Generation of four-partite GHZ and W states by using a high-finesse bimodal cavity

We propose two novel schemes to engineer four-partite entangled Greenberger-Horne-Zeilinger (GHZ) and W states in a deterministic way by using chains of (two-level) Rydberg atoms within the framework of cavity QED. These schemes are based on the resonant interaction of the atoms with a bimodal cavity that simultaneously supports, in contrast to a single-mode cavity, two independent modes of the photon field. In addition, we suggest the schemes to reveal the non-classical correlations for the engineered GHZ and W states. It is shown how these schemes can be extended in order to produce general N-partite entangled GHZ and W states.