The Mott insulator transition in two dimensions

Cold atoms in periodic potentials are remarkably versatile quantum systems for implementing simple models prevalent in condensed matter theory. Here we realize the 2D Bose-Hubbard model by loading a Bose-Einstein condensate into an optical lattice, and we study the resulting Mott insulating state (a phase of matter in which atoms are localized on specific lattice sites). We measure momentum distributions which agree quantitatively with theory (no adjustable parameters). In these systems, the Mott insulator forms in a spatially discrete shell structure which we probe by focusing on correlations in atom shot noise. These correlations show a marked dependence on the lattice depth, consistent with the changing size of the insulating shell expected from simple arguments.