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Observation of the all-optical Stern–Gerlach effect in nonlinear optics


Celebrating its centennial anniversary, the Stern–Gerlach experiment has proven to be one of the cornerstones of quantum mechanics, unravelling the quantized nature of the spin angular momentum, and being used in various applications ranging from matter-wave interferometry to weak measurements. Here we report an analogous all-optical Stern–Gerlach experiment in nonlinear optics, where the frequency of light acts as a pseudospin. We observe the splitting of light into two beams, each comprising a frequency-bin superposition, in the presence of a nonlinear coupling gradient. We further realize the phase-sensitive deflection of a distinct frequency-bin superposition into a single direction. Our work constitutes a frequency-domain all-optical coherent deflection of light, offering large bandwidths, fast switching rates and tunability, which are valuable for both classical and quantum information. Furthermore, our findings serve as experimental proof of concept for the emulation of spin transport phenomena using nonlinear optics.

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Fig. 1: Original and all-optical SG experiments.
Fig. 2: Experimental set-up of the all-optical SG effect.
Fig. 3: Far-field splitting for the idler input state |ωi〉.
Fig. 4: Coherent deflection of frequency-superposition eigenstates.


  1. Gerlach, W. & Stern, O. Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld. Z. Phys. 9, 349–352 (1922).

    ADS  Article  Google Scholar 

  2. Machluf, S., Japha, Y. & Folman, R. Coherent Stern–Gerlach momentum splitting on an atom chip. Nat. Commun. 4, 2424 (2013).

    ADS  Article  Google Scholar 

  3. Scully, M. O., Lamb, W. E. & Barut, A. Theory of the Stern-Gerlach apparatus. Found. Phys. 17, 575–583 (1987).

    ADS  MathSciNet  Article  Google Scholar 

  4. Englert, B.-G., Schwinger, J. & Scully, M. O. Is spin coherence like Humpty-Dumpty? I. Simplified treatment. Found. Phys. 18, 1045–1056 (1988).

  5. Chormaic, S. N. et al. Atomic Stern-Gerlach interferences with time-dependent magnetic fields. Phys. Rev. Lett. 72, 1–4 (1994).

    ADS  Article  Google Scholar 

  6. Viaris de Lesegno, B. et al. Stern Gerlach interferometry with metastable argon atoms: an immaterial mask modulating the profile of a supersonic beam. Eur. Phys. J. D 23, 25–34 (2003).

    ADS  Article  Google Scholar 

  7. Amit, O. et al. T3 Stern-Gerlach matter-wave interferometer. Phys. Rev. Lett. 123, 083601 (2019).

  8. Boustimi, M. et al. Atomic interference patterns in the transverse plane. Phys. Rev. A 61, 033602 (2000).

    ADS  Article  Google Scholar 

  9. Aharonov, Y., Albert, D. Z. & Vaidman, L. How the result of a measurement of a component of the spin of a spin-1/2 particle can turn out to be 100. Phys. Rev. Lett. 60, 1351–1354 (1988).

    ADS  Article  Google Scholar 

  10. Bose, S. et al. Spin entanglement witness for quantum gravity. Phys. Rev. Lett. 119, 240401 (2017).

  11. Chen, Z. & Huang, G. Stern–Gerlach effect of multi-component ultraslow optical solitons via electromagnetically induced transparency. J. Opt. Soc. Am. B 30, 2248–2256 (2013).

    Google Scholar 

  12. Cook, R. J. Optical Stern-Gerlach effect. Phys. Rev. A 35, 3844–3848 (1987).

    ADS  Article  Google Scholar 

  13. Hang, C. & Huang, G. Stern-Gerlach effect of weak-light ultraslow vector solitons. Phys. Rev. A 86, 043809 (2012).

    ADS  Article  Google Scholar 

  14. Guo, Y., Zhou, L., Kuang, L.-M. & Sun, C. P. Magneto-optical Stern–Gerlach effect in an atomic ensemble. Phys. Rev. A 78, 013833 (2008).

    ADS  Article  Google Scholar 

  15. Liu, Q., Li, N. & Tan, C. All-optical logic gate based on manipulation of surface polaritons solitons via external gradient magnetic fields. Phys. Rev. A 101, 023818 (2020).

    ADS  Article  Google Scholar 

  16. Edelstein, S. et al. Magneto-optical Stern-Gerlach forces and nonreciprocal torques on small particles. Phys. Rev. Res. 1, 013005 (2019).

    Article  Google Scholar 

  17. Karpa, L. & Weitz, M. A Stern–Gerlach experiment for slow light. Nat. Phys. 2, 332–335 (2006).

    Article  Google Scholar 

  18. Sleator, T., Pfau, T., Balykin, V., Carnal, O. & Mlynek, J. Experimental demonstration of the optical Stern–Gerlach effect. Phys. Rev. Lett. 68, 1996 (1992).

    ADS  Article  Google Scholar 

  19. Kravets, N., Aleksanyan, A. & Brasselet, E. Chiral optical Stern-Gerlach Newtonian experiment. Phys. Rev. Lett. 122, 024301 (2019).

    ADS  Article  Google Scholar 

  20. Arteaga, O., Garcia-Caurel, E. & Ossikovski, R. A Stern-Gerlach experiment with light: separating photons by spin with the method of A. Fresnel. Opt. Express 27, 4758–4768 (2019).

    ADS  Article  Google Scholar 

  21. Shaked, Y. et al. Lifting the bandwidth limit of optical homodyne measurement with broadband parametric amplification. Nat. Commun. 9, 609 (2018).

    ADS  Article  Google Scholar 

  22. Clemmen, S., Farsi, A., Ramelow, S. & Gaeta, A. L. Ramsey interference with single photons. Phys. Rev. Lett. 117, 223601 (2016).

    ADS  Article  Google Scholar 

  23. Joshi, C. et al. Frequency-domain quantum interference with correlated photons from an integrated microresonator. Phys. Rev. Lett. 124, 143601 (2020).

  24. Lu, H.-H. et al. Electro-optic frequency beam splitters and tritters for high-fidelity photonic quantum information processing. Phys. Rev. Lett. 120, 030502 (2018).

    ADS  Article  Google Scholar 

  25. Imany, P. et al. Frequency-domain Hong–Ou–Mandel interference with linear optics. Opt. Lett. 43, 2760–2763 (2018).

    Article  Google Scholar 

  26. Kues, M. et al. Quantum optical microcombs. Nat. Photon. 13, 170–179 (2019).

    ADS  Article  Google Scholar 

  27. Karnieli, A. & Arie, A. Frequency domain Stern–Gerlach effect for photonic qubits and qutrits. Optica 5, 1297–1303 (2018).

    Article  Google Scholar 

  28. Karnieli, A. & Arie, A. All-optical Stern-Gerlach effect. Phys. Rev. Lett. 120, 053901 (2018).

    ADS  Article  Google Scholar 

  29. Brackett, C. A. Dense wavelength division multiplexing networks: principles and applications. IEEE J. Sel. Areas Commun. 8, 948–964 (1990).

    ADS  Article  Google Scholar 

  30. Suchowski, H., Porat, G. & Arie, A. Adiabatic processes in frequency conversion. Laser Photon. Rev. 8, 333–367 (2014).

    ADS  Article  Google Scholar 

  31. Suchowski, H., Oron, D., Arie, A. & Silberberg, Y. Geometrical representation of sum frequency generation and adiabatic frequency conversion. Phys. Rev. A 78, 063821 (2008).

  32. Karnieli, A. & Arie, A. Fully controllable adiabatic geometric phase in nonlinear optics. Opt. Express 26, 4920–4932 (2018).

    Article  Google Scholar 

  33. Li, Y. et al. Adiabatic geometric phase in fully nonlinear three-wave mixing. Phys. Rev. A 101, 033807 (2020).

    ADS  Article  Google Scholar 

  34. Karnieli, A., Trajtenberg-Mills, S., Di Domenico, G. & Arie, A. Experimental observation of the geometric phase in nonlinear frequency conversion. Optica 6, 1401–1405 (2019).

    ADS  Article  Google Scholar 

  35. Karnieli, A., Tsesses, S., Bartal, G. & Arie, A. Emulating spin transport with nonlinear optics, from high-order skyrmions to the topological Hall effect. Nat. Commun. 12, 1092 (2021).

    ADS  Article  Google Scholar 

  36. Westerberg, N. et al. Synthetic magnetism for photon fluids. Phys. Rev. A 94, 023805 (2016).

    ADS  Article  Google Scholar 

  37. Everschor-Sitte, K. & Sitte, M. Real-space Berry phases: skyrmion soccer (invited). J. Appl. Phys. 115, 172602 (2014).

  38. Boyd, R. W. Nonlinear Optics (Academic Press, 2008).

  39. Karnieli, A., Tsesses, S., Kaminer, I., Bartal, G. & Arie, A. Nonlinear optical spintronics: topological Hall effect and Anderson localization. In Conference on Lasers and Electro-Optics FTh1J.2 (Optica Publishing Group, 2021).

  40. Griffiths, D. J. & Schroeter, D. F. Introduction to Quantum Mechanics (Cambridge Univ. Press, 2018).

  41. Bruno, P., Dugaev, V. K. & Taillefumier, M. Topological Hall effect and Berry phase in magnetic nanostructures. Phys. Rev. Lett. 93, 096806 (2004).

    ADS  Article  Google Scholar 

  42. Marte, M. A. M. & Stenholm, S. Paraxial light and atom optics: the optical Schrödinger equation and beyond. Phys. Rev. A 56, 2940–2953 (1997).

    ADS  Article  Google Scholar 

  43. Chávez-Cerda, S., Ruiz, U., Arrizón, V. & Moya-Cessa, H. M. Generation of Airy solitary-like wave beams by acceleration control in inhomogeneous media. Opt. Express 19, 16448–16454 (2011).

    ADS  Article  Google Scholar 

  44. Karnieli, A., Li, Y. & Arie, A. The geometric phase in nonlinear frequency conversion. Front. Phys. 17, 12301 (2022).

    ADS  Article  Google Scholar 

  45. Król, M. et al. Realizing optical persistent spin helix and Stern-Gerlach deflection in an anisotropic liquid crystal microcavity. Phys. Rev. Lett. 127, 190401 (2021).

  46. Kobayashi, T. et al. Frequency-domain Hong–Ou–Mandel interference. Nat. Photon. 10, 441–444 (2016).

    ADS  Article  Google Scholar 

  47. Lifshitz, R., Arie, A. & Bahabad, A. Photonic quasicrystals for nonlinear optical frequency conversion. Phys. Rev. Lett. 95, 133901 (2005).

    ADS  Article  Google Scholar 

  48. Imany, P., Odele, O. D., Jaramillo-Villegas, J. A., Leaird, D. E. & Weiner, A. M. Characterization of coherent quantum frequency combs using electro-optic phase modulation. Phys. Rev. A 97, 013813 (2018).

  49. Margalit, Y. et al. Realization of a complete Stern-Gerlach interferometer: towards a test of quantum gravity. Sci. Adv. 7, eabg2879 (2020).

  50. Sinkin, O. V., Holzlöhner, R., Zweck, J. & Menyuk, C. R. Optimization of the split-step Fourier method in modeling optical-fiber communications systems. J. Lightwave Technol. 21, 61–68 (2003).

    ADS  Article  Google Scholar 

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We acknowledge fruitful discussions with R. Folman. A.K. is supported by the Adams Fellowship of the Israeli Academy of Sciences and Humanities. S.T.-M. is supported by the Shulamit Aloni scholarship. This work was funded by the Israel Science Foundation (grant no. 1415/17).

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Authors and Affiliations



O.Y. and A.K. designed and conceived the experiments. O.Y. performed the experiments and analysed the data, with help from A.K., S.J. and G.D.D. O.Y. and A.K. performed the theoretical calculations. O.Y. and A.K. wrote the manuscript. S.J. designed and built the angle- and space-invariant phase shifter. G.D.D. and S.T.-M contributed to the final manuscript. S.T.-M helped design the adiabatic converter. A.A. supervised the study.

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Correspondence to Ady Arie.

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Nature Photonics thanks Mario Krenn and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Yesharim, O., Karnieli, A., Jackel, S. et al. Observation of the all-optical Stern–Gerlach effect in nonlinear optics. Nat. Photon. 16, 582–587 (2022).

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