  Being beneficial for the amplitude modulation of the pump laser, we propose a
simple yet surprisingly effective mechanical squeezing scheme in a standard
optomechanical system. By merely introducing a specific kind of periodic
modulation into the single-tone driving field to cool down the mechanical
Bogoliubov mode, the far beyond 3-dB strong mechanical squeezing can be
engineered without requiring any additional techniques. Specifically, we find
that the amount of squeezing is not simply dependent on the order of magnitude
of the effective optomechanical coupling but strongly on the ratio of sideband
strengths for it. To maximize the mechanical squeezing, we numerically and
analytically optimize this ratio in the steady-state regime, respectively. The
mechanical squeezing engineered in our scheme also has strong robustness and
can survive at a high bath temperature. Compared with previous schemes based on
the two-tone pump technique, our scheme involves fewer external control laser
source and can be extended to other quantum systems to achieve strong squeezing
effect.
