Probing and Controlling Quantum Matter Using Ultracold Quantum Gases in Optical Lattices

Abstract

These lecture notes provide an introduction into the field of strong correlation physics with ultracold atoms in optical lattices. After a basic introduction into the single particle bandstructure and lattice configurations, the effect of strong interactions in the Hubbard model are discussed. Detection methods are introduced, which allow one to reveal in-trap density and (quasi)-momentum distributions, as well as correlations between particles on the lattice. The fundamental phases of the bosonic and fermionic Hubbard model are discussed. Superexchange spin-spin interactions that form the basis of quantum magnetism are introduced and the current status on observing such magnetic phenomena are highlighted. Finally, the novel possibilities to detect and control individual atoms on single lattice sites are outlined.