Experimental Observation of a Generalized Gibbs Ensemble

Stefan K. Kehrein

Ph. Chomaz, Francesca Gulminelli, Olivier Juillet

Herbert Spohn

L. Lanz, G. Lupieri

Florentin Reiter, Florian Lange, Shreyans Jain +3 more

The concept of generalized Gibbs ensembles (GGEs) has been introduced to describe steady states of integrable models. Recent advances show that GGEs can also be stabilized in nearly integrable quantum systems when driven by external fields and open. Here, we present a weakly dissipative dynamics that drives towards a steady-state GGE and is realistic to implement in systems of trapped ions. We outline the engineering of the desired dissipation by a combination of couplings which can be realized with ion-trap setups and discuss the experimental observables needed to detect a deviation from a thermal state. We present a mixed-species motional mode engineering technique in an array of microtraps and demonstrate the possibility to use sympathetic cooling to construct many-body dissipators. Our paper provides a blueprint for experimental observation of GGEs in open systems and opens an avenue for quantum simulation of driven-dissipative quantum many-body problems.

Alvise Bastianello, Alexey M. Tikan, François Copie +2 more

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.