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:

Gap solitons in a one-dimensional driven-dissipative topological lattice

Nature Physics volume 18, pages 678–684 (2022)Cite this article

Subjects

Abstract

Nonlinear topological photonics is an emerging field that aims to extend the fascinating properties of topological states to a regime where interactions between the system constituents cannot be neglected. Interactions can trigger topological phase transitions, induce symmetry protection and robustness properties for the many-body system. Here, we report the nonlinear response of a polariton lattice that implements a driven-dissipative version of the Su–Schrieffer–Heeger model. We first demonstrate the formation of topological gap solitons bifurcating from a linear topological edge state. We then focus on the formation of gap solitons in the bulk of the lattice and show that they exhibit robust nonlinear properties against defects, owing to the underlying sublattice symmetry. Leveraging the driven-dissipative nature of the system, we discover a class of bulk gap solitons with high sublattice polarization. We show that these solitons provide an all-optical way to create a non-trivial interface for Bogoliubov excitations. Our results show that coherent driving can be exploited to stabilize new nonlinear phases and establish dissipatively stabilized solitons as a powerful resource for topological photonics.

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

Access options

Buy this article

  • Purchase on SpringerLink
  • Instant access to full article PDF
Buy now

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

Fig. 1: Implementation of the SSH lattice.
Fig. 2: Generation of topological gap solitons.
Fig. 3: Robustness of gap solitons against a defect.
Fig. 4: Spin-polarized solitons.

Similar content being viewed by others

Data availability

Source data are provided with this paper. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

References

  1. Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

    Article  ADS  Google Scholar 

  2. Qi, X. L. & Zhang, S. C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).

    Article  ADS  Google Scholar 

  3. Cooper, N. R., Dalibard, J. & Spielman, I. B. Topological bands for ultracold atoms. Rev. Mod. Phys. 91, 015005 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  4. Lu, L., Joannopoulos, J. D. & Soljačić, M. Topological photonics. Nat. Photon. 8, 821–829 (2014).

    Article  ADS  Google Scholar 

  5. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  6. Huber, S. D. Topological mechanics. Nat. Phys. 12, 621–623 (2016).

    Article  Google Scholar 

  7. Peano, V., Brendel, C., Schmidt, M. & Marquardt, F. Topological phases of sound and light. Phys. Rev. X 5, 031011 (2015).

    Google Scholar 

  8. Klembt, S. et al. Exciton-polariton topological insulator. Nature 562, 552–556 (2018).

    Article  ADS  Google Scholar 

  9. Gianfrate, A. et al. Measurement of the quantum geometric tensor and of the anomalous Hall drift. Nature 578, 381–385 (2020).

    Article  ADS  Google Scholar 

  10. Ozawa, T. & Price, H. M. Topological quantum matter in synthetic dimensions. Nat. Rev. Phys. 1, 349–357 (2019).

    Article  Google Scholar 

  11. Meier, E. J. et al. Observation of the topological Anderson insulator in disordered atomic wires. Science 362, 929–933 (2018).

    Article  ADS  Google Scholar 

  12. Stützer, S. et al. Photonic topological Anderson insulators. Nature 560, 461–465 (2018).

    Article  ADS  Google Scholar 

  13. Kraus, Y. E., Lahini, Y., Ringel, Z., Verbin, M. & Zilberberg, O. Topological states and adiabatic pumping in quasicrystals. Phys. Rev. Lett. 109, 106402 (2012).

    Article  ADS  Google Scholar 

  14. Serra-Garcia, M. et al. Observation of a phononic quadrupole topological insulator. Nature 555, 342–345 (2018).

    Article  ADS  Google Scholar 

  15. Peterson, C. W., Benalcazar, W. A., Hughes, T. L. & Bahl, G. A quantized microwave quadrupole insulator with topologically protected corner states. Nature 555, 346–350 (2018).

    Article  ADS  Google Scholar 

  16. Smirnova, D., Leykam, D., Chong, Y. & Kivshar, Y. Nonlinear topological photonics. Appl. Phys. Rev. 7, 021306 (2020).

    Article  ADS  Google Scholar 

  17. Bleu, O., Solnyshkov, D. D. & Malpuech, G. Interacting quantum fluid in a polariton Chern insulator. Phys. Rev. B 93, 085438 (2016).

    Article  ADS  Google Scholar 

  18. Hadad, Y., Soric, J. C., Khanikaev, A. B. & Alù, A. Self-induced topological protection in nonlinear circuit arrays. Nat. Electron. 1, 178–182 (2018).

    Article  Google Scholar 

  19. Maczewsky, L. J. et al. Nonlinearity-induced photonic topological insulator. Science 370, 701–704 (2020).

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. Kruk, S. et al. Nonlinear light generation in topological nanostructures. Nat. Nanotechnol. 14, 126–130 (2019).

    Article  ADS  Google Scholar 

  22. Lumer, Y., Plotnik, Y., Rechtsman, M. C. & Segev, M. Self-localized states in photonic topological insulators. Phys. Rev. Lett. 111, 243905 (2013).

    Article  ADS  Google Scholar 

  23. Solnyshkov, D. D., Bleu, O., Teklu, B. & Malpuech, G. Chirality of topological gap solitons in bosonic dimer chains. Phys. Rev. Lett. 118, 023901 (2017).

    Article  ADS  Google Scholar 

  24. Bisianov, A., Wimmer, M., Peschel, U. & Egorov, O. A. Stability of topologically protected edge states in nonlinear fiber loops. Phys. Rev. A 100, 063830 (2019).

    Article  ADS  Google Scholar 

  25. Mukherjee, S. & Rechtsman, M. C. Observation of Floquet solitons in a topological bandgap. Science 368, 856–859 (2020).

    Article  ADS  Google Scholar 

  26. Guo, M. et al. Weakly nonlinear topological gap solitons in Su–Schrieffer–Heeger photonic lattices. Opt. Lett. 45, 6466–6469 (2020).

    Article  ADS  Google Scholar 

  27. Jürgensen, M., Mukherjee, S. & Rechtsman, M. C. Quantized nonlinear Thouless pumping. Nature 596, 63–67 (2021).

    Article  ADS  Google Scholar 

  28. Jürgensen, M. & Rechtsman, M. C. The Chern number governs soliton motion in nonlinear Thouless pumps. Phys. Rev. Lett. 128, 113901 (2022).

    Article  ADS  Google Scholar 

  29. De Léséleuc, S. et al. Observation of a symmetry-protected topological phase of interacting bosons with Rydberg atoms. Science 365, 775–780 (2019).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  30. Clark, L. W., Schine, N., Baum, C., Jia, N. & Simon, J. Observation of Laughlin states made of light. Nature 582, 41–45 (2020).

    Article  ADS  Google Scholar 

  31. Bergholtz, E. J., Budich, J. C. & Kunst, F. K. Exceptional topology of non-Hermitian systems. Rev. Mod. Phys. 93, 015005 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  32. Solnyshkov, D. D., Nalitov, A. V. & Malpuech, G. Kibble-Zurek mechanism in topologically nontrivial zigzag chains of polariton micropillars. Phys. Rev. Lett. 116, 046402 (2016).

    Article  ADS  Google Scholar 

  33. St-Jean, P. et al. Lasing in topological edge states of a one-dimensional lattice. Nat. Photon. 11, 651–656 (2017).

    Article  ADS  Google Scholar 

  34. Zhao, H. et al. Topological hybrid silicon microlasers. Nat. Commun. 9, 981 (2018).

    Article  ADS  Google Scholar 

  35. Parto, M. et al. Complex edge-state phase transitions in 1D topological laser arrays. In Conference on Lasers and Electro-Optics FM2E.5 (Optica Publishing Group, 2018).

  36. Bahari, B. et al. Nonreciprocal lasing in topological cavities of arbitrary geometries. Science 358, 636–640 (2017).

    Article  ADS  Google Scholar 

  37. Bandres, M. A. et al. Topological insulator laser: experiments. Science 359, eaar4005 (2018).

    Article  Google Scholar 

  38. Weimann, S. et al. Topologically protected bound states in photonic parity-time-symmetric crystals. Nat. Mater. 16, 433–438 (2017).

    Article  ADS  Google Scholar 

  39. Xia, S. et al. Nonlinear tuning of PT symmetry and non-Hermitian topological states. Science 372, 72–76 (2021).

    Article  ADS  Google Scholar 

  40. Konotop, V. V., Yang, J. & Zezyulin, D. A. Nonlinear waves in PT-symmetric systems. Rev. Mod. Phys. 88, 035002 (2016).

    Article  ADS  Google Scholar 

  41. Jeon, D. H., Reisner, M., Mortessagne, F., Kottos, T. & Kuhl, U. Non-Hermitian CT-symmetric spectral protection of nonlinear defect modes. Phys. Rev. Lett. 125, 113901 (2020).

    Article  ADS  Google Scholar 

  42. Liu, Y. G. N., Jung, P. S., Parto, M., Christodoulides, D. N. & Khajavikhan, M. Gain-induced topological response via tailored long-range interactions. Nat. Phys. 17, 704–709 (2021).

    Article  Google Scholar 

  43. Bardyn, C. E., Karzig, T., Refael, G. & Liew, T. C. Chiral Bogoliubov excitations in nonlinear bosonic systems. Phys. Rev. B 93, 020502 (2016).

    Article  ADS  Google Scholar 

  44. Su, W. P., Schrieffer, J. R. & Heeger, A. J. Solitons in polyacetylene. Phys. Rev. Lett. 42, 1698–1701 (1979).

    Article  ADS  Google Scholar 

  45. Tanese, D. et al. Polariton condensation in solitonic gap states in a one-dimensional periodic potential. Nat. Commun. 4, 1749 (2013).

    Article  ADS  Google Scholar 

  46. Cerda-Méndez, E. A. et al. Exciton-polariton gap solitons in two-dimensional lattices. Phys. Rev. Lett. 111, 146401 (2013).

    Article  ADS  Google Scholar 

  47. Whittaker, C. E. et al. Effect of photonic spin-orbit coupling on the topological edge modes of a Su-Schrieffer-Heeger chain. Phys. Rev. B 99, 081402 (2019).

    Article  ADS  Google Scholar 

  48. Carusotto, I. & Ciuti, C. Quantum fluids of light. Rev. Mod. Phys. 85, 299–366 (2013).

    Article  ADS  Google Scholar 

  49. Delplace, P., Ullmo, D. & Montambaux, G. Zak phase and the existence of edge states in graphene. Phys. Rev. B 84, 195452 (2011).

    Article  ADS  Google Scholar 

  50. Mangussi, F. et al. Multi-orbital tight binding model for cavity-polariton lattices. J. Phys.: Condens. Matter 32, 315402 (2020).

    Google Scholar 

  51. Smirnova, D. A., Smirnov, L. A., Leykam, D. & Kivshar, Y. S. Topological edge states and gap solitons in the nonlinear Dirac model. Laser & Photonics Rev. 13, 1900223 (2019).

    Article  ADS  Google Scholar 

  52. Castin, Y. Bose-Einstein condensates in atomic gases: simple theoretical results. Coherent Atomic Matter Waves 1–136 (Springer, 2001).

  53. Diehl, S., Rico, E., Baranov, M. A. & Zoller, P. Topology by dissipation in atomic quantum wires. Nat. Phys. 7, 971–977 (2011).

    Article  Google Scholar 

  54. Bardyn, C.-E. et al. Topology by dissipation. New J. Phys. 15, 085001 (2013).

    Article  ADS  MATH  Google Scholar 

  55. Comaron, P., Shahnazaryan, V., Brzezicki, W., Hyart, T. & Matuszewski, M. Non-Hermitian topological end-mode lasing in polariton systems. Phys. Rev. Research 2, 022051 (2020).

    Article  ADS  Google Scholar 

  56. Kartashov, Y. V. & Skryabin, D. V. Modulational instability and solitary waves in polariton topological insulators. Optica 3, 1228–1236 (2016).

    Article  ADS  Google Scholar 

  57. Gulevich, D. R., Yudin, D., Skryabin, D. V., Iorsh, I. V. & Shelykh, I. A. Exploring nonlinear topological states of matter with exciton-polaritons: edge solitons in kagome lattice. Sci. Rep. 7, 1780 (2017).

    Article  ADS  Google Scholar 

  58. Mittal, S. et al. Photonic quadrupole topological phases. Nat. Photon. 13, 692–696 (2019).

    Article  ADS  Google Scholar 

  59. El Hassan, A. et al. Corner states of light in photonic waveguides. Nat. Photon. 13, 697–700 (2019).

    Article  ADS  Google Scholar 

  60. Banerjee, R., Mandal, S. & Liew, T. C. H. Coupling between exciton-polariton corner modes through edge states. Phys. Rev. Lett. 124, 063901 (2020).

    Article  ADS  Google Scholar 

  61. Sarchi, D., Carusotto, I., Wouters, M. & Savona, V. Coherent dynamics and parametric instabilities of microcavity polaritons in double-well systems. Phys. Rev. B 77, 125324 (2008).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We would like to thank I. Carusotto for fruitful discussions. This work was supported by the Paris Ile-de-France Région in the framework of DIM SIRTEQ (J.B.), the Marie Skłodowska-Curie individual fellowship ToPol (P.St-J.), the H2020-FETFLAG project PhoQus (820392) (J.B. and A.A.), the QUANTERA project Interpol (ANR-QUAN-0003-05) (J.B.), the French National Research Agency project Quantum Fluids of Light (ANR-16-CE30-0021) (G.M. and J.B.), European Research Council via projects EmergenTopo (865151) (A.A.) and ARQADIA (949730) (S.R.), the French RENATECH network, the French government through the Programme Investissement d’Avenir (I-SITE ULNE/ANR-16-IDEX-0004 ULNE) (G.M. and D.D.S.) and IDEX-ISITE initiative 16-IDEX-0001 (CAP 20-25), managed by the Agence Nationale de la Recherche, the Labex CEMPI (ANR-11-LABX-0007) (A.A.).

Author information

Author notes

  1. These authors contributed equally: N. Pernet, P. St-Jean.

Authors and Affiliations

  1. Université Paris-Saclay, CNRS, Centre de Nanosciences et de Nanotechnologies (C2N), Palaiseau, France

    Nicolas Pernet, Philippe St-Jean, Nicola Carlon Zambon, Quentin Fontaine, Aristide Lemaître, Martina Morassi, Luc Le Gratiet, Téo Baptiste, Abdelmounaim Harouri, Isabelle Sagnes, Sylvain Ravets & Jacqueline Bloch

  2. Institut Pascal, PHOTON-N2, Université Clermont Auvergne, CNRS, SIGMA Clermont, Clermont-Ferrand, France

    Dmitry D. Solnyshkov & Guillaume Malpuech

  3. Institut Universitaire de France (IUF), Paris, France

    Dmitry D. Solnyshkov

  4. Université de Lille, CNRS, Laboratoire de Physique des Lasers Atomes et Molécules (PhLAM), Lille, France

    Bastian Real, Omar Jamadi & Alberto Amo

Authors
  1. Nicolas Pernet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Philippe St-Jean
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dmitry D. Solnyshkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Guillaume Malpuech
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Nicola Carlon Zambon
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Quentin Fontaine
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Bastian Real
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Omar Jamadi
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Aristide Lemaître
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Martina Morassi
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Luc Le Gratiet
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Téo Baptiste
    View author publications

    You can also search for this author in PubMed Google Scholar

  13. Abdelmounaim Harouri
    View author publications

    You can also search for this author in PubMed Google Scholar

  14. Isabelle Sagnes
    View author publications

    You can also search for this author in PubMed Google Scholar

  15. Alberto Amo
    View author publications

    You can also search for this author in PubMed Google Scholar

  16. Sylvain Ravets
    View author publications

    You can also search for this author in PubMed Google Scholar

  17. Jacqueline Bloch
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

N.P. and P.St-J. performed the experiments and analysed the data. N.P. performed the initial theoretical modelling of the experiments using the tight-binding approach, which led to the discovery of spin-polarized topological solitons. D.D.S. and G.M. provided the theoretical guidance and performed the theoretical calculations in the 1D continuous model. N.P., P.St-J., D.D.S., G.M, N.C.Z., Q.F., B.R., O.J., A.A., S.R. and J.B. participated in the scientific discussions. N.P., P.St-J., D.D.S., G.M., A.A., S.R. and J.B. wrote the manuscript. N.C.Z., Q.F. and B.R. contributed to the editing of the manuscript. P.St-J., S.R., J.B. and A.A. designed the sample. A.L., L.L.G., T.B., A.H. and I.S. fabricated the samples. A.A., S.R. and J.B. supervised the work.

Corresponding author

Correspondence to Jacqueline Bloch.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Physics thanks the anonymous reviewers 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 Sections 1–9 and Figs. 1–10.

Source data

Source Data Fig. 1

Processed data of the Cartesian plots in Fig. 1.

Source Data Fig. 2

Processed data of the Cartesian plots in Fig. 2.

Source Data Fig. 3

Processed data of the Cartesian plots in Fig. 3.

Source Data Fig. 4

Processed data of the Cartesian plots in Fig. 4.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pernet, N., St-Jean, P., Solnyshkov, D.D. et al. Gap solitons in a one-dimensional driven-dissipative topological lattice. Nat. Phys. 18, 678–684 (2022). https://doi.org/10.1038/s41567-022-01599-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41567-022-01599-8

This article is cited by

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