Entanglement of two hybrid optomechanical cavities composed of BEC atoms under Bell detection

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 behaviour 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 which 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. By applying the Bell measurement 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.