Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Non-local skyrmions as topologically resilient quantum entangled states of light

Nature Photonics volume 18, pages 258–266 (2024)Cite this article

Subjects

Abstract

In the early 1960s, inspired by developing notions of topological structure, Tony Skyrme suggested that sub-atomic particles can be described as natural excitations of a single quantum field. Although never adopted for its intended purpose, the notion of a skyrmion as a topologically stable field configuration has proven to be highly versatile, finding application in condensed-matter physics, acoustics and more recently, optics, but it has been realized as localized fields and particles in all instances. Here we report the first non-local quantum entangled state with a non-trivial topology that is skyrmionic in nature, even though each individual photon has no salient topological structure. We demonstrate how the topology makes such quantum states robust to smooth deformations of the wavefunction, remaining intact until the entanglement itself vanishes. Our work points to a nascent connection between entanglement classes and topology, opens exciting questions into the nature of map-preserving quantum channels and offers a promising avenue for the preservation of quantum information by topologically engineered quantum states that persist even when entanglement is fragile.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Non-local quantum skyrmions.
Fig. 2: Experimental quantum skyrmion.
Fig. 3: Traversing the quantum skyrmionic landscape.
Fig. 4: Topology of quantum entangled states.
Fig. 5: Quantum topological invariance.

Similar content being viewed by others

Data availability

The data supporting the findings of this study are available from the corresponding author upon reasonable request.

Code availability

The code used to produce the results are available from the corresponding author upon reasonable request.

References

  1. Skyrme, T. H. R. A unified field theory of mesons and baryons. Nucl. Phys. 31, 556–569 (1962).

    MathSciNet  CAS  Google Scholar 

  2. Zahed, I. & Brown, G. The Skyrme model. Phys. Rep. 142, 1–102 (1986).

    ADS  MathSciNet  Google Scholar 

  3. Naya, C. & Sutcliffe, P. Skyrmions and clustering in light nuclei. Phys. Rev. Lett. 121, 232002 (2018).

    ADS  CAS  PubMed  Google Scholar 

  4. Eisenberg, J. & Kälbermann, G. The use of skyrmions for two-nucleon systems. Progr. Part. Nucl. Phys. 22, 1–42 (1989).

    ADS  CAS  Google Scholar 

  5. Shen, Y. et al. Topological quasiparticles of light: optical skyrmions and beyond. Preprint at https://arxiv.org/abs/2205.10329 (2022).

  6. He, C., Shen, Y. & Forbes, A. Towards higher-dimensional structured light. Light Sci. Appl. 11, 205 (2022).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  7. Yu, X. et al. Real-space observation of a two-dimensional skyrmion crystal. Nature 465, 901–904 (2010).

    ADS  CAS  PubMed  Google Scholar 

  8. Fert, A., Cros, V. & Sampaio, J. Skyrmions on the track. Nat. Nanotechnol. 8, 152–156 (2013).

    ADS  CAS  PubMed  Google Scholar 

  9. Fert, A., Reyren, N. & Cros, V. Magnetic skyrmions: advances in physics and potential applications. Nat. Rev. Mater. 2, 17031 (2017).

    ADS  CAS  Google Scholar 

  10. Nagaosa, N. & Tokura, Y. Topological properties and dynamics of magnetic skyrmions. Nat. Nanotechnol. 8, 899–911 (2013).

    ADS  CAS  PubMed  Google Scholar 

  11. Zhang, X. et al. Skyrmion-electronics: writing, deleting, reading and processing magnetic skyrmions toward spintronic applications. J. Phys.: Condens. Matter 32, 143001 (2020).

    ADS  CAS  PubMed  Google Scholar 

  12. Lima Fernandes, I., Blügel, S. & Lounis, S. Spin-orbit enabled all-electrical readout of chiral spin-textures. Nat. Commun. 13, 1576 (2022).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  13. Zheng, F. et al. Skyrmion–antiskyrmion pair creation and annihilation in a cubic chiral magnet. Nat. Phys. 18, 863–868 (2022).

  14. Psaroudaki, C., Hoffman, S., Klinovaja, J. & Loss, D. Quantum dynamics of skyrmions in chiral magnets. Phys. Rev. X 7, 041045 (2017).

    Google Scholar 

  15. Psaroudaki, C. & Panagopoulos, C. Skyrmion helicity: quantization and quantum tunneling effects. Phys. Rev. B 106, 104422 (2022).

    ADS  CAS  Google Scholar 

  16. Lohani, V., Hickey, C., Masell, J. & Rosch, A. Quantum skyrmions in frustrated ferromagnets. Phys. Rev. X 9, 041063 (2019).

    CAS  Google Scholar 

  17. Douçot, B., Goerbig, M. O., Lederer, P. & Moessner, R. Entanglement skyrmions in multicomponent quantum Hall systems. Phys. Rev. B 78, 195327 (2008).

    ADS  Google Scholar 

  18. Froehlich, J. & Marchetti, P. Quantum skyrmions. Nucl. Phys. B 335, 1–22 (1990).

    ADS  MathSciNet  Google Scholar 

  19. Siegl, P., Vedmedenko, E. Y., Stier, M., Thorwart, M. & Posske, T. Controlled creation of quantum skyrmions. Phys. Rev. Research 4, 023111 (2022).

    ADS  CAS  Google Scholar 

  20. Psaroudaki, C. & Panagopoulos, C. Skyrmion qubits: a new class of quantum logic elements based on nanoscale magnetization. Phys. Rev. Lett. 127, 067201 (2021).

    ADS  CAS  PubMed  Google Scholar 

  21. Zhou, H., Polshyn, H., Taniguchi, T., Watanabe, K. & Young, A. Solids of quantum Hall skyrmions in graphene. Nat. Phys. 16, 154–158 (2020).

    CAS  Google Scholar 

  22. Halcrow, C. & Harland, D. Attractive spin-orbit potential from the Skyrme model. Phys. Rev. Lett. 125, 042501 (2020).

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  23. Leslie, L., Hansen, A., Wright, K., Deutsch, B. & Bigelow, N. Creation and detection of skyrmions in a Bose-Einstein condensate. Phys. Rev. Lett. 103, 250401 (2009).

    ADS  CAS  PubMed  Google Scholar 

  24. Ackerman, P. J., Van De Lagemaat, J. & Smalyukh, I. I. Self-assembly and electrostriction of arrays and chains of Hopfion particles in chiral liquid crystals. Nat. Commun. 6, 6012 (2015).

    ADS  CAS  PubMed  Google Scholar 

  25. Ge, H. et al. Observation of acoustic skyrmions. Phys. Rev. Lett. 127, 144502 (2021).

    CAS  PubMed  Google Scholar 

  26. Tsesses, S. et al. Optical skyrmion lattice in evanescent electromagnetic fields. Science 361, 993–996 (2018).

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  27. Du, L., Yang, A., Zayats, A. V. & Yuan, X. Deep-subwavelength features of photonic skyrmions in a confined electromagnetic field with orbital angular momentum. Nat. Phys. 15, 650–654 (2019).

    CAS  Google Scholar 

  28. Gao, S. et al. Paraxial skyrmionic beams. Phys. Rev. A 102, 053513 (2020).

    ADS  CAS  Google Scholar 

  29. Kuratsuji, H. & Tsuchida, S. Evolution of the Stokes parameters, polarization singularities, and optical skyrmion. Phys. Rev. A 103, 023514 (2021).

    ADS  MathSciNet  CAS  Google Scholar 

  30. Shen, Y., Martínez, E. C. & Rosales-Guzmán, C. Generation of optical skyrmions with tunable topological textures. ACS Photonics 9, 296–303 (2022).

    CAS  Google Scholar 

  31. Shen, Y., Hou, Y., Papasimakis, N. & Zheludev, N. I. Supertoroidal light pulses as electromagnetic skyrmions propagating in free space. Nat. Commun. 12, 5891 (2021).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  32. Sugic, D. et al. Particle-like topologies in light. Nat. Commun. 12, 6785 (2021).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  33. Shen, Y. et al. Topological transformation and free-space transport of photonic hopfions. Adv. Photon. 5, 015001 (2023).

    ADS  Google Scholar 

  34. Yan, Q. et al. Quantum topological photonics. Adv. Opt. Mater. 9, 2001739 (2021).

    CAS  Google Scholar 

  35. Mehrabad, M. J. et al. Chiral topological photonics with an embedded quantum emitter. Optica 7, 1690–1696 (2020).

    ADS  Google Scholar 

  36. Dai, T. et al. Topologically protected quantum entanglement emitters. Nat. Photon. 16, 248–257 (2022).

    ADS  CAS  Google Scholar 

  37. Mittal, S., Goldschmidt, E. A. & Hafezi, M. A topological source of quantum light. Nature 561, 502–506 (2018).

    ADS  CAS  PubMed  Google Scholar 

  38. Barik, S. et al. A topological quantum optics interface. Science 359, 666–668 (2018).

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  39. Blanco-Redondo, A., Bell, B., Oren, D., Eggleton, B. J. & Segev, M. Topological protection of biphoton states. Science 362, 568–571 (2018).

    ADS  MathSciNet  CAS  PubMed  Google Scholar 

  40. Parmee, C. D., Dennis, M. R. & Ruostekoski, J. Optical excitations of skyrmions, knotted solitons, and defects in atoms. Commun. Phys. 5, 54 (2022).

    Google Scholar 

  41. Hiekkamäki, M., Barros, R. F., Ornigotti, M. & Fickler, R. Observation of the quantum Gouy phase. Nat. Photon. 16, 828–833 (2022).

    ADS  Google Scholar 

  42. Leach, J. et al. Violation of a Bell inequality in two-dimensional orbital angular momentum state-spaces. Opt. Express 17, 8287–8293 (2009).

    ADS  CAS  PubMed  Google Scholar 

  43. Shen, Y. Topological bimeronic beams. Opt. Lett. 46, 3737–3740 (2021).

    ADS  PubMed  Google Scholar 

  44. Forbes, A. & Nape, I. Quantum mechanics with patterns of light: progress in high dimensional and multidimensional entanglement with structured light. AVS Quantum Sci. 1, 011701 (2019).

    ADS  Google Scholar 

  45. Hatcher, A. Algebraic Topology (Cambridge Univ. Press, 2002).

  46. Stav, T. et al. Quantum entanglement of the spin and orbital angular momentum of photons using metamaterials. Science 361, 1101–1104 (2018).

    ADS  CAS  PubMed  Google Scholar 

  47. Nielsen, M. A. & Chuang, I. L. Quantum computation and quantum information. Phys. Today 54, 60 (2001).

    Google Scholar 

  48. Choi, M.-D. Completely positive linear maps on complex matrices. Linear Algebra Appl. 10, 285–290 (1975).

    MathSciNet  Google Scholar 

  49. Song, Q., Liu, X., Qiu, C.-W. & Genevet, P. Vectorial metasurface holography. Appl. Phys. Rev. 9, 011311 (2022).

    ADS  CAS  Google Scholar 

  50. Zheludev, N. I. & Kivshar, Y. S. From metamaterials to metadevices. Nat. Mater. 11, 917–924 (2012).

    ADS  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

This work was supported by the South African National Research Foundation/CSIR Rental Pool Programme and the South African Quantum Technology Initiative.

Author information

Authors and Affiliations

  1. School of Physics, University of the Witwatersrand, Wits, South Africa

    Pedro Ornelas, Isaac Nape & Andrew Forbes

  2. School of Science, Huzhou University, Huzhou, China

    Robert de Mello Koch

  3. Mandelstam Institute for Theoretical Physics, School of Physics, University of the Witwatersrand, Wits, South Africa

    Robert de Mello Koch

Authors
  1. Pedro Ornelas
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Isaac Nape
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Robert de Mello Koch
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Andrew Forbes
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

P.O. and I.N. performed the experiment, and P.O., I.N. and R.M.K. contributed to the theory. All authors contributed to the writing of the manuscript and analysis of data. A.F. conceived of the idea and supervised the project.

Corresponding author

Correspondence to Andrew Forbes.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Photonics thanks Cheng-Wei Qiu, Luping Du and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary Figs. 1–9, Table 1, text and discussion.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ornelas, P., Nape, I., de Mello Koch, R. et al. Non-local skyrmions as topologically resilient quantum entangled states of light. Nat. Photon. 18, 258–266 (2024). https://doi.org/10.1038/s41566-023-01360-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41566-023-01360-4

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing