Quantum gases in optical lattices

The experimental realization of correlated quantum phases with ultracold gases in optical lattices and their theoretical understanding has witnessed remarkable progress during the last decade. In this review we introduce basic concepts and tools to describe the many-body physics of quantum gases in optical lattices. This includes the derivation of effective lattice Hamiltonians from first principles and an overview of the emerging quantum phases. Additionally, state-of-the-art numerical tools to quantitatively treat bosons or fermions on different lattices are introduced.Comment: 29 pages, 3 figures. This article will be published as Chapter 2 in "Quantum gas experiments - exploring many-body states", edited by P. Torma and K. Sengstock, Imperial College Press, London, to be published 201

Cooling and thermometry of atomic Fermi gases

We review the status of cooling techniques aimed at achieving the deepest quantum degeneracy for atomic Fermi gases. We first discuss some physical motivations, providing a quantitative assessment of the need for deep quantum degeneracy in relevant physics cases, such as the search for unconventional superfluid states. Attention is then focused on the most widespread technique to reach deep quantum degeneracy for Fermi systems, sympathetic cooling of Bose-Fermi mixtures, organizing the discussion according to the specific species involved. Various proposals to circumvent some of the limitations on achieving the deepest Fermi degeneracy, and their experimental realizations, are then reviewed. Finally, we discuss the extension of these techniques to optical lattices and the implementation of precision thermometry crucial to the understanding of the phase diagram of classical and quantum phase transitions in Fermi gases.Comment: 33 pages, 15 figures, contribution to the 100th anniversary of the birth of Vitaly L. Ginzbur

Cavity Optomechanics with Ultra Cold Atoms in Synthetic Abelian and Non-Abelian Gauge Field

In this article we present a pedagogical discussion of some of the optomechanical properties of a high finesse cavity loaded with ultracold atoms in laser induced synthetic gauge fields of different types. Essentially, the subject matter of this article is an amalgam of two sub-fields of atomic molecular and optical (AMO) physics namely, the cavity optomechanics with ultracold atoms and ultracold atoms in synthetic gauge field. After providing a brief introduction to either of these fields we shall show how and what properties of these trapped ultracold atoms can be studied by looking at the cavity (optomechanical or transmission) spectrum. In presence of abelian synthetic gauge field we discuss the cold-atom analogue of Shubnikov de Haas oscillation and its detection through cavity spectrum. Then, in the presence of a non-abelian synthetic gauge field (spin-orbit coupling), we see when the electromagnetic field inside the cavity is quantized, it provides a quantum optical lattice for the atoms, leading to the formation of different quantum magnetic phases. We also discuss how these phases can be explored by studying the cavity transmission spectrum.Comment: Invited Review Article in the journal Ato

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

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.Comment: Review article. v2: published version, 135 pages, 34 figure

Cooling in strongly correlated optical lattices: prospects and challenges

Optical lattices have emerged as ideal simulators for Hubbard models of strongly correlated materials, such as the high-temperature superconducting cuprates. In optical lattice experiments, microscopic parameters such as the interaction strength between particles are well known and easily tunable. Unfortunately, this benefit of using optical lattices to study Hubbard models come with one clear disadvantage: the energy scales in atomic systems are typically nanoKelvin compared with Kelvin in solids, with a correspondingly miniscule temperature scale required to observe exotic phases such as d-wave superconductivity. The ultra-low temperatures necessary to reach the regime in which optical lattice simulation can have an impact-the domain in which our theoretical understanding fails-have been a barrier to progress in this field. To move forward, a concerted effort to develop new techniques for cooling and, by extension, techniques to measure even lower temperatures. This article will be devoted to discussing the concepts of cooling and thermometry, fundamental sources of heat in optical lattice experiments, and a review of proposed and implemented thermometry and cooling techniques.Comment: in review with Reports on Progress in Physic