We experimentally observe many-body localization of interacting fermions in a one-dimensional quasi-random optical lattice. We identify the manybody localization transition through the relaxation dynamics of an initially-prepared charge density wave. For sufficiently weak disorder the time evolution appears ergodic and thermalizing, erasing all remnants of the initial order. In contrast, above a critical disorder strength a significant portion of the initial ordering persists, thereby serving as an effective order parameter for localization. The stationary density wave order and the critical disorder value show a distinctive dependence on the interaction strength, in agreement with numerical simulations. We connect this dependence to the ubiquitous logarithmic growth of entanglement entropy characterizing the generic many-body localized phase.Introduction The ergodic hypothesis is one of the central principles of statistical physics. In ergodic time evolution of a quantum many-body system, local degrees of freedom become fully entangled with the rest of the system, leading to an effectively classical hydrodynamic evolution of the remaining slow observables [1]. Hence, ergodicity is responsible for the demise of observable quantum correlations in the dynamics of large many-body systems and forms the basis for the emergence of local thermodynamic equilibrium in isolated quantum systems [2,3,4]. It is therefore of fundamental interest to investigate how ergodicity breaks down and search for alternative, genuinely quantum paradigms in the dynamics, and to understand the long-time stationary states that ensue in the absence of ergodicity.One path to breaking ergodicity is provided by the study of integrable models, where thermalization is prevented due to the constraints imposed on the dynamics by an infinite set of conservation rules. Such models have been realized and studied in a number of experiments with ultracold atomic gases [5,6,7]. However, integrable models represent very special and fine-tuned situations, making it difficult to extract general underlying principles.Theoretical studies over the last decade point to many-body localization (MBL) in a disordered isolated quantum system as a more generic alternative to thermalization dynamics. In his original paper on single-particle localization, Anderson already speculated that interacting many-body systems subject to sufficiently strong disorder would also fail to thermalize [8]. Only recently, however, have convincing theoretical arguments been put forward that Anderson localization remains stable under the addition of moderate interactions, even in highly excited many-body states [9,10,11]. Further theoretical studies have established the many-body localized state as a distinct dynamical phase of matter that exhibits novel universal behavior [12,13,14,15,16,17,18,19,20,21,22]. In particular, the relaxation of local observables does not follow the conventional paradigm of thermalization and is expected to show explicit breaking of ergodicity. In many ways, ...

We experimentally study the effects of coupling one-dimensional many-body localized systems with identical disorder. Using a gas of ultracold fermions in an optical lattice, we artificially prepare an initial charge density wave in an array of 1D tubes with quasirandom on-site disorder and monitor the subsequent dynamics over several thousand tunneling times. We find a strikingly different behavior between many-body localization and Anderson localization. While the noninteracting Anderson case remains localized, in the interacting case any coupling between the tubes leads to a delocalization of the entire system.

In the presence of sufficiently strong disorder or quasiperiodic fields, an interacting many-body system can fail to thermalize and become many-body localized. The associated transition is of particular interest, since it occurs not only in the ground state but over an extended range of energy densities. So far, theoretical studies of the transition have focused mainly on the case of true-random disorder. In this work, we experimentally and numerically investigate the regime close to the many-body localization transition in quasiperiodic systems. We find slow relaxation of the density imbalance close to the transition, strikingly similar to the behavior near the transition in true-random systems. This dynamics is found to continuously slow down upon approaching the transition and allows for an estimate of the transition point. We discuss possible microscopic origins of these slow dynamics.