Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system

Abstract

Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters has been the focus of attention in non-equilibrium thermodynamics. And several experimentally unproven conjectures are proposed for the statistical description of quantum (non-)integrable models. The plausible eigenstate thermalization hypothesis (ETH), which suggests that each energy eigenstate itself is thermal, plays a crucial role in understanding the quantum thermalization in non-integrable systems; it is commonly believed that it does not exist in integrable systems. Nevertheless, integrable systems can still relax to the generalized Gibbs ensemble. From a microscopic perspective, understanding the origin of this generalized thermalization that occurs in an isolated integrable system is a fundamental open question lacking experimental investigations. Herein, we experimentally investigated the spin subsystem relaxation in an isolated spin–orbit coupling quantum system. By applying the quantum state engineering technique, we initialized the system with various distribution widths in the mutual eigenbasis of the conserved quantities. Then, we compared the steady state of the spin subsystem reached in a long-time coherent dynamics to the prediction of a generalized version of ETH and the underlying mechanism of the generalized thermalization is experimentally verified for the first time. Our results facilitate understanding the origin of quantum statistical mechanics.

Mesoscopic impurities in generalized hydrodynamics

“…For instance, this manifests in the equilibrium that the system approaches after a long time; it is characterized by a generalized Gibbs ensemble (GGE) [1,2], which takes into account all conserved quantities instead of the usual Gibbs ensembles. This failure of thermalization has been observed in experiments, such as the famous quantum Newton's cradle experiment [3] and others [4,5]. However, in one dimension, non-integrable systems often show effects linked to integrability (e.g.…”

“…Note that H(x, λ) is technically equal to E Dr , defined in a previous study [56, supplementary material, equation (5)]. However, the authors only looked at the λ dependence of E Dr (λ), which works in general for any T (λ, µ).…”

Efficient learning of mixed-state tomography for photonic quantum walk

“…For a discrete-time QW (21), the usual local tomographic technique was experimentally demonstrated that enables one to access the two correlated subsystems of coin (22)(23)(24)(25) and position (26,27), respectively. The tomography was subsequently extended to the walker's complete wave function with a pure-state hypothesis (28) or a lowrank state when decoherence should be estimated (29).…”