Generation of four-partite Greenberger-Horne-Zeilinger and W states by using a high-finesse bimodal cavity

We propose two 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 nonclassical 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.