  In this article the extended Bose-Hubbard model describing ultra-cold atoms
confined in a shallow, one-dimensional optical lattice is introduced and
studied by the exact diagonalization approach. All parameters of the model are
related to the only relevant parameter controlled experimentally -- the depth
of the optical potential. Changes in a shape of the insulating lobe in the
phase diagram of the system are explored and the value of the critical
tunneling for which the system undergoes the phase transition (from the
insulating to the superfluid phase) is predicted. It is shown that the value of
critical tunneling is substantially affected by the presence of the tunnelings
to distant sites of the optical lattice. The results may have some importance
in upcoming experiments on quantum quench through phase transition points.
