  Noise usually has an unwelcome influence on system performance. For instance,
noise inevitably affects the low-frequency mechanical freedom in optomechanical
experiments. However, we investigate here the beneficial effects of thermal
noise on a basic optomechanical system with parametric instability. In a regime
near parametric instability, it is found that thermal noise in the mechanical
freedom can sustain long-term quasi-coherent oscillations when the system would
otherwise remain in the equilibrium state. In an overlapping regime of
parametric instability and bistability, intermittent switching between a
self-sustained oscillating state and an equilibrium can be induced by adding a
certain amount of noise. When a subthreshold periodic signal is applied to the
mechanics, the switching between the self-sustained oscillations and the
equilibrium exhibits good periodicity at a rate that is synchronized to the
signal frequency, resulting in a significant amplification of the signal. Our
results deepen the understanding of the interplay between optomechanical
nonlinearity and noise and provide theoretical guidance for experimental
observation of noise-induced beneficial phenomena in optomechanics.
