Spatial correlations of trapped one-dimensional bosons in an optical lattice

We investigate a quasi-one-dimensional system of trapped cold bosonic atoms in an optical lattice by using the density-matrix renormalization group to study the Bose-Hubbard model at $T=0$ for experimentally realistic numbers of lattice sites. It is shown that a properly rescaled one-particle density matrix characterizes superfluid versus insulating states just as in the homogeneous system. For typical parabolic traps we also confirm the widely used local-density approach for describing correlations in the limit of weak interaction. Finally, we note that the superfluid to Mott-insulating transition is seen most directly in the half-width of the interference peak.