Abstract
Bound states in the continuum (BICs)1,2,3 are peculiar topological states that, when realized in a planar photonic crystal lattice, are symmetry-protected from radiating in the far field despite lying within the light cone4. These BICs possess an invariant topological charge given by the winding number of the polarization vectors5, similar to vortices in quantum fluids such as superfluid helium and atomic Bose–Einstein condensates. In spite of several reports of optical BICs in patterned dielectric slabs with evidence of lasing, their potential as topologically protected states with theoretically infinite lifetime has not yet been fully exploited. Here we show non-equilibrium Bose–Einstein condensation of polaritons—hybrid light–matter excitations—occurring in a BIC thanks to its peculiar non-radiative nature, which favours polariton accumulation. The combination of the ultralong BIC lifetime and the tight confinement of the waveguide geometry enables the achievement of an extremely low threshold density for condensation, which is reached not in the dispersion minimum but at a saddle point in reciprocal space. By bridging bosonic condensation and symmetry-protected radiation eigenmodes, we reveal ways of imparting topological properties onto macroscopic quantum states with unexplored dispersion features. Such an observation may open a route towards energy-efficient polariton condensation in cost-effective integrated devices, ultimately suited for the development of hybrid light–matter optical circuits.
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Data availability
The datasets generated and/or analysed during the current study are available in the Open Science Framework (OSF) repository, https://osf.io/x5nz3/?view_only=fada1eca509141eeb993453e2388a229. Data and any other information are also available upon reasonable request.
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Acknowledgements
We thank P. Cazzato for technical support. We are grateful to L. C. Andreani for discussions and support, and R. Rapaport for discussions and for sharing information about the sample design. We acknowledge the Italian Ministry of University (MIUR) for funding through the PRIN project ‘Interacting Photons in Polariton Circuits’ – INPhoPOL (grant 2017P9FJBS) and for the FISR 2020 – COVID, project ‘Sensore elettro-ottico a guida d'onda basato sull'interazione luce-materia’ (WaveSense), FISR2020IP-04324. Work at the Molecular Foundry was supported by the Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under contract number DE-AC02-05CH11231. We thank S. Dhuey at the Molecular Foundry for assistance with the electron-beam lithography. We acknowledge the project FISR – CNR ‘Tecnopolo di nanotecnologia e fotonica per la medicina di precisione’ – CUP B83B17000010001 and ‘Progetto Tecnopolo per la Medicina di precisione’, Deliberazione della Giunta Regionale number 2117 del 21/11/2018. We also acknowledge ‘Hardware implementation of a polariton neural network for neuromorphic computing’, Joint Bilateral Agreement CNR–RFBR (Russian Foundation for Basic Reaserach) – Triennal Programme 2021–2023. 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. H.S.N. is partly supported by the French National Research Agency (ANR) under the project POPEYE (ANR-17-CE24-0020), the IDEXLYON from Université de Lyon, Scientific Breakthrough project TORE within the Programme Investissements d’Avenir (ANR-19-IDEX0005) and the Vingroup Innovation Foundation (VINIF) annual research grant programme under project code VINIF.2021.DA00169. H.S.N. dedicates this work to V. H. Nguyen.
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V.A., D.S. and D.G. initiated the research project, V.A. and F.R. designed the grating structures with input from H.S.N.; F.R. processed the sample, growth was performed by K.B. and L.P.; V.A., F.R., A.G., D.G.S.-F., M.E.-T., H.S.N. and D.B. realized the experiments and carried out the data analysis; H.S.N., S.Z. and D.G. developed the theoretical background and performed the FDTD simulations. V.A., H.S.N., D.G. and D.S. drafted the manuscript, and all the authors were involved in the discussion of results and the final manuscript editing.
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Extended data figures and tables
Extended Data Fig. 1 Tuning the properties of the polariton BIC.
a, c, Grating pitch 240 nm and fill factors 0.5 (a) and 0.6 (c). b, d, Pitch 244 nm and fill factors 0.5 (b) and 0.6 (d).
Extended Data Fig. 2 Effect of the spot size.
a, b, Polariton condensation under a pumping spot of size S ≈ 30 μm; for pumping densities well above the condensation threshold two modes are visible: M0 and M1, with an energy separation of about 1 meV. c, d, Polariton condensation under a pumping spot of size S ≈ 120 μm; for pumping densities well above the condensation threshold three modes are visible: M0, M1 and M2, with an energy separation of about 0.3 meV. PL, photoluminescence. Light intensity increases from dark to light colours in Extended Data Figs. 2–4.
Extended Data Fig. 3 Polariton propagation.
a, Excitation scheme for propagation measurements; the red spot outside the grating represents the non-resonant exciting laser beam. b, Polariton dispersion obtained by pumping the sample with the scheme in a; only polaritons propagating upwards reach the grating. c, Polariton group velocity extracted from the fitted dispersion in b.
Extended Data Fig. 4 Energy- and space-resolved emission of the gratings of Extended Data Fig. 3b.
By fitting the emission at each energy with an exponential decay we can extract the polariton decay length. Here only a portion of the bright mode is visible as it has been filtered in reciprocal space.
Extended Data Fig. 5 Polariton lifetimes.
Polariton lifetimes for two gratings having a polariton BIC at excitonic fractions 0.25 (left) and 0.5 (right). The black dashed lines represent the energy of the BIC in each case. The error bars result from the errors in fitting the exponential decay of polariton propagation in real space and from the fitting of the group velocity; see Extended Data Fig. 3.
Extended Data Fig. 6 Coherence measurements.
a, Scheme of the experimental set-up used to measure the interferogram shown in b.
Extended Data Fig. 7 Polarization properties of the BIC and the bright states.
Measured polarization parameters from the BIC and the bright state. ϕ is the polarization axis direction and χ is the ellipticity.
Supplementary information
Supplementary Information
This file contains Supplementary Text, Supplementary Figures and Supplementary Equations.
Supplementary Video 1
Temporal dynamics of the polariton condensate from the BIC at a power excitation density close to the condensation threshold.
Supplementary Video 2
Temporal dynamics of the polariton condensate from the BIC at a power excitation density above the condensation threshold.
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Ardizzone, V., Riminucci, F., Zanotti, S. et al. Polariton Bose–Einstein condensate from a bound state in the continuum. Nature 605, 447–452 (2022). https://doi.org/10.1038/s41586-022-04583-7
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DOI: https://doi.org/10.1038/s41586-022-04583-7
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