STRONGLY CORRELATED BOSONS AND FERMIONS IN OPTICAL LATTICES

Interacting bosons, fermions and Bose-Fermi mixtures in optical lattices form novel model systems for the investigation of fundamental quantum many body effects. This article summarizes some of our recent work on interacting bosonic and fermionic quantum gases in optical lattices. We show how the compressibility of a fermionic quantum gas mixture can be evaluated by measuring its size vs trap confinement. The results are compared to ab-initio Dynamical Mean Field Theory (DMFT) calculations, for which we find very good agreement with the experiment. Furthermore, quantum phase diffusion is introduced as a powerful method for the measurement of the renormalized Hubbard parameters underlying most lattice models.