Out-of-equilibrium bosons on a one-dimensional optical random lattice

We study the transport properties of a one-dimensional hard-core boson lattice gas coupled to two particle reservoirs at different chemical potentials generating a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-\kappa(\tau)\nabla \rho$ where $\tau$ is a typical timescale of the lattice fluctuations and $\nabla \rho$ the density gradient imposed %on the system by the reservoirs

Localization of cold atoms in state-dependent optical lattices via a Rabi pulse

We propose a novel realization of Anderson localization in non-equilibrium states of ultracold atoms trapped in state-dependent optical lattices. The disorder potential leading to localization is generated with a Rabi pulse transfering a fraction of the atoms into a different internal state for which tunneling between lattice sites is suppressed. Atoms with zero tunneling create a quantum superposition of different random potentials, localizing the mobile atoms. We investigate the dynamics of the mobile atoms after the Rabi pulse for non-interacting and weakly interacting bosons, and we show that the evolved wavefunction attains a quasi-stationary profile with exponentially decaying tails, characteristic of Anderson localization. The localization length is seen to increase with increasing disorder and interaction strength, oppositely to what is expected for equilibrium localization.Comment: 4 pages, 4 figure

The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases

We compute the phase diagram of the one-dimensional Bose-Hubbard model with a quasi-periodic potential by means of the density-matrix renormalization group technique. This model describes the physics of cold atoms loaded in an optical lattice in the presence of a superlattice potential whose wave length is incommensurate with the main lattice wave length. After discussing the conditions under which the model can be realized experimentally, the study of the density vs. the chemical potential curves for a non-trapped system unveils the existence of gapped phases at incommensurate densities interpreted as incommensurate charge-density wave phases. Furthermore, a localization transition is known to occur above a critical value of the potential depth V_2 in the case of free and hard-core bosons. We extend these results to soft-core bosons for which the phase diagrams at fixed densities display new features compared with the phase diagrams known for random box distribution disorder. In particular, a direct transition from the superfluid phase to the Mott insulating phase is found at finite V_2. Evidence for reentrances of the superfluid phase upon increasing interactions is presented. We finally comment on different ways to probe the emergent quantum phases and most importantly, the existence of a critical value for the localization transition. The later feature can be investigated by looking at the expansion of the cloud after releasing the trap.Comment: 19 pages, 20 figure

Disordered quantum gases under control

When attempting to understand the role of disorder in condensed-matter physics, one faces severe experimental and theoretical difficulties and many questions are still open. Two of the most challenging ones, which have been debated for decades, concern the effect of disorder on superconductivity and quantum magnetism. Recent progress in ultracold atomic gases paves the way towards realization of versatile quantum simulators which will be useful to solve these questions. In addition, ultracold gases offer original situations and viewpoints, which open new perspectives to the field of disordered systems.Comment: text unchanged, submitted on June 2009; Final version on the website of Nature Physics at http://www.nature.com/nphys/journal/v6/n2/abs/nphys1507.htm

Quantum trajectories and open many-body quantum systems

The study of open quantum systems has become increasingly important in the past years, as the ability to control quantum coherence on a single particle level has been developed in a wide variety of physical systems. In quantum optics, the study of open systems goes well beyond understanding the breakdown of quantum coherence. There, the coupling to the environment is sufficiently well understood that it can be manipulated to drive the system into desired quantum states, or to project the system onto known states via feedback in quantum measurements. Many mathematical frameworks have been developed to describe such systems, which for atomic, molecular, and optical (AMO) systems generally provide a very accurate description of the open quantum system on a microscopic level. In recent years, AMO systems including cold atomic and molecular gases and trapped ions have been applied heavily to the study of many-body physics, and it has become important to extend previous understanding of open system dynamics in single- and few-body systems to this many-body context. A key formalism that has already proven very useful in this context is the quantum trajectories technique. This was developed as a numerical tool for studying dynamics in open quantum systems, and falls within a broader framework of continuous measurement theory as a way to understand the dynamics of large classes of open quantum systems. We review the progress that has been made in studying open many-body systems in the AMO context, focussing on the application of ideas from quantum optics, and on the implementation and applications of quantum trajectories methods. Control over dissipative processes promises many further tools to prepare interesting and important states in strongly interacting systems, including the realisation of parameter regimes in quantum simulators that are inaccessible via current techniques.Comment: 66 pages, 29 figures, review article submitted to Advances in Physics - comments and suggestions are welcom

Thermalization near integrability in a dipolar quantum Newton's cradle

Isolated quantum many-body systems with integrable dynamics generically do not thermalize when taken far from equilibrium. As one perturbs such systems away from the integrable point, thermalization sets in, but the nature of the crossover from integrable to thermalizing behavior is an unresolved and actively discussed question. We explore this question by studying the dynamics of the momentum distribution function in a dipolar quantum Newton's cradle consisting of highly magnetic dysprosium atoms. This is accomplished by creating the first one-dimensional Bose gas with strong magnetic dipole-dipole interactions. These interactions provide tunability of both the strength of the integrability-breaking perturbation and the nature of the near-integrable dynamics. We provide the first experimental evidence that thermalization close to a strongly interacting integrable point occurs in two steps: prethermalization followed by near-exponential thermalization. Exact numerical calculations on a two-rung lattice model yield a similar two-timescale process, suggesting that this is generic in strongly interacting near-integrable models. Moreover, the measured thermalization rate is consistent with a parameter-free theoretical estimate, based on identifying the types of collisions that dominate thermalization. By providing tunability between regimes of integrable and nonintegrable dynamics, our work sheds light both on the mechanisms by which isolated quantum many-body systems thermalize, and on the temporal structure of the onset of thermalization.Comment: 6 figures, 9 pages main text; 12 appendices with 12 figure

Fourier's law on a one-dimensional optical random lattice

We study the transport properties of a one-dimensional hard-core bosonic lattice gas coupled to two particle reservoirs at different chemical potentials which generate a current flow through the system. In particular, the influence of random fluctuations of the underlying lattice on the stationary-state properties is investigated. We show analytically that the steady-state density presents a linear profile. The local steady-state current obeys the Fourier law $j=-\kappa(\tau)\nabla n$ where $\tau$ is a typical timescale of the lattice fluctuations and $\nabla n$ the density gradient imposed by the reservoirs.Comment: 9 pages, 2 figure

Many-body localization of bosons in optical lattices

Many-body localization for a system of bosons trapped in a one dimensional lattice is discussed. Two models that may be realized for cold atoms in optical lattices are considered. The model with a random on-site potential is compared with previously introduced random interactions model. While the origin and character of the disorder in both systems is different they show interesting similar properties. In particular, many-body localization appears for a sufficiently large disorder as verified by a time evolution of initial density wave states as well as using statistical properties of energy levels for small system sizes. Starting with different initial states, we observe that the localization properties are energy-dependent which reveals an inverted many-body localization edge in both systems (that finding is also verified by statistical analysis of energy spectrum). Moreover, we consider computationally challenging regime of transition between many body localized and extended phases where we observe a characteristic algebraic decay of density correlations which may be attributed to subdiffusion (and Griffiths-like regions) in the studied systems. Ergodicity breaking in the disordered Bose-Hubbard models is compared with the slowing-down of the time evolution of the clean system at large interactions.Comment: expanded second version, comments welcom

Quantum gases in optical lattices

The experimental realization of correlated quantum phases with ultracold gases in optical lattices and their theoretical understanding has witnessed remarkable progress during the last decade. In this review we introduce basic concepts and tools to describe the many-body physics of quantum gases in optical lattices. This includes the derivation of effective lattice Hamiltonians from first principles and an overview of the emerging quantum phases. Additionally, state-of-the-art numerical tools to quantitatively treat bosons or fermions on different lattices are introduced.Comment: 29 pages, 3 figures. This article will be published as Chapter 2 in "Quantum gas experiments - exploring many-body states", edited by P. Torma and K. Sengstock, Imperial College Press, London, to be published 201