  Strong quantum nonlinearity gives rise to many interesting quantum effects
and has wide applications in quantum physics. Herewe investigate the quantum
nonlinear effect of an optomechanical system (OMS) consisting of both linear
and quadratic coupling. Interestingly, a controllable optomechanical
nonlinearity is obtained by applying a driving laser into the cavity. This
controllable optomechanical nonlinearity can be enhanced into a strong coupling
regime, even if the system is initially in the weak-coupling regime. Moreover,
the system dissipation can be suppressed effectively, which allows the
appearance of phonon sideband and photon blockade effects in the weak-coupling
regime. This work may inspire the exploration of a dual-coupling optomechanical
system as well as its applications in modern quantum science.
