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  • Open Access

Observation of a generalized Gibbs ensemble in photonics

Alvise Bastianello1,2,3,*, Alexey Tikan4,*, Francois Copie5, Stephane Randoux5, and Pierre Suret5,†

  • *These authors contributed equally to this work.
  • †Contact author: pierre.suret@univ-lille.fr
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Phys. Rev. A 113, 013514 – Published 9 January, 2026

DOI: https://doi.org/10.1103/xz2w-hndp

Abstract

In generic classical and quantum many-body systems, where typically energy and particle number are the only conserved quantities, stationary states are described by thermal equilibrium. In contrast, integrable systems showcase an infinite hierarchy of conserved quantities that inhibits conventional thermalization, forcing relaxation to a generalized Gibbs ensemble (GGE)—a concept first introduced in quantum many-body physics. In this study, we provide experimental evidence for the emergence of a GGE in a photonic system. By investigating partially coherent waves propagating in a normal dispersion optical fiber, governed by the one-dimensional defocusing nonlinear Schrödinger equation, we directly measure the density of states of the spectral parameter (rapidity) to confirm the time invariance of the full set of conserved charges. We also observe the relaxation of optical power statistics to the GGE's theoretical prediction, obtained using the experimentally measured density of states. These complementary measurements unambiguously establish the formation of a GGE in our photonic platform, highlighting its potential as a powerful tool for probing many-body integrability and bridging classical and quantum integrable systems.

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Phys. Rev. A 113, 013514– Published 9 January, 2026
  • Received 7 April 2025
  • Revised 5 June 2025
  • Accepted 17 December 2025
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