Compact generation of a two-photon multipath Dicke state from a single χ⁽²⁾ nonlinear photonic crystal

Multipartite quantum entanglement is a powerful resource for enriching the functionality of quantum computation and quantum communication. In this Letter, we propose a new method to generate a two-photon multipath Dicke state with concurrent spontaneous parametric downconversion processes from a single periodically poled nonlinear photonic crystal. We design the poling structure to produce a three-path Dicke state where three quasi-phase-matching conditions are fulfilled simultaneously by a hybrid one- and two-dimensionally poled nonlinear photonic crystal. We use genuine multipartite entanglement concurrence to quantify the entanglement of the Dicke state. Using a more complicated poling configuration like multiple-periodically poled two-dimensional nonlinear photonic crystal, we can also produce four-path, five-path, or multipath Dicke states by a single crystal. The multiple-periodically poled two-dimensional nonlinear photonic crystal provides a new method, to the best of our knowledge, for the integrated generation of multipartite quantum light sources.