Quantum simulations using ultracold atoms

Summary form only given. Over the past years, ultracold quantum gases have offered remarkable opportunities to investigate quantum matter through new probing techniques and in previously unexplored regimes. They can in fact be seen as one of the first realizations of Richard Feynman´s visionary concept of a quantum simulator offering far-reaching possibilities to engineer new phases of matter.In my talk, I will give an overview over some of the recent scientific highlights in the field. For example, I will explain how atoms can be imaged in optical lattices with single-site and single-atom resolution thereby allowing one to obtain single snapshots of a quantum many-body systems, where every individual atom of the system can be detected. Such high-resolution imaging has enabled our group to directly probe quantum fluctuations and reveal hidden order in a many-body setting. Having such high resolution at hand, it has also been possible to address and coherently control individual atoms, thereby allowing one to realize single atom impurities that can be tracked in a time resolved way during their propagation through a complex correlated quantum system. By making use of adiabatic state evolution in quantum mechanics or laser induced hopping in optical lattices, it has now also become possible to realize artificial magnetic fields for neutral particles. The field strengths that can be achieved for such systems can by far surpass even the strongest fields from the most powerful magnets on earth and allow one to probe quantum matter under the most extreme conditions.