Abstract

Cavity optomechanical systems have been widely studied for many of their interesting properties, which can be interpreted with their linearized dynamics. Previously, the genuine nonlinear dynamics of optomechanical systems was only considered for very few phenomena such as self-induced oscillation and optomechanical chaos. Beyond the scope of those previous studies, a phenomenon of frozen mechanical oscillation irrespective of the intensity variation on the driving fields was recently discovered for an optomechanical system under two pump fields having their frequencies properly matched [He et al., Phys. Rev. A 102, 011503(R) (2020)]. Here we significantly advance the study by showing that similar phenomena can manifest under more general conditions for the external driving fields. The mechanical oscillation in such doubly driven optomechanical systems can be locked in either its amplitude or both amplitude and phase. Simultaneous amplitude and phase locking is possible under a specific condition for the difference of the drive frequencies, whenever the drive intensity is sufficiently high. The variations of the phenomena also exist in two coupled cavities containing one mechanical breathing mode.