Manipulation of nanomechanical resonator via shaking optical frequency

In the usual optomechanical systems, the stability of the systems severely limits those researches of the macroscopic quantum effects. We study a usual cavity optomechanical system where the frequency of the optical mode is shaken periodically. We find that, when the optical shaking frequency is large enough, the shake of the optical mode can stabilize the system. That means we can study the macroscopic quantum effects of the mechanical resonator even in the strong coupling region where the standard optomechanical systems are always unstable. As examples, we study the ground-state cooling of the mechanical resonator and the entanglement between the optical and mechanical modes in the conventional unstable region, and the results indicate that the final mean phonon number and entanglement not only can be achieved but also can be modulated by the optical shaking parameters. Our proposal provides a method to study the macroscopic quantum effects even in conventional unstable region.