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

Thermoelectric transport and Peltier cooling of cold atomic gases

This brief review presents the emerging field of mesoscopic physics with cold atoms, with an emphasis on thermal and 'thermoelectric' transport, i.e. coupled transport of particle and entropy. We review in particular the comparison between theoretically predited and experimentally observed thermoelectric effects in such systems. We also show how combining well designed transport properties and evaporative cooling leads to an equivalent of the Peltier effect with cold atoms, which can be used as a new cooling procedure with improved cooling power and efficiency compared to the evaporative cooling currently used in atomic gases. This could lead to a new generation of experiments probing strong correlation effects of ultracold fermionic atoms at low temperatures.Comment: 33 pages, 9 figures, Review. To be published in the special issue "Mesoscopic Thermoelectric Phenomena" of C. R. Physique 17 (2016