  The nonlinear quantum regime is crucial for implementing interesting quantum
effects, which have wide applications in modern quantum science. Here we
propose an effective method to reach the nonlinear quantum regime in a
modulated optomechanical system (OMS), which is originally in the weak-coupling
regime. The mechanical spring constant and optomechanical interaction are
modulated periodically. This leads to the result that the resonant
optomechanical interaction can be effectively enhanced into the single-photon
strong-coupling regime by the modulation-induced mechanical parametric
amplification. Moreover, the amplified phonon noise can be suppressed
completely by introducing a squeezed vacuum reservoir, which ultimately leads
to the realization of photon blockade in a weakly coupled OMS. The reached
nonlinear quantum regime also allows us to engineer the nonclassical states
(e.g., Schr\"{o}dinger cat states) of cavity field, which are robust against
the phonon noise. This work offers an alternative approach to enhance the
quantum nonlinearity of an OMS, which should expand the applications of cavity
optomechanics in the quantum realm.
