Abstract
Second-order phase transitions are governed by a spontaneous symmetry-breaking mechanism, which yields collective excitations with a gapless spectrum called Nambu–Goldstone modes. Although these modes propagate as sound waves in conservative systems, non-equilibrium phase transitions have been predicted to feature a diffusive Nambu–Goldstone mode. Here, we present the experimental characterization of such a mode in a non-equilibrium Bose–Einstein condensate of microcavity polaritons. The mode appears in the spectroscopic response of the condensate to an extra probe laser as spectral narrowing, along with the emergence of a tilted frequency plateau. Breaking the symmetry with another phase-fixing beam causes a gap to open in the imaginary part of the spectrum and the disappearance of the Nambu–Goldstone mode. These observations confirm theoretical predictions for the Nambu–Goldstone mode of non-equilibrium phase transitions and reveal the symmetry-breaking mechanism underlying polariton condensation.
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The raw data are available via Zenodo at https://doi.org/10.5281/zenodo.15079205 (ref. 57).
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Acknowledgements
We are thankful to J. H. Wilson for enlightening conversations on NG modes in various field theories. We acknowledge financial support from the H2020-FETFLAG-2018-2020 project PhoQuS (n.820392). I.C. acknowledges financial support from the Provincia Autonoma di Trento, from the Q@TN Initiative and from the National Quantum Science and Technology Institute through the PNRR MUR Project (Grant No. PE0000023-NQSTI), co-funded by the European Union - NextGeneration EU. M.J.J. and A.B. acknowledge financial support from the Sirteq DIM. Q.G. and A.B. are members of the Institut Universitaire de France.
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F.C. performed the experiments. F.C. and M.J.J. analysed the data and prepared the figures. Q.G. advised on experimental technical details. M.W. and I.C. performed the theoretical analysis and the numerical calculation and interpreted the results with the help of F.C., M.J.J. and A.B. M.J.J. and I.C. wrote the manuscript with input from all authors. A.B. and E.G. reviewed the manuscript. This collaborative effort was led by A.B., who conceived and supervised the project.
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Claude, F., Jacquet, M.J., Glorieux, Q. et al. Observation of the diffusive Nambu–Goldstone mode of a non-equilibrium phase transition. Nat. Phys. 21, 924–930 (2025). https://doi.org/10.1038/s41567-025-02902-z
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DOI: https://doi.org/10.1038/s41567-025-02902-z
