Metallic and Insulating Phases of Repulsively Interacting Fermions in a   3D Optical Lattice
  The fermionic Hubbard model plays a fundamental role in the description of strongly correlated materials. Here we report on the realization of this Hamiltonian using a repulsively interacting spin mixture of ultracold $^{40}$K atoms in a 3D optical lattice. We have implemented a new method to directly measure the compressibility of the quantum gas in the trap using in-situ imaging and independent control of external confinement and lattice depth. Together with a comparison to ab-initio Dynamical Mean Field Theory calculations, we show how the system evolves for increasing confinement from a compressible dilute metal over a strongly-interacting Fermi liquid into a band insulating state. For strong interactions, we find evidence for an emergent incompressible Mott insulating phase. 
U. Schneider, L. Hackermuller, S. Will, Th. Best, I. Bloch, T. A.   Costi, R. W. Helmes, D. Rasch, and A. Rosch