Lasing in topological edge states of a one-dimensional lattice

Published online:


Topology describes properties that remain unaffected by smooth distortions. Its main hallmark is the emergence of edge states localized at the boundary between regions characterized by distinct topological invariants. Because their properties are inherited from the topology of the bulk, these edge states present a strong immunity to distortions of the underlying architecture. This feature offers new opportunities for robust trapping of light in nano- and micrometre-scale systems subject to fabrication imperfections and environmentally induced deformations. Here, we report lasing in such topological edge states of a one-dimensional lattice of polariton micropillars that implements an orbital version of the Su–Schrieffer–Heeger Hamiltonian. We further demonstrate that lasing in these states persists under local deformations of the lattice. These results open the way to the implementation of chiral lasers in systems with broken time-reversal symmetry and, when combined with polariton interactions, to the study of nonlinear phenomena in topological photonics.

  • Subscribe to Nature Photonics for full access:



Additional access options:

Already a subscriber?  Log in  now or  Register  for online access.


  1. 1.

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

  2. 2.

    Haldane, F. D. M. & Raghu, S. Possible realization of directional optical waveguides in photonic crystals with broken time-reversal symmetry. Phys. Rev. Lett. 100, 013904 (2008).

  3. 3.

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

  4. 4.

    Söllner, I. et al. Deterministic photonemitter coupling in chiral photonic circuits. Nat. Nanotech. 10, 775–778 (2015).

  5. 5.

    Mittal, S. et al. Topologically robust transport of photons in a synthetic gauge field. Phys. Rev. Lett. 113, 087403 (2014).

  6. 6.

    Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

  7. 7.

    Hafezi, M., Demler, E. A., Lukin, M. D. & Taylor, J. M. Robust optical delay lines with topological protection. Nat. Phys. 7, 907–912 (2011).

  8. 8.

    Hafezi, M., Mittal, S., Fan, J., Migdall, A. & Taylor, J. M. Imaging topological edge states in silicon photonics. Nat. Photon. 7, 1001–1005 (2013).

  9. 9.

    Rechtsman, M. C. et al. Photonic Floquet topological insulators. Nature 496, 196–200 (2013).

  10. 10.

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

  11. 11.

    Poli, C., Bellec, M., Kuhl, U., Mortessagne, F. & Schomerus, H. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat. Commun. 6, 6710 (2015).

  12. 12.

    Pilozzi, L. & Conti, C. Topological lasing in resonant photonic structures. Phys. Rev. B 93, 195317 (2016).

  13. 13.

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

  14. 14.

    Bajoni, D. et al. Polariton laser using single micropillar GaAs–GaAlAs semiconductor cavities. Phys. Rev. Lett. 100, 047401 (2008).

  15. 15.

    Deng, H., Weihs, G., Santori, C., Bloch, J. & Yamamoto, Y. Condensation of semiconductor microcavity exciton polaritons. Science 298, 199–202 (2002).

  16. 16.

    Kasprzak, J. et al. Bose–Einstein condensation of exciton polaritons. Nature 443, 409–414 (2006).

  17. 17.

    Christopoulos, S. et al. Room-temperature polariton lasing in semiconductor microcavities. Phys. Rev. Lett. 98, 126405 (2007).

  18. 18.

    Kéna-Cohen, S. & Forrest, S. R. Room-temperature polariton lasing in an organic single-crystal microcavity. Nat. Photon. 4, 371–375 (2010).

  19. 19.

    Milićević, M. et al. Orbital edge states in a photonic honeycomb lattice. Phys. Rev. Lett. 118, 107403 (2017).

  20. 20.

    Baboux, F. et al. Measuring topological invariants from generalized edge states in polaritonic quasicrystals. Phys. Rev. B 95, 161114 (2017).

  21. 21.

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

  22. 22.

    Jacqmin, T. et al. Direct observation of Dirac cones and a flatband in a honeycomb lattice for polaritons. Phys. Rev. Lett. 112, 116402 (2014).

  23. 23.

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

  24. 24.

    Kruk, S. et al. Edge states and topological phase transitions in chains of dielectric nanoparticles. Small 13, 1603190 (2017).

  25. 25.

    Sala, V. et al. Spin–orbit coupling for photons and polaritons in microstructures. Phys. Rev. X 5, 011034 (2015).

  26. 26.

    Sturm, C. et al. All-optical phase modulation in a cavity-polariton Mach–Zehnder interferometer. Nat. Commun. 5, 3278 (2014).

  27. 27.

    Richard, M. et al. Experimental evidence for nonequilibrium Bose condensation of exciton polaritons. Phys. Rev. B 72, 201301 (2005).

  28. 28.

    Wouters, M., Carusotto, I. & Ciuti, C. Spatial and spectral shape of inhomogeneous nonequilibrium exciton–polariton condensates. Phys. Rev. B 77, 115340 (2008).

  29. 29.

    Baboux, F. et al. Bosonic condensation and disorder-induced localization in a flat band. Phys. Rev. Lett. 116, 066402 (2016).

  30. 30.

    Levrat, J. et al. Condensation phase diagram of cavity polaritons in GaN-based microcavities: experiment and theory. Phys. Rev. B 81, 125305 (2010).

  31. 31.

    Wertz, E. et al. Spontaneous formation and optical manipulation of extended polariton condensates. Nat. Phys. 6, 860–864 (2010).

  32. 32.

    Zak, J. Symmetry criterion for surface states in solids. Phys. Rev. B 32, 2218–2226 (1985).

  33. 33.

    Malkova, N., Hromada, I., Wang, X., Bryant, G. & Chen, Z. Transition between Tamm-like and Shockley-like surface states in optically induced photonic superlattices. Phys. Rev. A 80, 043806 (2009).

  34. 34.

    Blanco-Redondo, A. et al. Topological optical waveguiding in silicon and the transition between topological and trivial defect states. Phys. Rev. Lett. 116, 163901 (2016).

  35. 35.

    Harari, G. et al. in Conference on Lasers and Electro-Optics, FM3A.3 (OSA, Washington, DC, 2016).

  36. 36.

    Nalitov, A., Solnyshkov, D. & Malpuech, G. Polariton Z topological insulator. Phys. Rev. Lett. 114, 116401 (2015).

  37. 37.

    Karzig, T., Bardyn, C.-E., Lindner, N. H. & Refael, G. Topological polaritons. Phys. Rev. X 5, 031001 (2015).

  38. 38.

    Hadad, Y., Khanikaev, A. B. & Alù, A. Self-induced topological transitions and edge states supported by nonlinear staggered potentials. Phys. Rev. B 93, 155112 (2016).

  39. 39.

    Galbiati, M. et al. Polariton condensation in photonic molecules. Phys. Rev. Lett. 108, 126403 (2012).

Download references


The authors thank M. Milicevic and G. Montambaux for discussions. This work was supported by the French National Research Agency (ANR) project Quantum Fluids of Light (ANR-16-CE30-0021) and program Labex NanoSaclay via the project ICQOQS (grant no. ANR-10-LABX-0035), the French RENATECH network, the ERC grant Honeypol and the EU-FET Proactive grant AQUS (project no. 640800). P.S.-J. acknowledges financial support from the Natural Sciences and Engineering Research Council of Canada (NSERC).

Author information


  1. Centre de Nanosciences et de Nanotechnologies, CNRS, Université Paris-Sud, Université Paris-Saclay, C2N - Marcoussis, 91460, Marcoussis, France

    • P. St-Jean
    • , V. Goblot
    • , E. Galopin
    • , A. Lemaître
    • , L. Le Gratiet
    • , I. Sagnes
    • , J. Bloch
    •  & A. Amo
  2. INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento, I-38123, Povo, Italy

    • T. Ozawa


  1. Search for P. St-Jean in:

  2. Search for V. Goblot in:

  3. Search for E. Galopin in:

  4. Search for A. Lemaître in:

  5. Search for T. Ozawa in:

  6. Search for L. Le Gratiet in:

  7. Search for I. Sagnes in:

  8. Search for J. Bloch in:

  9. Search for A. Amo in:


P.S.-J. performed the experiments with help from V.G., carried out the calculations, analysed the data and wrote the manuscript, with the guidance of J.B. and A.A. T.O. provided critical inputs to the theoretical analysis. E.G., A.L., L.L. and I.S. grew and processed the sample. J.B. and A.A. designed the sample and supervised the work. All authors revised the manuscript.

Competing interests

The authors declare no competing financial interests.

Corresponding author

Correspondence to P. St-Jean.

Electronic supplementary material

  1. Supplementary Information

    Supplementary Information