Abstract: Large Scale Quantum Simulations using Ultracold Atoms in Optical Lattices

40 years ago, Richard Feynman outlined his vision of a quantum simulator for carrying out complex calculations of physical problems. Today, his dream has become a reality and a highly active field of resarch across different platforms ranging from ultracold atoms and ions, to superconducting qubits and photons. In my talk, I will outline how ultracold atoms in optical lattices played a vital contribution in starting this vibrant and interdisciplinary research field 20 years ago and now allow probing and controlling of quantum phases in- and out-of-equilibrium with fundamentally new tools and single particle resolution. Novel (hidden) order parameters, entanglement properties, full counting statistics or topological features can now be measured routinely and provide deep new insight into the world of correlated quantum matter. I will introduce measurement and control techniques and discuss a few highlight applications from the field of 1) strongly correlated quantum systems, 2) topological quantum matter and 3) out-of equilibrium dynamics in quantum many-body systems and provide an outlook for future challenges and opportunities in this system.