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Kardar–Parisi–Zhang universality in a one-dimensional polariton condensate


Revealing universal behaviours is a hallmark of statistical physics. Phenomena such as the stochastic growth of crystalline surfaces1 and of interfaces in bacterial colonies2, and spin transport in quantum magnets3,4,5,6 all belong to the same universality class, despite the great plurality of physical mechanisms they involve at the microscopic level. More specifically, in all these systems, space–time correlations show power-law scalings characterized by universal critical exponents. This universality stems from a common underlying effective dynamics governed by the nonlinear stochastic Kardar–Parisi–Zhang (KPZ) equation7. Recent theoretical works have suggested that this dynamics also emerges in the phase of out-of-equilibrium systems showing macroscopic spontaneous coherence8,9,10,11,12,13,14,15,16,17. Here we experimentally demonstrate that the evolution of the phase in a driven-dissipative one-dimensional polariton condensate falls in the KPZ universality class. Our demonstration relies on a direct measurement of KPZ space–time scaling laws18,19, combined with a theoretical analysis that reveals other key signatures of this universality class. Our results highlight fundamental physical differences between out-of-equilibrium condensates and their equilibrium counterparts, and open a paradigm for exploring universal behaviours in driven open quantum systems.

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Fig. 1: KPZ physics in the phase dynamics of a 1D polariton condensate.
Fig. 2: Probing the coherence of 1D polariton condensates.
Fig. 3: KPZ scaling in the coherence decay of a 1D polariton condensate.
Fig. 4: Analysis of the simulated phase dynamics.

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Data availability

All datasets generated and analysed during this study are available upon request from the corresponding authors. Source data are provided with this paper.

Code availability

All codes generated during this study are available upon request from the corresponding authors.


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We thank V. Goblot, D. Vajner and A. Toor for their assistance in the early development of the experiment. This work was supported by the Paris Ile-de-France Région in the framework of DIM SIRTEQ, the French RENATECH network, the H2020-FETFLAG project PhoQus (820392), the QUANTERA project Interpol (ANR-QUAN-0003-05), the European Research Council via the project ARQADIA (949730), EmergenTopo (865151) and RG.BIO (785932), the French government through the Programme Investissement d’Avenir (I-SITE ULNE / ANR-16-IDEX-0004 ULNE) managed by the Agence Nationale de la Recherche, and the Labex CEMPI (ANR-11-LABX-0007). L.C. acknowledges support from ANR (grant ANR-18-CE92-0019) and from Institut Universitaire de France.

Author information

Authors and Affiliations



Q.F. built the experimental set-up, performed the experiments and analysed the data. D.S. realized the theoretical calculations and numerical simulations. F.B. contributed to the design of the sample structure and initial characterization of the sample. A.L. and M.M. grew the sample by molecular beam epitaxy. I.S., L.L.G. and A.H. fabricated the polariton lattices. Q.F., D.S., I.A., M.W., I.C., A.A., M.R., A.M., L.C., S.R. and J.B. participated in the scientific discussions about all aspects of the work. Q.F., A.M., L.C., S.R. and J.B. wrote the original draft of the paper. Q.F., D.S., I.A., M.W., I.C., A.A., M.R., A.M., L.C., S.R. and J.B. reviewed and edited the paper into its current form. A.M., L.C., S.R. and J.B. supervised the work.

Corresponding authors

Correspondence to Léonie Canet or Jacqueline Bloch.

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The authors declare no competing interests.

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Nature thanks Sebastian Diehl, Michael Fraser and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

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Supplementary information

Supplementary Information

This Supplementary Information file contains four sections with 16 figures: (I) Overview; (II) The theoretical model: emergence of KPZ dynamics in incoherently pumped polaritons; (III) Experiments: additional information and data; and (IV) Numerical simulations: discussion.

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Fontaine, Q., Squizzato, D., Baboux, F. et al. Kardar–Parisi–Zhang universality in a one-dimensional polariton condensate. Nature 608, 687–691 (2022).

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