Anisotropic 2D diffusive expansion of ultracold atoms in a disordered potential

One-Dimensional Disordered Bosonic Systems

Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic states of matter such as quantum glasses or many-body localization. In this review, we will present an overview of experimental observations with disordered quantum gases, focused on one-dimensional bosons, and we will connect them with theoretical predictions.

Observation of two-dimensional Anderson localisation of ultracold atoms

Anderson localisation -the inhibition of wave propagation in disordered media- is a surprising interference phenomenon which is particularly intriguing in two-dimensional (2D) systems. While an ideal, non-interacting 2D system of infinite size is always localised, the localisation length-scale may be too large to be unambiguously observed in an experiment. In this sense, 2D is a marginal dimension between one-dimension, where all states are strongly localised, and three-dimensions, where a well-defined phase transition between localisation and delocalisation exists as the energy is increased. Here, we report the results of an experiment measuring the 2D transport of ultracold atoms between two reservoirs, which are connected by a channel containing pointlike disorder. The design overcomes many of the technical challenges that have hampered observation of localisation in previous works. We experimentally observe exponential localisation in a 2D ultracold atom system.

Anomalous transport in the soft-sphere Lorentz model

The sensitivity of anomalous transport in crowded media to the form of the inter-particle interactions is investigated through computer simulations. We extend the highly simplified Lorentz model towards realistic natural systems by modeling the interactions between the tracer and the obstacles with a smooth potential. We find that the anomalous transport at the critical point happens to be governed by the same universal exponent as for hard exclusion interactions, although the mechanism of how narrow channels are probed is rather different. The scaling behavior of simulations close to the critical point confirm this exponent. Our result indicates that the simple Lorentz model may be applicable to describing the fundamental properties of long-range transport in real crowded environments.

Introducing non-local correlations into laser speckles

Laser speckles have become a fundamental component of the modern optics-research toolbox. Not only are speckle patterns the basis of numerous imaging techniques, but also, they are employed to generate optical potentials for cold atoms and colloidal particles. The ability to manipulate a speckle pattern's spatial intensity correlations, particularly long-range (non-local) ones, is essential in numerous applications. A typical fully-developed speckle pattern, however, only possesses short-ranged (local) intensity correlations which are determined by the spatial field correlations. Here we experimentally demonstrate and theoretically develop a general method for creating fully-developed speckles with strong non-local intensity correlations. The functional form of the spatial intensity correlations can be arbitrarily tailored without altering the field correlations. Our approach provides a versatile and utilitarian framework for enhancing and controlling non-local correlations in speckle patterns.

Two-terminal transport measurements with cold atoms

In recent years, the ability of cold atom experiments to explore condensed-matter-related questions has dramatically progressed. Transport experiments, in particular, have expanded to the point in which conductance and other transport coefficients can now be measured in a way that is directly analogous to solid-state physics, extending cold-atom-based quantum simulations into the domain of quantum electronic devices. In this topical review, we describe the transport experiments performed with cold gases in the two-terminal configuration, with an emphasis on the specific features of cold atomic gases compared to solid-state physics. We present the experimental techniques and the main experimental findings, focusing on-but not restricted to-the recent experiments performed by our group. We finally discuss the perspectives opened up by this approach, the main technical and conceptual challenges for future developments, and potential applications in quantum simulation for transport phenomena and mesoscopic physics problems.

Subwavelength-width optical tunnel junctions for ultracold atoms

We propose a method for creating far-field optical barrier potentials for ultracold atoms with widths that are narrower than the diffraction limit and can approach tens of nanometers. The reduced widths stem from the nonlinear atomic response to control fields that create spatially varying dark resonances. The subwavelength barrier is the result of the geometric scalar potential experienced by an atom prepared in such a spatially varying dark state. The performance of this technique, as well as its applications to the study of many-body physics and to the implementation of quantum-information protocols with ultracold atoms, are discussed, with a focus on the implementation of tunnel junctions.

Experimental Observation of Two-Dimensional Anderson Localization with the Atomic Kicked Rotor

Dimension 2 is expected to be the lower critical dimension for Anderson localization in a time-reversal-invariant disordered quantum system. Using an atomic quasiperiodic kicked rotor-equivalent to a two-dimensional Anderson-like model-we experimentally study Anderson localization in dimension 2 and we observe localized wave function dynamics. We also show that the localization length depends exponentially on the disorder strength and anisotropy and is in quantitative agreement with the predictions of the self-consistent theory for the 2D Anderson localization.

Superfluidity with disorder in a thin film of quantum gas

We investigate the properties of a strongly interacting superfluid gas of (6)Li(2) Feshbach molecules forming a thin film confined in a quasi-two-dimensional channel with a tunable random potential, creating a microscopic disorder. We measure the atomic current, extract the resistance of the film in a two-terminal configuration, and identify a superfluid state at low disorder strength, which evolves into a normal poorly conducting state for strong disorder. The transition takes place when the chemical potential reaches the percolation threshold of the disorder. The evolution of the conduction properties contrasts with the smooth behavior of the density and compressibility across the transition, measured in situ at equilibrium. These features suggest the emergence of a glasslike phase at strong disorder.

Coherent backscattering of ultracold atoms

We report on the direct observation of coherent backscattering (CBS) of ultracold atoms in a quasi-two-dimensional configuration. Launching atoms with a well-defined momentum in a laser speckle disordered potential, we follow the progressive build up of the momentum scattering pattern, consisting of a ring associated with multiple elastic scattering, and the CBS peak in the backward direction. Monitoring the depletion of the initial momentum component and the formation of the angular ring profile allows us to determine microscopic transport quantities. We also study the time evolution of the CBS peak and find it in fair agreement with predictions, at long times as well as at short times. The observation of CBS can be considered a direct signature of coherence in quantum transport of particles in disordered media. It is responsible for the so called weak localization phenomenon, which is the precursor of Anderson localization.

Three-dimensional clustered speckle fields: theory, simulations and experimental verification

Clustered speckle patterns are a particular type of speckles that appear when a coherently illuminated diffuser is imaged through a multiple aperture pupil mask attached to a lens. The cluster formation is the result of the complex speckle modulations of the multiple interferences produced by the apertures. In this paper, a three-dimensional analytical approach to simulate cluster speckles everywhere after the lens is presented. This approach has the possibility of including multiple aperture masks at the lens and at the diffuser, in contrast to previous works which were also limited to the description of the patterns only at the image plane. This model contributes to the development of tailor made speckle patterns that can be used in diverse optical applications, including those lying in the focus region. The approach is validated under different conditions by comparing experimental results with simulations on a statistical basis. Some aspects of possible uses of these clusters are briefly revised, such as optical trapping, manipulation and metrology.

Conduction of ultracold fermions through a mesoscopic channel

In a mesoscopic conductor, electric resistance is detected even if the device is defect-free. We engineered and studied a cold-atom analog of a mesoscopic conductor. It consists of a narrow channel connecting two macroscopic reservoirs of fermions that can be switched from ballistic to diffusive. We induced a current through the channel and found ohmic conduction, even when the channel is ballistic. We measured in situ the density variations resulting from the presence of a current and observed that density remains uniform and constant inside the ballistic channel. In contrast, for the diffusive case with disorder, we observed a density gradient extending through the channel. Our approach opens the way toward quantum simulation of mesoscopic devices with quantum gases.

Fokker-Planck equation for transport of wave packets in nonlinear disordered media

Starting from first principles, we formulate a theory of wave-packet propagation in a nonlinear, disordered medium of any dimension, through the derivation of a Fokker-Planck transport equation. Our theory is based on a diagrammatic expansion of the wave packet's density, and is supported by a heuristic picture that involves a Boltzmann equation with an effective, external potential. Our approach also confirms results obtained in previous work for two-dimensional, nonlinear disordered media.