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Quantum Science and Technology

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

Youngwoong Choi, Jinhyuk Bae, Han Seb Moon

Published Aug 21, 2026• 0 citations
Publisher

Abstract

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 5S 1/2 –5P 3/2 –5D 5/2 from a warm 87 Rb 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 133 Cs (6S 1/2 -6P 3/2 ) 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.

DOI
10.1088/2058-9565/ae9cd8

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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 5S 1/2 –5P 3/2 –5D 5/2 from a warm 87 Rb 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 133 Cs (6S 1/2 -6P 3/2 ) 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.
We experimentally demonstrate Franson interference of a time–energy entangled photon pair generated via collective two-photon coherence in the 5S1/2−5P3/2−5D5/2 transition of warm Rb87 atoms. The two unbalanced Michelson interferometers used in our setup are spatially separated in order to understand entanglement as a nonlocal property of the photon pairs from the warm atomic ensemble. We observe a Franson interference fringe with a high visibility of 99.1±1.3% with continuous-wave-mode photon pairs from the cascade-type atomic ensemble. To the best of our knowledge, this work is the first demonstration of the nonlocal two-photon interference experiment in separated photon channels by use of two-photon pairs emitted from a cascade-type atomic system as originally proposed by Franson [Phys. Rev. Lett.62, 2205 (1989)PRLTAO0031-900710.1103/PhysRevLett.62.2205].
Narrowband biphotons from an atomic ensemble are an extraordinary source for quantum information science. The generation of biphotons in the warm atomic system has many applicable prospects for its simplicity, stability, and compactness. In this article we experimentally demonstrate the generation of biphotons from the spontaneous four-wave mixing (SFWM) process in a warm rubidium vapor cell. By performing high-dimensional Bell-type measurements and mutually unbiased measurements, we maximally obtain a three-dimensional orbital-angular-momentum discrete-variable (DV) entangled state. The violation of high-dimensional Bell inequalities shows the great potential of warm atomic systems in generating DV high-dimensional entanglement. Such narrowband photon pairs may find applications in quantum-memory-based quantum communication networks. Through integration with the continuous-variable (CV) entanglement already existing in the same SFWM platform, our results here pave the way to construct atomic-ensemble-based DV-CV hybrid quantum information protocols.
Abstract A Greenberger–Horne–Zeilinger (GHZ) entangled state with a phase is crucial for realizing desired multipartite quantum states for practical applications. Here, it is reported that the violations of the general Bell inequality (GBI) introduced in using the four‐photon polarization‐entangled phase‐GHZ state realized via intrinsic polarization correlation and collective two‐photon coherence in the 5S 1/2 –5P 3/2 –5D 5/2 transition of 87 Rb atoms. The phase‐GHZ state can be achieved by the unitary transformation of only one local phase of the four photons. Theoretically, the GHZ state with the π/4 phase affords maximal violation of the GBI of 2√2 at the local measurement settings of the Pauli operators σ x and σ y . Strong violations of the GBI of the phase‐GHZ state by 47 standard deviations are experimentally demonstrated. In addition to the entanglement witness for the phase‐GHZ state, the results represent a genuine four‐photon entanglement of the phase‐GHZ state, thereby providing a novel resource for realizing photonic quantum computation, magic‐state distillation from entangled states, and quantum networks based on atom–photon interactions.
We report a polarization-entangled photon-pair source obtained via spontaneous four-wave mixing (SFWM) in a Doppler-broadened atomic ensemble of ^{87}Rb atoms using a Sagnac interferometer. Collective two-photon coherence occurs in the Doppler-broadened ladder-type atomic system with bidirectional counterpropagating two-photon resonant pump and coupling fields; hence, polarization-entangled photon pairs are collectively radiated in the phase-matched direction. Without phase stabilization of the interferometry for polarization entanglement, we robustly produce all four Bell states via a polarization Sagnac configuration. The brightness, stability, and temporal purity advantages provided by our polarization-entangled SFWM photon-pair source have very important applications in the context of a practical scalable quantum network.
Photon-pair sources from atomic ensembles are considered essential to the development of quantum science and technology based on atom-photon interfaces. The measurement of spectral-temporal biphoton wave forms is important for the characterization of frequency-time entangled photon pairs. Here, we demonstrate a stimulated measurement of the biphoton spectral wave form (BSW) of narrow-band photon pairs emitted from a Doppler-broadened cascade-type atomic ensemble. A BSW with submegahertz resolution is obtained as a function of the absolute optical frequency determined by atomic transitions, which reveals a spectral shift of approximately 510 MHz from the expected resonance frequency of the $5{P}_{3/2}\ensuremath{-}5{D}_{5/2}$ and $5{S}_{1/2}\ensuremath{-}5{P}_{3/2}$ transitions of 87Rb^{87}\mathrm{Rb}87Rb atoms.
Entanglement swapping forms a key concept in the realization of scalable quantum networks and large-scale quantum communication. For the practical implementation of entanglement swapping, completely autonomous entanglement sources and a joint Bell-state measurement (BSM) between two independent photons are essential. Here, we experimentally demonstrate entanglement swapping between two independent polarization-entangled photon-pair sources obtained via spontaneous four-wave mixing (SFWM) in a Doppler-broadened atomic ensemble of 87 R b atoms. From the joint BSM, we estimate the S parameter in the Clauser–Horne–Shimony–Holt (CHSH) form of Bell’s inequality and confirm the violation of the Bell–CHSH inequality by S = 2.32 ± 0.07 with 4.5 standard deviations. We believe that this work is an important step toward realizing practical scalable quantum networks.