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Disordered, ultracold quantum gases: Theoretical studies and experimental perspectives

Laurent Sanchez-Palencia

Published Feb 3, 2011• 0 citations
OpenAlex

Abstract

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.

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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.
The understanding of disordered quantum systems is still far from being complete, despite many decades of research on a variety of physical systems. In this review we discuss how Bose–Einstein condensates of ultracold atoms in disordered potentials have opened a new window for studying fundamental phenomena related to disorder. In particular, we direct our attention to recent experimental studies on Anderson localization and on the interplay of disorder and weak interactions. These realize a very promising starting point for a deeper understanding of the complex behaviour of interacting, disordered systems.
This chapter starts with an introduction to disordered systems, with an emphasis on disorder in condensed matter, and discusses such phenomena as the Anderson localization, and quantum phases such as with Bose glass. It then turns to various experimental realizations of disorder in ultracold atomic gases. The chapter focuses on disordered Bose-Einstein condensates and the phenomenon of Anderson localization in speckle or quasi-periodic, quasi-random potential. It moves on to disordered ultracold fermionic systems, and disordered ultracold Bose–Fermi (B–F) and Bose–Bose (B–B) mixtures. Finally, the chapter examines spin glasses (providing a brief presentation of the mean field theory of Parisi, and the droplet model) and disorder induced order.
In this thesis we address relevant problems of the physics of quantum disordered systems from a numerical and theoretical point of view, with specific attention to the connection of our findings with ultracold atomic gases experiments. We concentrate on two main issues: the interplay between localization and interaction in disordered systems and the problem of localization in correlated random potentials. The first problem is investigated considering the expansion of a weakly interacting Bose gas in a bichromtic optical lattice. We observe that interaction has a destructive effect on the disorder-induced localization and leads to a subdiffusive expansion of the atomic gas. By comparing three characteristic energy scales of the system one can identify three different spreading regimes: weak chaos, strong chaos and self-trapping. The spreading behaviour in these regimes is predicted theoretically and verified numerically. We also interpreted existing experimental data on the basis of our findings and showed that there is a qualitative agreement between our numerical simulations and experiments. The second problem is investigated proposing a new model of correlated disorder that can be implemented experimentally using ultracold dipolar gases. We show that this model is characterized by the presence of both short and long range correlations. We study the localization properties of the model and highlight the role played by short and long range correlations in the determination of those properties. In particular we show that when short-range correlations are dominant, extended states can appear in the spectrum. The effect of long-range correlations is instead to restore localization over the whole spectrum and lead to counterintuitive behaviours of the localization length. More precisely, depending on the localization regime they can enhance or reduce the localization length at the centre of the band.
This chapter extends the investigation of ultracold atoms in optical lattices to the emerging field of ‘quantum simulation’, in which atoms are used to experimentally realize basic condensed-matter models to precisely investigate their properties and their quantum phase transitions in an ultimately clean setting, where decoherence or unwanted interactions with the environment can be avoided. The chapter discusses the superfluid/metal-to-insulator transition exhibited by strongly-interacting atoms realizing Hubbard models, as well as the Anderson localization determining the suppression of transport for atoms moving in a disordered potential. It concludes with an illustration of the most recent developments in the field, discussing novel experimental techniques and important frontiers in this research.
Abstract. We investigate theoretically the low-temperature physics of ultracold Fermi-Bose mixtures in optical lattices. We show that composite Fermions form under specific conditions in the srongly correlated regime. The composite picture is used to derive an effective Hamiltonian whose parameters can be controlled. We finally investigate the quantum phase diagram of the composites and show that it corresponds to the formation of Fermi glasses, spin glasses, and quantum percolation regimes. PACS numbers: 03.75.Kk,03.75.Lm,05.30.Jp,64.60.CnStrongly correlated Fermi-Bose mixtures in disordered optical lattices 2 1. Introduction to disordered quantum systems 1.1. From condensed matter physics to ultracold atomic gases Quantum disordered systems is a very active research field in condensed matter physics (CM) initiated by the work by P.W. Anderson [1] who first pointed out that quenched disorder can dramatically change the properties of a quantum system compared to
We review recent developments in the physics of ultracold atomic and molecular gases in optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard models, and as such may very well serve to mimic condensed matter phenomena. We show how these systems may be employed as quantum simulators to answer some challenging open questions of condensed matter, and even high energy physics. After a short presentation of the models and the methods of treatment of such systems, we discuss in detail, which challenges of condensed matter physics can be addressed with (i) disordered ultracold lattice gases, (ii) frustrated ultracold gases, (iii) spinor lattice gases, (iv) lattice gases in “artificial” magnetic fields, and, last but not least, (v) quantum information processing in lattice gases. For completeness, also some recent progress related to the above topics with trapped cold gases will be discussed. Motto: There are more things in heaven and earth, Horatio, Than are dreamt of in your philosophy Citation1