Abstract
We consider a three-mode optomechanical system in which two mechanical oscillators are independently coupled to a cavity mode driven by two controllable lasers. By controlling the two-tone driving, one can prepare the entanglement and Einstein-Podolsky-Rosen (EPR) steering of two mechanical modes, in which the cavity mode acts as a single reservoir to cool two Bogoliubov modes. We find that the direction of EPR steering can be manipulated effectively by adjusting the damping rates and the thermal noises of two mechanical modes. In addition, we show that the entanglement and EPR steering between two mechanical modes can be enhanced by adding a parametric amplifier (PA) into the cavity. The effects of the strength and phase of the PA on the mechanical entanglement and EPR steering are analyzed and discussed in detail. Meanwhile, the additional PA can also expand the region of the one-way steering and strengthen the robustness of the entanglement and EPR steering against the thermal noise. The present scheme may provide effective resources for quantum information processing.
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