Mechanical PT symmetry in coupled optomechanical systems

We propose to realize mechanical parity-time PT symmetry in two coupled optomechanical systems. To provide gain to one mechanical resonator and the same amount of damping to the other, the two optical cavities should be driven by blue- and red-detuned laser fields, respectively. After adiabatically eliminating the degrees of freedom of the cavity modes, we derive a formula to describe the PT symmetry of two coupled mechanical resonators. Mechanical PT-symmetric phase transition is demonstrated by the dynamical behavior of the mechanical resonators. Moreover, we study the effect of the quantum noises on the dynamical behavior of the mechanical resonators when the system is in the quantum regime.