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

The density-matrix renormalization group was used to investigate a quasi-one-dimensional system of trapped cold bosonic atoms in an optical lattice. The Bose-Hubbard model was studied for realistic numbers of lattice sites. A rescaled one-particle density matrix characterizes superfluid was shown to be versing with the insulating states. The results show that in the half-width of the interference peak, the superfluid to Mott-transition is most direct.