Abstract
In this paper, firstly, we consider bipartite entanglement between each part of an optomechanical cavity composed of one dimensional Bose-Einstein condensate (BEC). we investigate atomic collision on the behavior of the BEC in the week photon-atom coupling constant, and use Bogoliubov approximation for the BEC. Secondly under above condition, we propose a scheme for entanglement swapping protocol wich involves tripartite systems. In our investigation, we consider a scenario where BECs, moving mirrors, and optical cavity modes are given in a Gaussian state with a covariance matrix (CM). By applying the Bell measurment to the output optical field modes, we show how the remote entanglement between two BECs, two moving mirrors, and BEC-mirror modes in different optomechanical cavity can be generated.
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