Scheme for generation of four-atom Greenberger-Horne-Zeilinger states in an optical cavity

We propose a scheme for generating maximally GHZ state for four atoms trapped in a two-mode optical cavity via combination of cavity QED and linear optics system. The GHZ state can be not only generated deterministically with a single resonant interaction in cavity QED, but also can be prepared probabilistically based on cavity QED and linear optics elements. The fidelity of the entangled states is not affected by the atomic spontaneous, cavity decay, and imperfection of the photon-detectors. Finally, we briefly analyze and discuss the experimental feasibility of the proposed scheme.