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Engineering entanglement mechanically

We propose entanglement for hybrid optomechanical system consisting of Bose-Einstein condensate (BEC) inside a single-mode high-Q Fabry-Perot cavity with a vibrating end mirror (mechanical mirror). The intracavity field couples the vibrating end mirror with collective atomic density of the BEC. We show that the radiation pressure generates the stationary entanglement of three bipartite subsystems, i.e, field-mechanical mirror, field-BEC and mechanical mirror-atoms. The resulting entanglement is fragile with respect to temperature.