- Open Access
Reversible optical nonreciprocity and its scaling optimization in cold atoms via coherently induced four-wave mixing
Phys. Rev. Research 8, 023212 – Published 27 May, 2026
DOI: https://doi.org/10.1103/t29c-cm3b
Abstract
We present a further investigation on the optical nonreciprocity based on four-wave mixing (FWM) by leveraging coherently driven cold atoms, as a beneficial supplement to the usual cavity-waveguide solution in virtue of the on-demand tunability and broadband advantage. We consider two parameter regimes unexplored yet, where the probe and coupling fields are set with vanishing or large detunings while the dressing field is kept on resonance. Numerical results reveal that the forward (backward) probe exhibits a high transmittance (is strongly absorbed) in the resonant regime, but may be largely converted into an FWM field (propagate almost freely) in the far-detuned regime. The optimization of such a reversible unidirectional transmission featured by large isolation ratios and low insertion losses can be attained only when the coupling and dressing fields fulfill different scaling relations in amplitude, which has been well explained via analytical results. It is also viable to achieve reversible unidirectional transmission for a probe field of fixed large detunings by simply tuning the coupling field in a wide spectral range. Our findings provide additional insights into the FWM-based optical nonreciprocity and may enable more powerful unidirectional devices in quantum networks.
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References (60)
- D. Jalas, A. Petrov, M. Eich, W. Freude, S. Fan, Z. Yu, R. Baets, M. Popović, A. Melloni, J. D. Joannopoulos, M. Vanwolleghem, C. R. Doerr, and H. Renner, What is—and what is not—an optical isolator, Nat. Photon. 7, 579 (2013).
- C. Caloz, A. Alù, S. Tretyakov, D. Sounas, K. Achouri, and Z.-L. Deck-Léger, Electromagnetic nonreciprocity, Phys. Rev. Appl. 10, 047001 (2018).
- L. Fan, J. Wang, L. T. Varghese, H. Shen, B. Niu, Y. Xuan, A. M. Weiner, and M. Qi, An all-silicon passive optical diode, Science 335, 447 (2012).
- Y. Hadad and B. Z. Steinberg, Magnetized spiral chains of plasmonic ellipsoids for one-way optical waveguides, Phys. Rev. Lett. 105, 233904 (2010).
- F. D. M. Haldane and S. Raghu, Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry, Phys. Rev. Lett. 100, 013904 (2008).
- L. Bi, J. Hu, P. Jiang, D. H. Kim, G. F. Dionne, L. C. Kimerling, and C. Ross, On-chip optical isolation in monolithically integrated non-reciprocal optical resonators, Nat. Photon. 5, 758 (2011).
- D. Dai, J. Bauters, and J. E. Bowers, Passive technologies for future large-scale photonic integrated circuits on silicon: Polarization handling, light non-reciprocity and loss reduction, Light: Sci. Appl. 1, e1 (2012).
- N. A. Estep, D. L. Sounas, J. Soric, and A. Alù, Magnetic-free non-reciprocity and isolation based on parametrically modulated coupled-resonator loops, Nat. Phys. 10, 923 (2014).
- H. Li, S. Yin, and A. Alù, Nonreciprocity and Faraday rotation at time interfaces, Phys. Rev. Lett. 128, 173901 (2022).
- H. Ramezani, P. K. Jha, Y. Wang, and X. Zhang, Nonreciprocal localization of photons, Phys. Rev. Lett. 120, 043901 (2018).
- J. Wu and B. Yousefzadeh, Nonreciprocal phase shifts in spatiotemporally modulated systems, Phys. Rev. B 112, 104321 (2025).
- Z. Shen, Y.-L. Zhang, Y. Chen, C.-L. Zou, Y.-F. Xiao, X.-B. Zou, F.-W. Sun, G.-C. Guo, and C.-H. Dong, Experimental realization of optomechanically induced non-reciprocity, Nat. Photon. 10, 657 (2016).
- F. Ruesink, M.-A. Miri, A. Alù, and E. Verhagen, Nonreciprocity and magnetic-free isolation based on optomechanical interactions, Nat. Commun. 7, 13662 (2016).
- G. A. Peterson, F. Lecocq, K. Cicak, R. W. Simmonds, J. Aumentado, and J. D. Teufel, Demonstration of efficient nonreciprocity in a microwave optomechanical circuit, Phys. Rev. X 7, 031001 (2017).
- S. Barzanjeh, M. Wulf, M. Peruzzo, M. Kalaee, P. Dieterle, O. Painter, and J. M. Fink, Mechanical on-chip microwave circulator, Nat. Commun. 8, 953 (2017).
- S.-T. Huang, Y.-B. Qian, Z.-Y. Zhang, L. Sun, B.-P. Hou, and L. Tang, Nonreciprocal photon transport in a chiral optomechanical system, Adv. Quantum Technol. 7, 2400217 (2024).
- K. Fang, J. Luo, A. Metelmann, M. H. Matheny, F. Marquardt, A. A. Clerk, and O. Painter, Generalized non-reciprocity in an optomechanical circuit via synthetic magnetism and reservoir engineering, Nat. Phys. 13, 465 (2017).
- H. Xu, L. Jiang, A. Clerk, and J. Harris, Nonreciprocal control and cooling of phonon modes in an optomechanical system, Nature (London) 568, 65 (2019).
- H. Zhang, X. Shang, Q. Liao, A. Chen, and W. Nie, Nonreciprocal quantum coherence in spinning magnomechanical systems, Phys. Rev. A 109, 013719 (2024).
- S. A. R. Horsley, J.-H. Wu, M. Artoni, and G. C. La Rocca, Optical nonreciprocity of cold atom Bragg mirrors in motion, Phys. Rev. Lett. 110, 223602 (2013).
- D. L. Sounas, C. Caloz, and A. Alù, Giant non-reciprocity at the subwavelength scale using angular momentum-biased metamaterials, Nat. Commun. 4, 2407 (2013).
- L. D. Tzuang, K. Fang, P. Nussenzveig, S. Fan, and M. Lipson, Non-reciprocal phase shift induced by an effective magnetic flux for light, Nat. Photon. 8, 701 (2014).
- L. Feng, M. Ayache, J. Huang, Y.-L. Xu, M.-H. Lu, Y.-F. Chen, Y. Fainman, and A. Scherer, Nonreciprocal light propagation in a silicon photonic circuit, Science 333, 729 (2011).
- X. Liu and J.-H. Wu, Unidirectional and bidirectional photon transport blockade in driven atomic lattices of parity-time antisymmetry, New J. Phys. 26, 013048 (2024).
- L. Jin and Z. Song, Incident direction independent wave propagation and unidirectional lasing, Phys. Rev. Lett. 121, 073901 (2018).
- S. Yang, G. Xu, C. Zhou, M. Liu, L. Qu, J. Chen, J. Li, J. Wu, Z. Li, and C.-W. Qiu, Non-Hermitian thermophotonic funneling via nonreciprocal surface waves, Phys. Rev. Lett. 134, 196901 (2025).
- Z. Zhang, Z. Xu, R. Huang, X. Lu, F. Zhang, D. Li, S. K. Ozdemir, F. Nori, H. Bao, Y. Xiao, B. Chen, H. Jing, and H. Shen, Chirality-induced quantum non-reciprocity, Nat. Photon. 19, 840 (2025).
- X. Lu, W. Cao, W. Yi, H. Shen, and Y. Xiao, Nonreciprocity and quantum correlations of light transport in hot atoms via reservoir engineering, Phys. Rev. Lett. 126, 223603 (2021).
- C. Liang, B. Liu, A.-N. Xu, X. Wen, C. Lu, K. Xia, M. K. Tey, Y.-C. Liu, and L. You, Collision-induced broadband optical nonreciprocity, Phys. Rev. Lett. 125, 123901 (2020).
- L. Chen, J. Li, Z. Zheng, J. Yan, F. Li, Y. Zhang, and Y. Cai, Dissipation-induced transition between optical reciprocity and nonreciprocity, Phys. Rev. A 112, 013116 (2025).
- S. Zhang, G. Lin, Y. Hu, Y. Qi, Y. Niu, and S. Gong, Cavity-free circulator with low insertion loss using hot atoms, Phys. Rev. Appl. 14, 024032 (2020).
- S. Zhang, Y. Hu, G. Lin, Y. Niu, K. Xia, J. Gong, and S. Gong, Thermal-motion-induced non-reciprocal quantum optical system, Nat. Photon. 12, 744 (2018).
- K. Xia, F. Nori, and M. Xiao, Cavity-free optical isolators and circulators using a chiral cross-Kerr nonlinearity, Phys. Rev. Lett. 121, 203602 (2018).
- J. Kim, M. C. Kuzyk, K. Han, H. Wang, and G. Bahl, Non-reciprocal Brillouin scattering induced transparency, Nat. Phys. 11, 275 (2015).
- A. B. Khanikaev and A. Alù, Nonlinear dynamic reciprocity, Nat. Photon. 9, 359 (2015).
- L. Del Bino, J. M. Silver, M. T. Woodley, S. L. Stebbings, X. Zhao, and P. Del’Haye, Microresonator isolators and circulators based on the intrinsic nonreciprocity of the Kerr effect, Optica 5, 279 (2018).
- D. L. Sounas, J. Soric, and A. Alu, Broadband passive isolators based on coupled nonlinear resonances, Nat. Electron. 1, 113 (2018).
- J. Wang, Q. Liu, J. Lin, P. Jin, S. Liu, and K. Zhou, Asymmetric modal coupling in a passive resonator towards integrated isolators, Phys. Rev. A 110, 023520 (2024).
- S. Pontula, S. Vaidya, C. Roques-Carmes, S. Z. Uddin, M. Soljačić, and Y. Salamin, Non-reciprocal frequency conversion in a non-Hermitian multimode nonlinear system, Nat. Commun. 16, 7544 (2025).
- G. Lin, S. Zhang, Y. Hu, Y. Niu, J. Gong, and S. Gong, Nonreciprocal amplification with four-level hot atoms, Phys. Rev. Lett. 123, 033902 (2019).
- Y.-D. Hu and G.-Q. Zhang, Multichannel nonreciprocal amplifications using cesium vapor, Phys. Rev. A 107, 053716 (2023).
- A. M. de las Heras and I. Carusotto, Optical isolators based on nonreciprocal four-wave mixing, Phys. Rev. A 106, 063523 (2022).
- S. Hua, J. Wen, X. Jiang, Q. Hua, L. Jiang, and M. Xiao, Demonstration of a chip-based optical isolator with parametric amplification, Nat. Commun. 7, 13657 (2016).
- Y. Zheng, J. Yang, Z. Shen, J. Cao, X. Chen, X. Liang, and W. Wan, Optically induced transparency in a micro-cavity, Light: Sci. Appl. 5, e16072 (2016).
- C. Li, Q. Yu, Y. Zhang, M. Xiao, and Z. Zhang, Optical isolation with optical parametric amplification in an atomic system, Laser Photonics Rev. 17, 2200267 (2023).
- C. Li, J. Yuan, R. He, J. Yu, Y. Zhang, M. Xiao, K. Xia, and Z. Zhang, Nonreciprocal spontaneous parametric process, Light: Sci. Appl. 14, 200 (2025).
- T. Shui, W.-X. Yang, M.-T. Cheng, and R.-K. Lee, Optical nonreciprocity and nonreciprocal photonic devices with directional four-wave mixing effect, Opt. Express 30, 6284 (2022).
- J. Kitching, Chip-scale atomic devices, Appl. Phys. Rev. 5, 031302 (2018).
- R. Zektzer, N. Mazurski, Y. Barash, and U. Levy, Nanoscale atomic suspended waveguides for improved vapour coherence times and optical frequency referencing, Nat. Photon. 15, 772 (2021).
- P. Skakunenko, D. Bykova, A. Afanasiev, A. Kalmykov, R. Kirtaev, and V. Balykin, Efficient cold atom source from a single-layer atom chip, Chin. Opt. Lett. 22, 060201 (2024).
- R. Calviac, A. Rouxel, S. Charlot, D. Bourrier, A. Arnoult, A. Monmayrant, O. Gauthier-Lafaye, A. Gauguet, and B. Allard, Bose-Einstein-condensate source on an optical-grating-based atom chip for quantum sensor applications, Phys. Rev. Appl. 23, L011001 (2025).
- M. Fleischhauer, A. Imamoglu, and J. P. Marangos, Electromagnetically induced transparency: Optics in coherent media, Rev. Mod. Phys. 77, 633 (2005).
- S. Deng, Z.-Y. Shi, P. Diao, Q. Yu, H. Zhai, R. Qi, and H. Wu, Observation of the Efimovian expansion in scale-invariant Fermi gases, Science 353, 371 (2016).
- H. Zhang, V. Eremeev, J. Wu, M. Orszag, and B. He, Scaling behaviors in optomechanically induced nonlinear oscillation, Phys. Rev. E 111, 014208 (2025).
- Q.-T. Cao, Q.-X. Ji, P.-J. Zhang, C. Wang, H. T. Quan, P. Peng, W. Liu, and Y.-F. Xiao, Power-law scaling of lasing-state switching in optical microcavities, Phys. Rev. Lett. 136, 053803 (2026).
- D. A. Steck, Rubidium 87 D line data, https://steck.us/alkalidata.
- A. Schilke, C. Zimmermann, P. W. Courteille, and W. Guerin, Photonic band gaps in one-dimensionally ordered cold atomic vapors, Phys. Rev. Lett. 106, 223903 (2011).
- A. Schilke, C. Zimmermann, and W. Guerin, Photonic properties of one-dimensionally-ordered cold atomic vapors under conditions of electromagnetically induced transparency, Phys. Rev. A 86, 023809 (2012).
- M. Frometa, J. P. Lopez, and J. W. R. Tabosa, Magnetically assisted optical gain in Zeeman degenerate two-level systems of cold atoms, Opt. Commun. 433, 111 (2019).
- D. H. Fernandes, R. S. N. Moreira, J. C. de Aquino Carvalho, and J. P. Lopez, Optical gain in a degenerate two-level system in the presence of a transverse magnetic field, Opt. Commun. 565, 130645 (2024).