Phase Control of Stationary Entanglement and Ground-State Cooling of Distant Rotating Mirrors

The realization of the distant entanglement, especially in the macroscopic domain, is crucial for advancing quantum technology. Here, a scheme is presented to enhance the stationary entanglement between two distant rotating mirrors in a cascaded Laguerre-Gaussian cavity optorotational system by adjusting the phase difference between two counterpropagating driving lasers. These findings indicate that the entanglement between two rotating mirrors can be significantly enhanced by increasing the phase difference between two input lasers. Additionally, the maximum entanglement between two rotating mirrors depends on the effective cavity detuning. Furthermore, increasing the phase difference between two input lasers can enhance the robustness of the entanglement between two mechanical modes against the thermal noise of the environment. Moreover, the phonon numbers of the two rotating mirrors can be reduced by controlling the phase difference of input lasers. And the ground-state cooling of the two rotating mirrors can be achieved at two different phase differences of input lasers, whose difference is about pi$\pi$.