Abstract
We show that it is possible to generate a quadripartite square graph-state entanglement in two-photon resonant systems. Every vertex of the square represents an optical field and every side stands for the entanglement of the two vertices. Four optical fields of different frequencies are coupled to coherently driven three-level ladder atoms. Through such a system, quantum beats and two-photon resonant interactions combine to cause the collective-mode parametric interactions. This results in the collective-mode entanglement, which corresponds to the square graph-state entanglement of the four individual fields.
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