Interacting Fermi gases and Bose-Fermi mixtures in optical lattices

Interacting fermionic quantum gases form the basis of solid state physics. In this thesis we choose a novel approach to explore such systems by creating quantum degenerate atomic Fermi gases and mixtures of bosonic and fermionic atoms in three-dimensional optical lattices. The collisional interaction between the atoms can be arbitrarily tuned between strongly repulsive and strongly attractive in the vicinity of a Feshbach resonance. This tuneability allows us to create weakly bound molecules from pairs of fermionic atoms confined to one-dimensional motion or trapped in isolated potential wells. For negative scattering lengths the bound states are solely stabilised by the tight confinement of the optical lattice. In a further experiment we realise low-dimensional p-wave interacting Fermi gases for the first time. By properly aligning the atomic spins with respect to the symmetry axis of the confining potential we can prohibit specific asymptotic scattering states due to their anisotropic character. The suppressed scattering manifests itself in the absence of atom losses close to the corresponding p-wave Feshbach resonance. We also observe a shift of the resonance position with respect to the three-dimensional case which is a consequence of the increased ground state energy. A range of new phenomena becomes accessible when a mixture of bosonic and fermionic atoms is prepared. We load Bose-Fermi mixtures into threedimensional optical lattices and probe the phase coherence of the bosonic cloud by means of the visibility of the matter wave interference pattern and the coherence length. We observe that an increasing admixture of the fermionic species diminishes the coherence. Moreover, the attractive interspecies interaction leads to an enhanced bosonic density in the lattice, which we measure by studying the three-body recombination. These experiments demonstrate the unprecedented versatility of atomic quantum gases in optical lattices and reveal the special nature of collisional interactions in these potentials. The realisation of strongly interacting gases and the direct access to low-dimensional systems opens up new perspectives for the investigation of fundamental questions of modern quantum many-body physics