Greenberger-Horne-Zeilinger state generation of three atoms trapped in two remote cavities

We consider a system composed of a single-atom-trapped cavity (A) and a remote two-atom-trapped cavity (B) which are connected by an optical fibre. It is shown that a shared Greenberger-Horne-Zeilinger (GHZ) state of the three atoms can be deterministically generated by controlling the time of interaction or via the adiabatic passage based on this system. The influence of various decoherence processes such as spontaneous emission and photon loss on the fidelity is also investigated. It is found that our schemes can be realized with high fidelity even when these decoherence processes are considered.