Quantum thermalization through entanglement in an isolated many-body system

Abstract

The concept of entropy is fundamental to thermalization, yet appears at odds with basic principles in quantum mechanics. While statistical mechanics relies on the maximization of entropy for a system at thermal equilibrium, an isolated many-body system undergoing Schr\"odinger dynamics has zero entropy because, at any given time, it is described by a single quantum state. The underlying role of quantum mechanics in many-body physics is then seemingly antithetical to the success of statistical mechanics in a large variety of systems. Here we observe experimentally how this conflict is resolved: we perform microscopy on an evolving quantum state, and we see thermalization occur on a local scale, while we measure that the full quantum state remains pure. We directly measure entanglement entropy and observe how it assumes the role of the thermal entropy in thermalization. Although the full state has zero entropy, entanglement creates local entropy that validates the use of statistical physics for local observables. In combination with number-resolved, single-site imaging, we demonstrate how our measurements of a pure quantum state agree with the Eigenstate Thermalization Hypothesis and thermal ensembles in the presence of a near-volume law in the entanglement entropy.