Ultracold atomic gases in optical lattices: mimicking condensed matter and beyond

Immanuel Bloch

Maciej Lewenstein, Anna Sanpera, V. Ahufinger +3 more

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

Immanuel Bloch

Seventy years after Einstein's prediction, the seminal achievement of Bose–Einstein condensation in dilute atomic gases in 1995 has provided us with a new form of quantum matter. Such quantum matter can be described as a single giant matter wave. By loading it into an artificial periodic potential formed by laser light—a so-called optical lattice—it has become possible to probe matter far beyond the wave-like description. In a review of a series of experiments with ultracold quantum gases in optical lattices, we show that the granularity of the matter wave field, caused by the discreteness of atoms, gives rise to effects going beyond the simple single matter wave description. Bose–Einstein condensates in optical lattices have thereby opened novel possibilities for investigating strongly correlated many-particle phenomena of condensed matter physics and have opened new opportunities for quantum information processing with neutral atoms

Immanuel Bloch, P. Zoller

Kazuma Nagao

Maciej Lewenstein, Anna Sanpera, V. Ahufinger

Quantum computers, although not yet available on the market, will revolutionise the future of information processing. Already now, quantum computers of special purpose, i.e., quantum simulators, are within reach. The physics of ultracold atoms, ions, and molecules offers unprecedented possibilities of control of quantum many systems, and novel possibilities of applications for quantum information and quantum metrology. Particularly fascinating is the possibility of using ultracold atoms in lattices to simulate condensed matter or even high energy physics. This book provides a comprehensive overview of ultracold lattice gases as quantum simulators, an interdisciplinary field involving atomic, molecular, and optical physics; quantum optics; quantum information; and condensed matter and high energy physics. It includes some introductory chapters on basic concepts and methods, and focuses on the physics of spinor, dipolar, disordered, and frustrated lattice gases, before reviewing in detail artificial lattice gauge fields with ultracold gases. The last part of the book moves onto a discussion of possible implementations universal quantum computers with ultracold atoms. After a crash course in quantum information theory, several models of quantum computation with ultracold gases are presented, as well as the current understanding of condensed matter from a quantum information perspective. The book ends with the general discussion of various detection methods that are unique for ultracold atoms.