A simple scheme is presented for generating four-photon Greenberger-Horne-Zeilinger states with a large detuned interaction between a three-level atom and two bimodal cavities. In the proposed protocol, the quantum information is encoded on Fock states of the cavity-fields, and the atomic spontaneous emission can be effectively suppressed due to the fact that the excited state of the atom is adiabatically eliminated under the large detuning condition. The detection of the atom can collapse the cavity to the desired state. The experimental feasibilit...
