Coherence and correlations in a Mott insulator

The observation of the super fluid to Mott insulator transition has triggered an intense interest in studying ultracold quantum gases in optical lattices. Such a transition is commonly associated with the disappearance of the interference pattern observed when releasing a coherent (i.e. Bose condensed) ensemble from the lattice. In this talk, I will show that even in the insulating phase, the visibility of this interference pattern remains finite. Our results show that although long-range order is absent, short-range coherence still persists in a rather broad range, and that this can be identified as a characteristic feature of the system for large, but finite lattice depths. For even deeper lattices, the visibility is close to zero, and the interference pattern unobservable. I will explain that information is still present in such featureless images, and can be extracted by studying the density-density correlation function of the expanded cloud, as proposed theoretically. A sharp diffraction-like pattern observed in the correlations reveals the underlying lattice structure, and can be understood by generalizing the well-known Hanbury-Brown and Twiss effect to many bosonic sources '' emitting '' from each lattice site. This new detection method allows in principle the detection of spin ordering in a multi-component Mott insulator. As a first step in this direction, we have recently observed spin dynamics in a Mott insulator, where a spin-dependent collisional coupling induces strongly under damped Rabi oscillations between two-particle states with the same total magnetization. I will briefly report on these results. (author)