  Starting from a quantum two-mode Bose-Hubbard Hamiltonian we determine the
ground state properties, momentum distribution and dynamical evolution for a
Bose Josephson junction realized by an ultracold Bose gas in a double-well
trap. Varying the well asymmetry we identify Mott-like regions of parameters
where number fluctuations are suppressed and the interference fringes in the
momentum distribution are strongly reduced. We also show how Schroedinger cat
states, realized from an initially phase coherent state by a sudden rise of the
barrier among the two wells, will give rise to a destructive interference in
the time-dependent momentum distribution.
