Signatures of the superfluid to Mott insulator transition in cold bosonic atoms in a one dimensional optical lattice

We study the Bose-Hubbard model using the finite size density matrix renormalization group method. We obtain for the first time a complete phase diagram for a system in the presence of a harmonic trap and compare it with that of the homogeneous system. To realize the transition from the superfluid to the Mott insulator phase we investigate different experimental signatures of these phases in quantities such as momentum distribution, visibility, condensate fraction and the total number of bosons at a particular density. The relationships between the various experimental signatures and the phase diagram are highlighted.