Interacting Fermions and Bose-Fermi mixtures in Optical Lattices*

When fermionic atoms are placed in the focus of several interfering laser beams, they feel a periodic potential and behave very much like electrons in a solid. However, the properties of this synthetic material can be changed at will. Here, we report on the realization of a strongly interacting Fermi gas in a 3D optical lattice, which opens the way to study condensed matter physics with light and atoms. For instance, the Fermi surface of the fermions in the lattice can be imaged and a dynamical transition from a band insulating state to a conductive state observed. The focus of the talk we will be on the behaviour of the system with changing interaction. By accessing a Feshbach resonance, we have formed molecules in the optical lattice and studied interaction induced coupling between the lowest Bloch bands as well as low-dimensional interacting Fermi gases. Finally, experiments with an interacting Bose-Fermi mixture in the lattice will be presented.