  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.
