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Reconfigurable quantum fluid molecules of bound states in the continuum

Abstract

Topological bound states in the continuum are confined wave-mechanical objects that offer advantageous ways to enhance light–matter interactions in compact photonic devices. In particular, their large quality factor in the strong-coupling regime has recently enabled the demonstration of Bose–Einstein condensation of bound-state-in-the-continuum polaritons. Here we show that polariton condensation into a negative-mass bound state in the continuum exhibits interaction-induced state confinement, opening opportunities for optically reprogrammable molecular arrays of quantum fluids of light. We exploit this optical-trapping mechanism to demonstrate that such artificial molecular complexes show hybridization into macroscopic modes with unusual topological charge multiplicity. Additionally, we demonstrate the scalability of our technique by constructing extended mono- and diatomic chains of bound-state-in-the-continuum polariton fluids that display non-Hermitian band formation and the opening of a minigap. Our findings offer insights into large-scale, reprogrammable, driven, dissipative many-body systems in the strong-coupling regime.

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Fig. 1: The exciton-polariton BIC condensate in a quantum-well grating waveguide.
Fig. 2: BIC molecule condensate characterization.
Fig. 3: Momentum-space PL characteristics in the double-spot arrangement.
Fig. 4: 10-BIC condensate chain.

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Data availability

The raw experimental data used in this study are available from the corresponding author upon reasonable request.

Code availability

The code used in this study is available from the corresponding author upon reasonable request.

References

  1. Hsu, C. W., Zhen, B., Stone, A. D., Joannopoulos, J. D. & Soljačić, M. Bound states in the continuum. Nat. Rev. Mater. 1, 16048 (2016).

    Article  ADS  Google Scholar 

  2. Azzam, S. I. & Kildishev, A. V. Photonic bound states in the continuum: from basics to applications. Adv. Opt. Mater. 9, 2001469 (2021).

    Article  Google Scholar 

  3. Kodigala, A. et al. Lasing action from photonic bound states in continuum. Nature 541, 196 (2017).

    Article  ADS  Google Scholar 

  4. Hwang, M.-S. et al. Ultralow-threshold laser using super-bound states in the continuum. Nat. Commun. 12, 4135 (2021).

    Article  ADS  Google Scholar 

  5. Zhen, B., Hsu, C. W., Lu, L., Stone, A. D. & Soljačić, M. Topological nature of optical bound states in the continuum. Phys. Rev. Lett. 113, 257401 (2014).

    Article  ADS  Google Scholar 

  6. Doeleman, H. M., Monticone, F., den Hollander, W., Alù, A. & Koenderink, A. F. Experimental observation of a polarization vortex at an optical bound state in the continuum. Nat. Photonics 12, 397 (2018).

    Article  ADS  Google Scholar 

  7. Chen, H., Wang, H., yin Wong, K. & Lei, D. High-q localized surface plasmon resonance based on bound states in the continuum for enhanced refractive index sensing. Opt. Lett. 47, 609 (2022).

    Article  ADS  Google Scholar 

  8. Foley, J. M., Young, S. M. & Phillips, J. D. Symmetry-protected mode coupling near normal incidence for narrow-band transmission filtering in a dielectric grating. Phys. Rev. B 89, 165111 (2014).

    Article  ADS  Google Scholar 

  9. Aigner, A. et al. Plasmonic bound states in the continuum to tailor light-matter coupling. Sci. Adv. 8, eadd4816 (2022).

    Article  Google Scholar 

  10. Krasikov, S. D., Bogdanov, A. A. & Iorsh, I. V. Nonlinear bound states in the continuum of a one-dimensional photonic crystal slab. Phys. Rev. B 97, 224309 (2018).

    Article  ADS  Google Scholar 

  11. Dolinina, D. & Yulin, A. Interactions of the solitons in periodic driven-dissipative systems supporting quasibound states in the continuum. Phys. Rev. E 104, 054214 (2021).

    Article  ADS  Google Scholar 

  12. Lu, L. et al. Engineering a light-matter strong coupling regime in perovskite-based plasmonic metasurface: quasi-bound state in the continuum and exceptional points. Photonics Res. 8, A91 (2020).

    Article  Google Scholar 

  13. Kravtsov, V. et al. Nonlinear polaritons in a monolayer semiconductor coupled to optical bound states in the continuum. Light Sci. Appl. 9, 56 (2020).

    Article  ADS  Google Scholar 

  14. Dang, N. H. M. et al. Realization of polaritonic topological charge at room temperature using polariton bound states in the continuum from perovskite metasurface. Adv. Opt. Mater. 10, 2102386 (2022).

    Article  Google Scholar 

  15. Byrnes, T., Kim, N. Y. & Yamamoto, Y. Exciton–polariton condensates. Nat. Phys. 10, 803 (2014).

    Article  Google Scholar 

  16. Ardizzone, V. et al. Polariton Bose–Einstein condensate from a bound state in the continuum. Nature 605, 447 (2022).

    Article  ADS  Google Scholar 

  17. Deng, H., Haug, H. & Yamamoto, Y. Exciton-polariton Bose-Einstein condensation. Rev. Mod. Phys. 82, 1489 (2010).

    Article  ADS  Google Scholar 

  18. Ciuti, C., Savona, V., Piermarocchi, C., Quattropani, A. & Schwendimann, P. Role of the exchange of carriers in elastic exciton-exciton scattering in quantum wells. Phys. Rev. B 58, 7926 (1998).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  20. Sanvitto, D. et al. Persistent currents and quantized vortices in a polariton superfluid. Nat. Phys. 6, 527 (2010).

    Article  Google Scholar 

  21. Berloff, N. G. et al. Realizing the classical XY Hamiltonian in polariton simulators. Nat. Mater. 16, 1120 (2017).

    Article  ADS  Google Scholar 

  22. Tao, R. et al. Halide perovskites enable polaritonic XY spin Hamiltonian at room temperature. Nat. Mater. 21, 761 (2022).

    Article  ADS  Google Scholar 

  23. Ohadi, H. et al. Spin order and phase transitions in chains of polariton condensates. Phys. Rev. Lett. 119, 067401 (2017).

    Article  ADS  Google Scholar 

  24. Schneider, C. et al. Exciton-polariton trapping and potential landscape engineering. Rep. Prog. Phys. 80, 016503 (2016).

    Article  ADS  Google Scholar 

  25. Amo, A. & Bloch, J. Exciton-polaritons in lattices: a non-linear photonic simulator. C. R. Phys. 17, 934 (2016).

    Article  ADS  Google Scholar 

  26. Kavokin, A. et al. Polariton condensates for classical and quantum computing. Nat. Rev. Phys. 4, 435 (2022).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  28. Kaitouni, R. I. et al. Engineering the spatial confinement of exciton polaritons in semiconductors. Phys. Rev. B 74, 155311 (2006).

    Article  ADS  Google Scholar 

  29. Jayaprakash, R. et al. Two-dimensional organic-exciton polariton lattice fabricated using laser patterning. ACS Photonics 7, 2273 (2020).

    Article  Google Scholar 

  30. Kim, N. Y. et al. Dynamical d-wave condensation of exciton–polaritons in a two-dimensional square-lattice potential. Nat. Phys. 7, 681 (2011).

    Article  Google Scholar 

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

    Article  Google Scholar 

  32. Alyatkin, S., Sigurdsson, H., Askitopoulos, A., Töpfer, J. D. & Lagoudakis, P. G. Quantum fluids of light in all-optical scatterer lattices. Nat. Commun. 12, 5571 (2021).

    Article  ADS  Google Scholar 

  33. Cristofolini, P. et al. Optical superfluid phase transitions and trapping of polariton condensates. Phys. Rev. Lett. 110, 186403 (2013).

    Article  ADS  Google Scholar 

  34. Askitopoulos, A. et al. Polariton condensation in an optically induced two-dimensional potential. Phys. Rev. B 88, 041308 (2013).

    Article  ADS  Google Scholar 

  35. Pickup, L., Sigurdsson, H., Ruostekoski, J. & Lagoudakis, P. G. Synthetic band-structure engineering in polariton crystals with non-Hermitian topological phases. Nat. Commun. 11, 4431 (2020).

    Article  ADS  Google Scholar 

  36. Pieczarka, M. et al. Topological phase transition in an all-optical exciton-polariton lattice. Optica 8, 1084 (2021).

    Article  ADS  Google Scholar 

  37. Baboux, F. et al. Unstable and stable regimes of polariton condensation. Optica 5, 1163 (2018).

    Article  ADS  Google Scholar 

  38. 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 

  39. Riminucci, F. et al. Nanostructured GaAs/(Al, Ga)As waveguide for low-density polariton condensation from a bound state in the continuum. Phys. Rev. Appl. 18, 024039 (2022).

    Article  ADS  Google Scholar 

  40. Sigurðsson, H., Nguyen, H. C. & Nguyen, H. S. Dirac exciton-polariton condensates in photonic crystal gratings. Preprint at arXiv https://doi.org/10.48550/arXiv.2310.08423 (2023).

  41. Nigro, D. & Gerace, D. Theory of exciton-polariton condensation in gap-confined eigenmodes. Phys. Rev. B 108, 085305 (2023).

  42. Gati, R. & Oberthaler, M. K. A bosonic Josephson junction. J. Phys. B: At. Mol. Opt. Phys. 40, R61 (2007).

    Article  ADS  Google Scholar 

  43. Lagoudakis, K. G., Pietka, B., Wouters, M., André, R. & Deveaud-Plédran, B. Coherent oscillations in an exciton-polariton Josephson junction. Phys. Rev. Lett. 105, 120403 (2010).

    Article  ADS  Google Scholar 

  44. Abbarchi, M. et al. Macroscopic quantum self-trapping and Josephson oscillations of exciton polaritons. Nat. Phys. 9, 275 (2013).

    Article  Google Scholar 

  45. Kurtscheid, C. et al. Thermally condensing photons into a coherently split state of light. Science 366, 894 (2019).

    Article  ADS  Google Scholar 

  46. Allain, P. E. & Fuchs, J. N. Klein tunneling in graphene: optics with massless electrons. Eur. Phys. J. B 83, 301 (2011).

    Article  ADS  Google Scholar 

  47. Khamehchi, M. A. et al. Negative-mass hydrodynamics in a spin-orbit–coupled Bose-Einstein condensate. Phys. Rev. Lett. 118, 155301 (2017).

    Article  ADS  Google Scholar 

  48. Wurdack, M. et al. Negative-mass exciton polaritons induced by dissipative light-matter coupling in an atomically thin semiconductor. Nat. Commun. 14, 1026 (2023).

    Article  ADS  Google Scholar 

  49. Schäfer, F., Fukuhara, T., Sugawa, S., Takasu, Y. & Takahashi, Y. Tools for quantum simulation with ultracold atoms in optical lattices. Nat. Rev. Phys. 2, 411 (2020).

    Article  Google Scholar 

  50. Hartmann, M. J., Brand ao, F. G. S. L. & Plenio, M. B. Strongly interacting polaritons in coupled arrays of cavities. Nat. Phys. 2, 849 (2006).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  52. Ni, J. et al. Multidimensional phase singularities in nanophotonics. Science 374, eabj0039 (2021).

    Article  Google Scholar 

  53. Atala, M. et al. Direct measurement of the zak phase in topological bloch bands. Nat. Phys. 9, 795 (2013).

    Article  Google Scholar 

  54. Lu, L., Fu, L., Joannopoulos, J. D. & Soljačić, M. Weyl points and line nodes in gyroid photonic crystals. Nat. Photonics 7, 294 (2013).

    Article  ADS  Google Scholar 

  55. Li, Y., Chan, C. T. & Mazur, E. Dirac-like cone-based electromagnetic zero-index metamaterials. Light Sci. Appl. 10, 203 (2021).

    Article  ADS  Google Scholar 

  56. Król, M. et al. Annihilation of exceptional points from different dirac valleys in a 2d photonic system. Nat. Commun. 13, 5340 (2022).

    Article  ADS  Google Scholar 

  57. Milićević, M. et al. Type-iii and tilted dirac cones emerging from flat bands in photonic orbital graphene. Phys. Rev. X 9, 031010 (2019).

    Google Scholar 

  58. Polimeno, L. et al. Experimental investigation of a non-abelian gauge field in 2D perovskite photonic platform. Optica 8, 1442 (2021).

    Article  ADS  Google Scholar 

  59. Jackiw, R. & Rebbi, C. Solitons with fermion number 1/2. Phys. Rev. D 13, 3398 (1976).

    Article  ADS  MathSciNet  Google Scholar 

  60. Tran, T. X. & Biancalana, F. Linear and nonlinear photonic Jackiw-Rebbi states in interfaced binary waveguide arrays. Phys. Rev. A 96, 013831 (2017).

    Article  ADS  Google Scholar 

  61. Lee, K. Y. et al. Topological guided-mode resonances at non-Hermitian nanophotonic interfaces. Nanophotonics 10, 1853 (2021).

    Article  Google Scholar 

  62. Suárez-Forero, D. G. et al. Electrically controlled waveguide polariton laser. Optica 7, 1579 (2020).

    Article  ADS  Google Scholar 

  63. Töpfer, J. D. et al. Engineering spatial coherence in lattices of polariton condensates. Optica 8, 106 (2021).

    Article  ADS  Google Scholar 

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Acknowledgements

H.S. acknowledges the project no. 2022/45/P/ST3/00467 co-funded by the Polish National Science Centre and the European Union Framework Programme for Research and Innovation Horizon 2020 under the Marie Skłodowska-Curie grant agreement no. 945339; and the Icelandic Research Fund (Rannis), grant no. 239552-051. A.G., V.A., D.T., M.D., D.B. and D.S. acknowledge the Italian Ministry of University (MUR) for funding through the PRIN project ‘Interacting Photons in Polariton Circuits’—INPhoPOL (grant 2017P9FJBS), the project ‘Hardware implementation of a polariton neural network for neuromorphic computing’—Joint Bilateral Agreement CNR–RFBR (Russian Foundation for Basic Research)–Triennal Program 2021–2023, the MAECI project ‘Novel photonic platform for neuromorphic computing’, Joint Bilateral Project Italia–Polonia 2022–2023, PNRR MUR project: ‘National Quantum Science and Technology Institute’—NQSTI (PE0000023), PNRR MUR project: ‘Integrated Infrastructure Initiative in Photonic and Quantum Sciences’—I-PHOQS (IR0000016), and the project FISR–C.N.R. ‘Tecnopolo di nanotecnologia e fotonica per la medicina di precisione’—CUP B83B17000010001 and ‘Progetto Tecnopolo per la Medicina di precisione’, Deliberazione della Giunta Regionale n. 2117 del 21/11/2018. H.S.N. is funded by the French National Research Agency (ANR) under the project POPEYE (ANR-17-CE24-0020) and the IDEXLYON from Université de Lyon, Scientific Breakthrough project TORE within the Programme Investissements d’Avenir (ANR-19-IDEX-0005). He is also supported by the Auvergne–Rhône–Alpes region in the framework of PAI2020 and the Vingroup Innovation Foundation (VINIF) annual research grant programme under Project Code VINIF.2021.DA00169. H.C.N. acknowledges the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation, project numbers 447948357 and 440958198), the Sino–German Center for Research Promotion (Project M-0294), the German Ministry of Education and Research (Project QuKuK, BMBF grant no. 16KIS1618K) and the ERC (Consolidator grant 683107/TempoQ). This research is funded in part by the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant GBMF9615 to L.P., and by the National Science Foundation MRSEC grant DMR 2011750 to Princeton University. Work at the Molecular Foundry is supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract no. DE-AC02-05CH11231. We thank S. Dhuey for assistance with electron beam lithography and P. Cazzato for the technical support.

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A.G. performed the experiments and the data analysis with the support of M.E.-T. and V.A. H.S., V.A. and A.G. edited the manuscript with the input of all the authors. L.N.P., K.W.B. and F.R. fabricated and postprocessed the sample. H.S., H.S.N. and H.C.N. provided the theoretical framework and reproduced the experimental results through numerical simulation. D.T. and M.D.G. provided insight on the physical processes and helped in the data interpretation. D.T. provided the code to control the setup. D.B. and D.S. supervised the work.

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Correspondence to Helgi Sigurðsson or Dario Ballarini.

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Nature Physics thanks Edgar Cerda-Mendez, Huawen Xu and Michael Fraser for their contribution to the peer review of this work.

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Supplementary Figs. 1–10 and Sections 1–9.

Supplementary Video 1

Energy-resolved photoluminescence reciprocal-space dynamic. Here we report the dynamical formation of the polariton Bloch band in the case of a regular (that is, mono-atomic) 10-spot chain. The horizontal blue lines mark the energy position of the BIC gap in absence of blueshift. The t = 0 is set at the arrival of the excitation laser.

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Gianfrate, A., Sigurðsson, H., Ardizzone, V. et al. Reconfigurable quantum fluid molecules of bound states in the continuum. Nat. Phys. 20, 61–67 (2024). https://doi.org/10.1038/s41567-023-02281-3

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