Cold atoms in optical lattices are flexible model systems where quantum many-body phenomena can be realized which are out of reach in electronic solids. One key advantage of cold gases is the tunability of interactions, quantum statistics and geometry. In addition, cold gases have a large number of internal degrees of freedom, which can be used to prepare ordered states with higher symmetry. I will focus on the following topics: I) Multi-component gases (e.g. Fermi systems with several hyperfine states) can give rise to new exotic ground states like supersolids or "color" superfluids, and can even be used to realize analogies to Quantum Chromodynamics. II) Optical lattices are also ideal tools to study quantum many-body sytems with disorder, introduced by random optical potentials. I will discuss Anderson-localization of ultracold Fermions in the presence of interactions, and show that competition between interactions and disorder can induce delocalization, as well as disordered magnetism. III) Bose-Fermi mixtures with strong onsite repulsion give rise to a checkerboard supersolid phase with coexisting diagonal and off-diagonal long-range order. I will discuss new nonperturbative results obtained by dynamical mean-field theory.
10 Minute Talk: RF spectroscopy of imbalanced Fermi gases