Abstract
A supersolid is a counter-intuitive phase of matter in which its constituent particles are arranged into a crystalline structure, yet they are free to flow without friction. This requires the particles to share a global macroscopic phase while being able to reduce their total energy by spontaneous, spatial self-organization. The existence of the supersolid phase of matter was speculated more than 50 years ago1,2,3,4. However, only recently has there been convincing experimental evidence, mainly using ultracold atomic Bose–Einstein condensates (BECs) coupled to electromagnetic fields. There, various guises of the supersolid were created using atoms coupled to high-finesse cavities5,6, with large magnetic dipole moments7,8,9,10,11,12,13, and spin–orbit-coupled, two-component systems showing stripe phases14,15,16. Here we provide experimental evidence of a new implementation of the supersolid phase in a driven-dissipative, non-equilibrium context based on exciton–polaritons condensed in a topologically non-trivial, bound state in the continuum (BiC) with exceptionally low losses, realized in a photonic-crystal waveguide. We measure the density modulation of the polaritonic state indicating the breaking of translational symmetry with a precision of several parts in a thousand. Direct access to the phase of the wavefunction allows us to also measure the local coherence of the supersolid. We demonstrate the potential of our synthetic photonic material to host phonon dynamics and a multimode excitation spectrum.
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Data availability
The data of this study are available at https://doi.org/10.5281/zenodo.14251103 (ref. 54). Raw data can be obtained from the corresponding author on reasonable request.
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Acknowledgements
We acknowledge fruitful discussions with V. Ardizzone, M. Pieczarka and A. Recati. We are thankful to G. Lerario for his valuable feedback on the manuscript. This project was financed by 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); Quantum Optical Networks based on Exciton-polaritons – (Q-ONE) funding from the HORIZON-EIC-2022-PATHFINDER CHALLENGES EU programme under grant agreement no. 101115575; Neuromorphic Polariton Accelerator – (PolArt) funding from the Horizon-EIC-2023-Pathfinder Open EU programme under grant agreement no. 101130304; 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; the PRIN project ‘QNoRM: A quantum neuromorphic recognition machine of quantum states’ – (grant 20229J8Z4P). Views and opinions expressed are however those of the author(s) only and do not necessarily reflect those of the European Union or European Innovation Council and SMEs Executive Agency (EISMEA). Neither the European Union nor the granting authority can be held responsible for them. M.L. acknowledges support through the FWF-funded QuantERA project QuSiED with project number I 6008-N. I.C. acknowledges support from the Provincia Autonoma di Trento, partly through the Q@TN initiative. This research is financed in part by the Gordon and Betty Moore Foundation’s EPiQS Initiative, grant GBMF9615 to L.N.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 U.S. 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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D.T. and M.L. conceived the experiment and convinced D.S. to proceed with it. A.G. took the data and, together with D.T., performed the analysis. D.T., A.G. and M.L. wrote the manuscript. D.N., D.G., G.I.M. and I.C. provided theoretical support. F.R. processed the sample; growth was performed by K.W.B. and L.N.P. D.S. supervised the work, discussed the data and tirelessly explained to D.T. how polariton optical parametric oscillations should behave. D.T. tried to use the best photonics language he could muster but, in the end, had to use KETs. D.B. and M.D.G. assisted with the experimental set-up and interpretation of the data. All authors contributed to discussions and editing of the manuscript.
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Extended Data Fig. 1 Holographic imaging.
a, Fourier transform of the interferogram in c showing the main peak around 7.5 μm−1 and sidebands at ±kr from it. b, In energy-resolved measurements, the BiC is dark in the middle. c, An interferogram as given by the Michelson interferometer described in Methods. The bright spot in the middle is coming directly from the exciton reservoir and its size is comparable with the laser spot. d, Retaining only the middle frequencies leads to a density without the middle spot (bottom panel) as it is incoherent, as opposed to retaining the low frequencies (top panel). e, In both cases, the amplitude of the modulation and the density in the lobes of the BiC are exactly the same.
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Trypogeorgos, D., Gianfrate, A., Landini, M. et al. Emerging supersolidity in photonic-crystal polariton condensates. Nature 639, 337–341 (2025). https://doi.org/10.1038/s41586-025-08616-9
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DOI: https://doi.org/10.1038/s41586-025-08616-9
