Observation of the diffusive Nambu–Goldstone mode of a non-equilibrium phase transition
Open accessAbstract
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. Gapless modes emerging from non-equilibrium phase transitions are predicted to diffuse rather than propagate as sound waves. Now, the diffusion of these modes and their suppression under symmetry breaking are confirmed in a polariton condensate.
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While particle-number conservation makes it difficult to verify this prediction in atomic condensates at equilibrium, the phase of an optical condensate can be pinned by an additional incident coherent laser, and a clear gap in the Goldstone mode dispersion is observed in experiments.
“While particle-number conservation makes it difficult to verify this prediction in atomic condensates at equilibrium [124], the phase of an optical condensate can be pinned by an additional incident coherent laser [125] and a clear gap in the Goldstone mode dispersion is clearly observed in experiments [106].”
From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [106]
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Experimental — accuracy not yet measuredThe theoretical prediction of a diffusive Goldstone mode in a nonequilibrium condensate has been confirmed in a pump-and-probe experimental measurement of the collective-mode dispersion of an exciton-polariton condensate.
“The theoretical prediction of a diffusive behaviour of the Goldstone mode of a nonequilibrium condensate has been recently confirmed in a pump-and-probe experimental measurement of the dispersion of the collective modes of an exciton-polariton condensate [106].”
From How to exploit driving and dissipation to stabilize and manipulate quantum many-body states (2025) · cites this paper as [106]
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- Authors
- Claude, F., Jacquet, M. J., Glorieux, Q., Wouters, M., Giacobino, E., Carusotto, I., & Bramati, A.
- Affiliations
- Centre National de la Recherche Scientifique (FR)
- University of Antwerp (BE)
- University of Trento (IT)
- ORCID
- Venue
- Nature Physics
- Published
- 2025-05-02
- Volume
- 21
- Issue
- 6
- Pages
- 924-930
- ISSN
- 1745-2473 (ISSN-L)
- 1745-2481
- OpenAlex
- W4410043733
- Semantic Scholar
- 1f52c8c99c8cefb1975147bb0349de36b975d2eb
- Cited by
- 7
- References
- 58
- Citations by year
- 2026: 5 · 2025: 2
- FWCI
- 2.56
- Type
- journal article
- Language
- en
- Open access
- green
- hal.science
- Licence
- Locations
- Nature Physics (publishedVersion)
- HAL (submittedVersion)
- Funders
- Institut Universitaire de France
- Provincia Autonoma di Trento (820392, PE0000023-NQSTI)
- Horizon 2020 Framework Programme (PE0000023-NQSTI, 820392)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Strong Light-Matter Interactions
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Keywords
- Goldstone modes, diffusive modes, nonequilibrium phase transitions, exciton-polariton condensates, gapless modes, symmetry breaking, exciton-polaritons
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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