Interacting Fermions in Optical Lattices

Optical lattices are a powerful tool to create novel many-body quantum systems with ultra-cold atoms. They allow it to tune the role of interactions in the system or to change its dimensionality. The atoms inside an optical lattice experience a periodic potential which is formed by mutually perpendicular standing-wave laser fields. In this talk I will report on first experiments with a quantum degenerate two-component Fermi-gas in a three-dimensional optical lattice. We directly image the Fermi surface of the atoms in the lattice by turning off the optical lattice adiabatically. Due to the confining potential gradual filling of the lattice transforms the system from a normal state into a band insulator. The dynamics of the transition from a band insulator to a normal state is studied and the time scale is measured to be an order of magnitude larger than the tunnelling time in the lattice. Using a Feshbach resonance we tune the interaction between atoms in two different spin states, allowing us to dynamically induce a coupling between the lowest energy bands or to form molecules.