Optomechanical dynamics in the mathcal{PT}- and broken-mathcal{PT}-symmetric regimes

We theoretically study the dynamics of typical optomechanical systems, consisting of a passive optical mode and an active mechanical mode, in the mathcal{PT}- and broken-mathcal{PT}-symmetric regimes. By fully analytical treatments for the dynamics of the average displacement and particle numbers, we reveal the phase diagram under different conditions and the various regimes of both mathcal{PT}-symmetry and stability of the system. We find that by appropriately tuning either mechanical gain or optomechanical coupling, both phase transitions of the mathcal{PT}-symmetry and stability of the system can be flexibly controlled. As a result, the dynamical behaviors of the average displacement, photons, and phonons are radically changed in different regimes. Our study shows that mathcal{PT}-symmetric optomechanical devices can serve as a powerful tool for the manipulation of mechanical motion, photons, and phonons.