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

TL;DR

This paper explores entanglement in hybrid optomechanical cavities with BEC atoms, analyzing bipartite and tripartite entanglement generation via Bell detection, highlighting the effects of atomic collisions and weak photon-atom coupling.

Contribution

It introduces a scheme for entanglement swapping in hybrid optomechanical systems involving BECs, moving mirrors, and optical modes, under Gaussian state assumptions.

Findings

Atomic collisions affect BEC entanglement behavior.

Bell measurement enables remote entanglement generation.

Tripartite entanglement can be established between distant systems.

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.