Experimental observation of a generalized Gibbs ensemble

Abstract

The description of the non-equilibrium dynamics of isolated quantum many-body systems within the framework of statistical mechanics is a fundamental open question. Conventional thermodynamical ensembles fail to describe the large class of systems that exhibit nontrivial conserved quantities, and generalized ensembles have been predicted to maximize entropy in these systems. We show experimentally that a degenerate one-dimensional Bose gas relaxes to a state that can be described by such a generalized ensemble. This is verified through a detailed study of correlation functions up to 10th order. The applicability of the generalized ensemble description for isolated quantum many-body systems points to a natural emergence of classical statistical properties from the microscopic unitary quantum evolution.

Experimental characterization of a quantum many-body system via higher-order correlations

“…The connected correlation function G (N ) con (z, z ) for N > 2 is therefore a direct measure of their interactions. In contrast, the more commonly used correlation functions e i[ϕ(z)−ϕ(z )] and their higher-order generalisations [20] contain G (N ) con (z, z ) up to arbitrary order even for the 2 nd -order function and are therefore not suitable for studying these interaction properties (see Methods and the SI).…”

“…With the rapid progress in quantum gas experiments [16], measuring higher-order correlation functions [17][18][19][20] is now within reach. To illustrate the power of the above concepts to analyse a non trivial interacting quantum many-body system, we experimentally investigate two tunnel-coupled one-dimensional (1D) bosonic superfluids, realised with quantum degenerate 87 Rb atoms trapped in a double-well (DW) potential with a freely relative DOF DW potential adjustable tunnel-coupling FIG.…”

Prethermalization and thermalization of a quenched interacting Luttinger liquid

“…In particular, in Refs. [16][17][18]24] prethermal states in the relative phase of a suddenly split condensate have been identified that have been stable on the experimentally accessible time scales. For the latter experiments, the cubic nonlinearity studied in the present work constitutes the leading order correction to the quadratic theory in a gradient expansion.…”

“…Concerning the relevance of the interacting Luttinger model, before closing the section, we would like to mention that only recently pioneering experiments in ultra-cold gases both in and out of equilibrium explored the transient and prethermalization dynamics of systems [16][17][18][19][20][21][22][23][24][25][26][68][69][70] effectively described by a quadratic Luttinger model, the bosonic theory of the Hamiltonian in Eq. (2.2).…”

“…Importantly, these experiments share a remarkable isolation from the environment, thereby probing the purely coherent unitary time evolution on the experimentally relevant time scales. This has paved the way to experimentally study the constrained relaxational dynamics of quantum systems close to integrability [15,[24][25][26], showing unconventional properties due to the anticipated (quasi-)local conservation laws. Although the inherent integrability breaking terms, resulting from, e.g., imperfections in the particle-particle interactions or higher orbital modes, are considered to be weak, they are believed to eventually cause relaxation to thermal states on long-time scales.…”