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 a complete phase diagram for a system in the presence of a harmonic trap and compare it with that of the homogeneous system. The superfluid to the Mott-insulator phase transition is investigated using 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