2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/166279We 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.6 pages, 4 figures; final published version with small changes in response to reviewer commentsOther Condensed MatterPattern Formation and SolitonsQuantum Physicstext