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, ...

For strong interactions, we find evidence for an emergent incompressible Mott insulating phase.

W e review dynami c processes i n supercooled liqui ds and glasses as studi ed by dielectri c spectroscopy. It i s the only experim ental techni que whi ch allows one to follow the tremendous slow-down of di OE usi ve motion of parti cles i n di sordered condensed matter over m ore than 18 decades in frequency or ti me. The di electri c techniques used are treated in detai l. As an i ntroducti on for non-speciali sts, the ti me and temperature evolution of the basi c spectral features associated with vari ous dynami c relaxation processes are di scussed in detai l. Among them are the structural relaxati on, the occurrence of fast processes and the boson peak. The relevance of these features for glass formation i s discussed. T he present arti cle may also serve as a review for recent experi mental and theoretical studi es on glassforming liqui ds.

Transport properties are among the defining characteristics of many important phases in condensed matter physics. In the presence of strong correlations they are difficult to predict even for model systems like the Hubbard model. In real materials they are in general obscured by additional complications including impurities, lattice defects or multi-band effects. Ultracold atoms in contrast offer the possibility to study transport and out-of-equilibrium phenomena in a clean and well-controlled environment and can therefore act as a quantum simulator for condensed matter systems. Here we studied the expansion of an initially confined fermionic quantum gas in the lowest band of a homogeneous optical lattice. While we observe ballistic transport for non-interacting atoms, even small interactions render the expansion almost bimodal with a dramatically reduced expansion velocity. The dynamics is independent of the sign of the interaction, revealing a novel, dynamic symmetry of the Hubbard model.In solid state physics, transport properties are among the key observables, the most prominent example being the electrical conductivity, which e.g. allows to distinguish normal conductors from insulators or superconductors. Furthermore, many of today's most intriguing solid state phenomena manifest themselves in transport properties, examples including high-temperature superconductivity, giant magnetoresistance, quantum hall physics, topological insulators and disorder phenomena. Especially in strongly correlated systems, where the interactions between the conductance electrons are important, transport properties are difficult to calculate beyond the linear response regime. In general, predicting out-of-equilibrium fermionic dynamics represents an even harder problem than the prediction of static properties like the nature of the ground state. In real solids further complications arise due to the effects of e.g. impurities, lattice defects and phonons. These complications render an experimental investigation in a clean and well controlled ultracold atom system highly desirable. While the last years have seen dramatic progress in the control of quantum gases in optical lattices [1-3], a thorough understanding of the dynamics in these systems is still lacking. Genuine dynamical experiments can not only uncover new dynamic phenomena but are also essential to gain insight into the timescales needed to achieve equilibrium in the lattice [4,5] or to adiabatically load into the lattice [6,7].Using both bosonic and fermionic [8-10] atoms, it has become possible to simulate models of strongly interacting quantum particles, for which the Hubbard model [11] * ulrich.schneider@lmu.de is probably the most important example. A major advantage of these systems compared to real solids is the possibility to change all relevant parameters in real-time by e.g. varying laser intensities or magnetic fields. While first studies of dynamical properties of both bosonic and fermionic quantum gases [12][13][14] have already been performed, a remaining...

We experimentally and numerically investigate the expansion of initially localized ultracold bosons in homogeneous one- and two-dimensional optical lattices. We find that both dimensionality and interaction strength crucially influence these nonequilibrium dynamics. While the atoms expand ballistically in all integrable limits, deviations from these limits dramatically suppress the expansion and lead to the appearance of almost bimodal cloud shapes, indicating diffusive dynamics in the center surrounded by ballistic wings. For strongly interacting bosons, we observe a dimensional crossover of the dynamics from ballistic in the one-dimensional hard-core case to diffusive in two dimensions, as well as a similar crossover when higher occupancies are introduced into the system.

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.

Interactions lie at the heart of correlated many-body quantum phases. Typically, the interactions between microscopic particles are described as two-body interactions. However, it has been shown that higher-order multi-body interactions could give rise to novel quantum phases with intriguing properties. So far, multi-body interactions have been observed as inelastic loss resonances in three- and four-body recombinations of atom-atom and atom-molecule collisions. Here we demonstrate the presence of effective multi-body interactions in a system of ultracold bosonic atoms in a three-dimensional optical lattice, emerging through virtual transitions of particles from the lowest energy band to higher energy bands. We observe such interactions up to the six-body case in time-resolved traces of quantum phase revivals, using an atom interferometric technique that allows us to precisely measure the absolute energies of atom number states at a lattice site. In addition, we show that the spectral content of these time traces can reveal the atom number statistics at a lattice site, similar to foundational experiments in cavity quantum electrodynamics that yield the statistics of a cavity photon field. Our precision measurement of multi-body interaction energies provides crucial input for the comparison of optical-lattice quantum simulators with many-body quantum theory.

Dielectric loss spectra of glass-forming propylene carbonate and glycerol at temperatures above and below T(g) are presented. By performing aging experiments lasting up to five weeks, equilibrium spectra below T(g) have been obtained. During aging, the excess wing, showing up as a second power law at high frequencies, develops into a shoulder. The results strongly suggest that the excess wing, observed in a variety of glass formers, is the high-frequency flank of a beta relaxation.