Towards correlated photon triplets using six-wave mixing in a cold atomic ensemble

While correlated photon pairs have been extensively investigated in various schemes, like spontaneous down-conversion in nonlinear medium and four-wave mixing from an atomic ensemble, the direct generation of correlated photon triplets is still challenging due to its weak nonlinearities and stringent phase matching requirements. Here, we explore a new approach for directly generating correlated photon triplets from a phase-matched parametric nonlinear process in a Rb⁸⁷ cold atom ensemble. We propose a scheme to integrate electromagnetically-induced-transparency-based (EIT-based) photon pair generation in double-Λ energy levels with a four-wave mixing process in ladder energy levels. This results in a higher-order nonlinear parametric process referred to as six-wave mixing. The correlated photon triplets generated through this method have the potential to form a Greenberger-Horne-Zeilinger state of light, providing a distinct quantum source for investigating quantum entanglement and potential uses in three-party quantum communication protocols. Additionally, the narrow bandwidth of the generated photons, derived from the atomic natural linewidth, makes them appropriate for direct interaction with atoms. Therefore they have potential applications in quantum networks utilizing atom-based quantum repeaters.