Understanding relaxation processes is an important unsolved problem in many areas of physics. A key challenge is the scarcity of experimental tools for the characterization of complex transient states. We used measurements of full quantum mechanical probability distributions of matter-wave interference to study the relaxation dynamics of a coherently split one-dimensional Bose gas and obtained comprehensive information about the dynamical states of the system. After an initial rapid evolution, the full distributions reveal the approach toward a thermal-like steady state characterized by an effective temperature that is independent from the initial equilibrium temperature of the system before the splitting process. We conjecture that this state can be described through a generalized Gibbs ensemble and associate it with prethermalization.

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.It has been theoretically suggested that relaxation in generic isolated quantum many-body systems proceeds through the dephasing of the quantum states populated at the onset of the non-equilibrium evolution 8,9 . It is generally believed that this dynamically leads to relaxed states that can be well described either by the usual thermodynamical ensembles or by generalized Gibbs ensembles that take into account dynamical constraints 10 . However, it remains an open question how these relaxed states form dynamically, and in particular, whether they emerge gradually on a global scale, or appear locally and then spread in space and time 3 .Ultracold atomic gases offer an ideal test bed to explore such quantum dynamics. Their almost perfect isolation from the environment and the many available methods to probe their quantum states make it possible to reveal the dynamical evolution of a many-body system at a very detailed level 4,7,11-16 .In our experiment, a phase-fluctuating ultracold onedimensional (1D) Bose gas 17 is split coherently 18 . The splitting creates a non-equilibrium state consisting of two gases with almost identical phase profiles. Interactions in the many-body system drive the relaxation of this highly phase-correlated state to a prethermalized state, characterized by thermal phase correlations 4,19 . The dynamics is monitored by time-resolved measurements of the relative phase field using matter-wave interferometry 20 .The experimental procedure starts with a 1D degenerate gas of 4,000-12,000 87 Rb atoms trapped at temperatures between 30-110 nK in a magnetic trap, formed 100 µm below the trapping wires of an atom chip 21 . By applying radiofrequency fields through additional wires on the chip, we rapidly transform the initial harmonic trapping potential into a double well, thereby realizing the matter-wave analogue of a coherent beamsplitter 18 (see Methods).The system is allowed to evolve in the double well for a variable time t , before the gases are ...

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.