In a solid material strong interactions between the electrons can lead to surprising properties. A prime example is the Mott insulator, where the suppression of conductivity is a result of interactions and not the consequence of a filled Bloch band. The proximity to the Mott insulating phase in fermionic systems is the origin for many intriguing phenomena in condensed matter physics, most notably high-temperature superconductivity. The physics of this paradigm of strong correlations is well captured by the celebrated Hubbard model, which is widely used to describe strongly interacting electrons in a solid.

In my talk I will present experiments in which we have realized the Fermi-Hubbard model with ultracold atoms and investigated equilibrium and non-equilibrium properties. The unique tunability of the system has allowed us to enter the Mott insulating regime and observe a drastic suppression of double occupancy and the appearance of a gapped mode in the excitation spectrum. The far-from equilibrium dynamics of such strongly correlated systems is mostly unchartered territory and I will present experimental and theoretical results revealing the importance of higher order processes for thermalization.