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Acta Physica Polonica B

TIGHT BINDING MODELS IN COLD ATOMS PHYSICS

Jakub Zakrzewski

Published May 1, 2007• 0 citations
OpenAlex

Abstract

Cold atomic gases placed in optical lattice potentials offer a unique tool to study simple tight binding models. Both the standard cases known from the condensed matter theory as well as novel situations may be addressed. Cold atoms setting allows for a precise control of parameters of the systems discussed, stimulating new questions and problems. The attempts to treat disorder in a controlled fashion are addressed in detail. PACS numbers: 03.75.Lm, 73.43.Nq 1.

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Cold atomic gases placed in optical lattice potentials offer a unique tool to study simple tight binding models. Both the standard cases known from the condensed matter theory as well as novel situations may be addressed. Cold atoms setting allows for a precise control of parameters of the systems discussed, stimulating new questions and problems. The attempts to treat disorder in a controlled fashion are addressed in detail. PACS numbers: 03.75.Lm, 73.43.Nq 1.
Cold atoms in optical lattices allow for accurate studies of many body dynamics. Rapid time-dependent modifications of optical lattice potentials may result in significant excitations in atomic systems. The dynamics in such a case is frequently quite incompletely described by standard applications of tight-binding models (such as, e.g., Bose-Hubbard model or its extensions) that typically neglect the effect of the dynamics on the transformation between the real space and the tight-binding basis. We illustrate the importance of a proper quantum mechanical description using a multiband extended Bose-Hubbard model with time-dependent Wannier functions. We apply it to situations directly related to experiments.
Cold atomic gases placed in optical lattices enable studies of simple con- densed matter theory models with parameters that may be tuned relatively easily. When the optical potential is randomized (e.g. using laser speckle to create a random intensity distribution) one may be able to observe Anderson localization of matter waves for non-interacting bosons, the so-called Bose glass in the presence of interactions, as well as the Fermi glass or quantum spin glass for mixtures of fermions and bosons.
Optical lattices in cold atomic systems offer an excellent setting for realizing quantum condensed matter phenomena. Here, a glimpse of such a setting is provided for the non-specialist. Some basic aspects of cold atomic gases and optical lattices are reviewed. Quantum many-body physics is explored in the case of interacting bosons on a lattice. Quantum behaviour in the presence of a potential landscape is examined for three different cases: a hexagonal lattice potential, a quasi-periodic potential and a disorder potential.
We review recent theoretical advances in cold atom physics concentrating on strongly correlated cold atoms in optical lattices. We discuss recently developed quantum optical tools for manipulating atoms and show how they can be used to realize a wide range of many body Hamiltonians. Then we describe connections and differences to condensed matter physics and present applications in the fields of quantum computing and quantum simulations. Finally we explain how defects and atomic quantum dots can be introduced in a controlled way in optical lattice systems. Key words: cold atom, optical lattice, Hubbard model, quantum computing, atomic quantum dot PACS: 03.75.-b, 32.80.Pj, 32.80.Qk, 03.67.Lx 1
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