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arXiv:1911.04858 · Nature Communications

Observation of two-dimensional Anderson localisation of ultracold atoms

Donald H. White, Thomas Alan Haase, Dylan J. Brown, Maarten D. Hoogerland, Mojdeh S. Najafabadi, John L. Helm, Christopher Gies, Dániel Schumayer, David A. W. Hutchinson

Published Oct 2, 2020• 87 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1038/s41467-020-18652-w

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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.
Anderson localization of waves in disordered media was originally predicted[1] fifty years ago, in the context of transport of electrons in crystals[2]. The phenomenon is much more general[3] and has been observed in a variety of systems, including light waves[4, 5]. However, Anderson localization has not been observed directly for matter waves. Owing to the high degree of control over most of the system parameters (in particular the interaction strength), ultracold atoms offer opportunities for the study of disorder-induced localization[6]. Here we use a non-interacting Bose-Einstein condensate to study Anderson localization. The experiment is performed with a one-dimensional quasi-periodic lattice - a system that features a crossover between extended and exponentially localized states, as in the case of purely random disorder in higher dimensions. Localization is clearly demonstrated through investigations of the transport properties and spatial and momentum distributions. We characterize the crossover, finding that the critical disorder strength scales with the tunnelling energy of the atoms in the lattice. This controllable system may be used to investigate the interplay of disorder and interaction (ref. 7 and references therein), and to explore exotic quantum phases[8, 9].
Anderson localization of particles -- the complete halt of wave transport through multiple scattering and phase coherence -- is a paradigmatic manifestation of quantum interference in disordered media. In three dimensions, the scaling theory predicts a quantum phase transition at a critical energy, the mobility edge, separating localized from diffusive states and underpinning metal-insulator transitions in electronic systems. Despite decades of experimental efforts, a direct observation of this emblematic transition for matter waves has remained elusive. Previous attempts with ultracold atoms were hindered by strong and uncontrolled energy broadening, resulting in indirect, sometimes inaccurate, and model-dependent estimates of the mobility edge. Here we implement a novel energy-resolved scheme to prepare atomic matter waves with a narrow energy distribution and track their expansion dynamics over long timescales. This allows for a direct observation of the three-dimensional Anderson transition in a laser-speckle disordered potential, and for a precise measurement of the mobility edge that is independent of any underlying theoretical modeling. Our measurements show excellent agreement with state-of-the-art numerical predictions over a wide range of disorder strengths, resolving long-standing discrepancies between prior experiments and theory. Beyond the three-dimensional Anderson transition, our approach opens new avenues for quantitative investigations of quantum critical phenomena in spatially disordered systems, including the roles of dimensionality, symmetry class, and interactions.
Anderson localization has been observed for a variety of media, including ultracold atomic gases with speckle disorder in one and three dimensions. However, observation of Anderson localization in a two-dimensional geometry for ultracold gases has been elusive. We show that a cause of this difficulty is the relatively high percolation threshold of a speckle potential in two dimensions, resulting in strong classical localization. We propose a realistic pointlike disorder potential that circumvents this percolation limit with localization lengths that are experimentally observable. The percolation threshold is evaluated for experimentally realistic parameters, and a regime of negligible classical trapping is identified. Localization lengths are determined via scaling theory, using both exact scattering cross sections and the Born approximation, and by direct simulation of the time-dependent Schr\"odinger equation. We show that the Born approximation can underestimate the localization length by four orders of magnitude at low energies, while exact cross sections and scaling theory provide an upper bound. Achievable experimental parameters for observing localization in this system are proposed.
Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium.We observe three-dimensional AL of non-interacting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential.A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component.We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy.These measurements provide a benchmark for more sophisticated theories of AL.Wave propagation in disordered media is affected by scattering from random impurities.When those scattered waves self-interfere destructively, a phenomenon known as Anderson localization (AL) can arise (1).AL occurs in a wide variety of classical and quantum materials, impacting the transport of light (2, 3), acoustic (4), and matter (5, 6) waves.Localization is known to affect electrical conductivity in solids as a result of scattering from impurities and 1
Experiments have been conducted observing Anderson localisation in a two-dimensional ultracold gas. The atomic transport of a Rb87 Bose-Einstein condensate through a dumbbell shaped optical trap was examined, with a connecting channel containing impurities providing the only path. We have utilised a synthetic gauge field to demonstrate, theoretically, negative magneto-resistance in systems comparable to these experiments. This pro- vides us with strong evidence for the existence of Anderson localisation, an intriguing interference phenomenon, in these systems. Similar systems are examined with impurities distributed periodically, contrasting the ran- dom distributions required for Anderson localisation. It is demonstrated, through a comparison to the periodic case, that the negative magneto- resistance observed must be the result of the destruction of Anderson local- isation. Corresponding localisation lengths are also examined. We see that under that application of a synthetic gauge field, localisation lengths in- crease. A BEC localised within the channel can become delocalised on that scale with the application of a synthetic gauge field, with the correspond- ing localisation length transitioning from smaller than the channel length to larger. Experimental verification of our theoretical predictions would provide strong evidence confirming the existence of Anderson localisation in the experiments.
Anderson localization (AL) is a ubiquitous interference phenomenon in which waves fail to propagate in a disordered medium. We observe three-dimensional AL of noninteracting ultracold matter by allowing a spin-polarized atomic Fermi gas to expand into a disordered potential. A two-component density distribution emerges consisting of an expanding mobile component and a nondiffusing localized component. We extract a mobility edge that increases with the disorder strength, whereas the thermally averaged localization length is shown to decrease with disorder strength and increase with particle energy. These measurements provide a benchmark for more sophisticated theories of AL.