  We propose an exactly solvable model to reveal the physics of the interplay
between interaction and disorder in bosonic systems. Considering interacting
bosons in a double-well potential, in which disorder is mimicked by taking the
energy level mismatch between the two wells to be randomly distributed, we find
"two negatives make a positive" effect. While disorder or interaction by itself
suppresses the phase coherence between the two wells, both together enhance the
phase coherence. This model also captures several striking features of the
disordered Bose-Hubbard model found in recent numerical simulations. Results at
finite temperatures may help explain why a recent experiment did not find any
evidence for the enhancement of phase coherence in a disordered bosonic system.
