Local emergence of thermal correlations in an isolated quantum many-body system

Understanding the dynamics of isolated quantum manybody systems is a central open problem at the intersection between statistical physics and quantum physics. Despite important theoretical effort(1), no generic framework exists yet to understand when and how an isolated quantum system relaxes to a steady state. Regarding the question of how, it has been conjectured(2,3) that equilibration must occur on a local scale in systems where correlations between distant points can establish only at a finite speed. Here, we provide the first experimental observation of this local equilibration hypothesis. In our experiment, we quench a one-dimensional Bose gas by coherently splitting it into two parts. By monitoring the phase coherence between the two parts we observe that the thermal correlations of a prethermalized state(4,5) emerge locally in their final form and propagate through the system in a light-cone-like evolution. Our results underline the close link between the propagation of correlations(2,3,6,7) and relaxation processes in quantum many-body systems.