  We study the localization of bosonic atoms in an optical lattice, which
interact in a spatially confined region. The classical theory predicts that
there is no localization below a threshold value for the strength of
interaction that is inversely proportional to the number of participating
atoms. In a full quantum treatment, however, we find that localized states
exist for arbitrarily weak attractive or repulsive interactions for any number
($>1$) of atoms. We further show, using an explicit solution of the
two-particle bound state and an appropriate measure of entanglement, that the
entanglement tends to a finite value in the limit of weak interactions. Coupled
with the non-existence of localization in an optimized quantum product state,
we conclude that the localization exists by virtue of entanglement.
