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Lasing in topological edge states of a one-dimensional lattice

Nature Photonics volume 11, pages 651–656 (2017)Cite this article

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An Author Correction to this article was published on 07 July 2021

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Abstract

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.

Topological phase transitions in condensed matter have been studied extensively over the past decade. A key manifestation of these transitions is the emergence, at the frontier between materials exhibiting distinct topological phases, of localized states that are unaffected by disorder. One example of this topological protection is provided by chiral edge states at the surface of topological insulators that allow unidirectional transport immune to backscattering1.

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Fig. 1: Tight-binding calculations of the orbital SSH Hamiltonian.
Fig. 2: Momentum and real-space imaging of the polariton modes.
Fig. 3: Emission in the lasing regime.
Fig. 4: SSH Hamiltonian with broken chiral symmetry.

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References

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. 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 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

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

    Article  ADS  MathSciNet  Google Scholar 

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

    Google Scholar 

  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).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

Download references

Acknowledgements

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).

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Authors and Affiliations

  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

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Contributions

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.

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St-Jean, P., Goblot, V., Galopin, E. et al. Lasing in topological edge states of a one-dimensional lattice. Nature Photon 11, 651–656 (2017). https://doi.org/10.1038/s41566-017-0006-2

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