Abstract

Ultracold atoms combine the high level of experimental control and the powerful detection methods available in quantum optical systems with typical many-body features such as emergent or collective phenomena. In an optical lattice, they can be used to study e.g. intriguing phenomena known from solid state physics, such as insulating states, quantum magnetism and – in the very near future – topological insulators and quantum hall physics. Furthermore, ultracold atoms offer the potential to create new phases of matter without known analogons and enable out-of-equilibrium studies of many-body systems. Following a general introduction into optical lattices, I will focus on three recent examples, namely the realisation of negative absolute temperatures, the observation of out-of-equilibrium dynamics after quantum quenches, and the measurement of local topological properties in a Graphene-type hexagonal lattice. I will close with an outlook into the future, where we will introduce novel interactions and disorder into these systems.