  We study the quantum phases of bosons confined in a combined potential of a
one-dimensional double-well optical lattice and a parabolic trap. We apply the
time-evolving block decimation method to the corresponding two-legged
Bose-Hubbard model. In the absence of a parabolic trap, the system of bosons in
the double-well optical lattice exhibits a reentrant quantum phase transition
between Mott insulator and superfluid phases at unit filling as the tilt of the
double-wells is increased. We show that the reentrant phase transition occurs
also in the presence of a parabolic trap and suggest that it can be detected in
experiments by measuring the matter-wave interference pattern.
