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Quantum-Atom Optics Downunder (QAO)

Two-dimensional localization of matter waves by disorder

David A. W. Hutchinson, Yvan Castin

Published Jan 1, 2007• 0 citations
Publisher

Abstract

The possibility of using ultracold atoms to observe localization of matter waves is now a subject of significant interest. These systems offer unprecedented control over inter-particle interactions, imposed potentials and the level of disorder as compared to their condensed matter analogues. The two-dimensional (2D) case is of particular interest. The prevailing view has been that in the 2D electron gas there is no metallic state, but recent experiments are suggestive of a metal-insulator transition in very dilute systems. We investigate theoretically the possibility of observing strongly localized states, corresponding to the insulating phase, in the dilute 2D gas.

DOI
10.1364/qao.2007.qme5

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The possibility of using ultracold atoms to observe localization of matter waves is now a subject of significant interest. These systems offer unprecedented control over inter-particle interactions, imposed potentials and the level of disorder as compared to their condensed matter analogues. The two-dimensional (2D) case is of particular interest. The prevailing view has been that in the 2D electron gas there is no metallic state, but recent experiments are suggestive of a metal-insulator transition in very dilute systems. We investigate theoretically the possibility of observing strongly localized states, corresponding to the insulating phase, in the dilute 2D gas.
The interplay between strong Coulomb interactions and randomness has been a long-standing problem in condensed matter physics. According to the scaling theory of localization in two-dimensional systems of non-interacting or weakly interacting electrons, the ever-present randomness causes the resistance to rise as the temperature is decreased, leading to an insulating ground state. However, new evidence has emerged within the past decade indicating a transition from the insulating to metallic phase in two-dimensional systems of strongly interacting electrons. We review earlier experiments that demonstrate the unexpected presence of a metallic phase in two dimensions, and present an overview of recent experiments with emphasis on the anomalous magnetic properties that have been observed in the vicinity of the transition.
We present a theory of the metal-insulator transition in a disordered two-dimensional electron gas. A quantum critical point, separating the metallic phase, which is stabilized by electronic interactions, from the insulating phase, where disorder prevails over the electronic interactions, has been identified. The existence of the quantum critical point leads to a divergence in the density of states of the underlying collective modes at the transition, causing the thermodynamic properties to behave critically as the transition is approached. We show that the interplay of electron-electron interactions and disorder can explain the observed transport properties and the anomalous enhancement of the spin susceptibility near the metal-insulator transition.
Recent developments in laser cooling and trapping opened the door to a world full of new opportunities for research in atomic, molecular and optical physics as well as condensed matter physics. It became possible to do experiments under conditions that are hard to achieve in condensed matter systems but recently have been observed in atomic systems. Bose Einstein Condensation, the Mott insulator transition, and superfluidity are examples of such achievements. Another considerable interest to both condensed matter and atomic physics is Anderson localization of light. The localization phenomenon is named after P. W. Anderson who suggested the possibility of localization of electrons in a disordered medium. Localization of light is an interference effect in a disordered medium and there have been a number of observations in different types of media. It has still not been observed in atomic systems in three dimensions. We report experimental results obtained from an ultracold 87Rb gas of atoms near the localization limit from the F=2 to F=3 transition. I will discuss the sample formation, characterization of the sample and the progress made towards achievement of light localization in an ultracold atomic gas, including difficulties which so far have frustrated observation.
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.
Disorder plays a fundamental role in many fields of physics such as condensed-matter physics, optics, acoustics, or atomic physics. It is responsible for a number of surprizing effects, such as Anderson localization, metal-insulator transitions and intriguing glass phases. The inherent complexity of disordered systems poses outstanding challenges to the full understanding of these phenomena. In the last years, disorder has emerged as a major line of research in the field of ultracold quantum gases. The latter offer fascinating perspectives to better understand the effects of disorder in quantum systems, thanks not only to an unprecedented control of parameters, but also to their original properties. This Habilitation thesis reviews our recent contributions to the theory of disordered quantum gases along three main lines: - Anderson localization in disordered quantum gases; - Disorder in interacting Bose gases; - Simulating extended Hubbard and spin models with ultracold gases. On the one hand, we propose and analyze experiments aiming at realizing quantum simulators to address open questions of fundamental importance for the field of disordered systems. In this respect, we show that quantum gases offer promising perspectives. On the other hand, we lead prospective works, which in particular show that quantum gases have original properties. They hence shed new light on issues of broad interest in the field of disordered systems.
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].