  In the usual optomechanical cooling, even if the system has no thermal
component, it still has a quantum limit-known as the quantum backaction limit
(QBL)-on the minimum phonon number related to shot noise. By studying the
side-band cooling regime in optomechanical system (OMS), we find that the
cooling can be improved significantly when the frequency modulation (FM) that
can suppress the Stokes heating processes is introduced into the system. We
analyze and demonstrate the reasons of the phonon number below the QBL
redefined in the whole stable region of the standard OMSs. The above analyses
are further checked by numerically solving the differential equations of second
order moments derived from the quantum master equation with broad system
parameters, ranging from weak coupling (WC) to ultra-strong coupling (USC) and
resolved side-band (RSB) to unresolved side-band (USB) regimes. Comparing with
the cases of those without FM, the stable ground-state cooling can also be
achieved even in the conventional unstable region.
