mechanical resonator. And jointing the two kinds
of interactions can enhance the squeezing effect. Comparing with the usual
Markovian regime, we can obtain stronger squeezing, and significantly the
squeezing can approach a low asymptotic stable value.
