Near-maximal Bell inequality violation of time–frequency entangled photon pairs from a warm atomic vapor

Abstract

The realization of high-quality and stable entangled states is crucial for the advancement of quantum information science and technology. The entangled photons generated from a warm atomic ensemble exhibit high spectral purity and indistinguishability, offering significant potential for atom–photon-based quantum networks. We report high-quality time–frequency entangled continuous-wave (CW) photon pairs via a spontaneous four-wave mixing process in the cascade-type atomic transition of 5S1/2–5P3/2–5D5/2 from a warm 87Rb atomic ensemble. We observed Franson interference with the visibility of 99.6(8) % using two independent Franson interferometers, obtained by post-selecting the temporally indistinguishable two-photon events. The interferometer phases were actively stabilized using the reference laser frequency-locked to the 133Cs (6S1/2-6P3/2) transition. Beyond stabilizing the interferometers, the active control of these phases allowed us to measure the CHSH S-value directly and achieve a near-maximal Bell inequality violation with S = 2.83(7). This result demonstrates that warm atomic ensembles can serve as bright sources of time–frequency entanglement, which combined with active interferometer stabilization enable stable high-visibility operation for practical applications in quantum network.