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  • Open Access

Optimizing conditional-π phase shift between two weak coherent pulses via a closed double-Λ atomic system

Gyu-Hyeok Lee*, U-Shin Kim*,†, and Yoon-Ho Kim‡

  • *These authors contributed equally to this work.
  • †Contact author: usinkimphysics@gmail.com
  • ‡Contact author: yoonho72@gmail.com
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Phys. Rev. Research 8, 023035 – Published 10 April, 2026

DOI: https://doi.org/10.1103/g75t-x4bj

Abstract

Conditional-π phase shift between two photons is essential for entanglement generation and universal quantum logic. For photons, however, direct conditional controls are not possible and must be mediated by nonlinear media. Achieving such operations for photonic polarization qubits has remained difficult due to intrinsically weak photon-photon nonlinearities in atomic systems. Here, we show that a conditional-π phase shift between two weak coherent pulses can be realized via a cavityless closed double-Λ atomic system, where quantum interference between linear and nonlinear atom-photon interactions enables conditional control. By optimizing the interaction parameters, including amplitude and phase compensations, we identify the conditions for conditional-π phase shift between two weak coherent pulses. Experimentally, we observe the conditional-π phase shift with relative output amplitude 0.74±0.06 and phase shift (0.95±0.03)π between the two-photon amplitudes |HH〉 and |VV〉. A theoretical analysis of Bell-state generation from weak coherent pulses further shows Clauser-Horne-Shimony-Holt inequality violation and nonzero concurrence. Our results clarify both the theoretical requirements and the experimental feasibility of cavityless atom-mediated nonlinearities for photonic quantum logic, establishing a scalable route toward nonlinear quantum photonics.

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Phys. Rev. Research 8, 023035– Published 10 April, 2026
  • Received 10 September 2025
  • Accepted 25 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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