  We consider $N$ interacting dipolar bosonic atoms at zero temperature in a
double-well potential. This system is described by the two-space-mode extended
Bose-Hubbard (EBH) Hamiltonian which includes (in addition to the familiar BH
terms) the nearest-neighbor interaction, correlated hopping and bosonic-pair
hopping. For systems with $N=2$ and $N=3$ particles we calculate analytically
both the ground state and the Fisher information, the coherence visibility, and
the entanglement entropy that characterize the correlations of the lowest
energy state. The structure of the ground state crucially depends on the
correlated hopping $K_c$. On one hand we find that this process makes possible
the occurrence of Schr\"odinger-cat states even if the onsite interatomic
attraction is not strong enough to guarantee the formation of such states. On
the other hand, in the presence of a strong onsite attraction, sufficiently
large values of $|K_c|$ destroys the cat-like state in favor of a delocalized
atomic coherent state.
