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.

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From the work by W. Perrie et al. ͓Phys. Rev. Lett. 54, 1790 ͑1985͔͒, it is known that the photon pairs that are emitted in the 2s 1/2 → 1s 1/2 ͑two-photon͒ decay of atomic hydrogen are quantum mechanically correlated, i.e., entangled. However, less information is available about the degree of polarization entanglement between the two photons if an arbitrary geometry is considered for collecting the photons. In this paper, we study the effect of the decay geometry on the degree of polarization entanglement between the two emitted photons. Results are shown for the 2s 1/2 → 1s 1/2 and 3d 5/2 → 1s 1/2 two-photon transitions of atomic hydrogen. The outlined theory is general and can be applied also to heavier elements. To demonstrate the influence of relativistic and multipole effects, results are also shown for the 3d 5/2 → 1s 1/2 transition of hydrogenlike uranium.

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