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

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.

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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.

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).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    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).

    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).

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    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).

    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).

    Google Scholar 

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

    ADS  MathSciNet  Google Scholar 

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

    ADS  Google Scholar 

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

    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).

    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).

    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).

    ADS  Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    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).

    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).

    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).

    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).

    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).

    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).

    ADS  Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    Google Scholar 

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

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    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).

    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).

    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).

    ADS  Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    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).

    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).

    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).

    Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    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).

    ADS  Google Scholar 

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

    ADS  Google Scholar 

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

    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).

    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).

    ADS  Google Scholar 

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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.).

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Authors

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.

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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.

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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

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