Localization by entanglement

¹  Centre of Theoretical Chemistry and Physics, Institute of Fundamental Sciences, Massey University Auckland New Zealand
²  Max-Planck-Institut für Physik komplexer Systeme - Nöthnitzer Str. 38, D-01187 Dresden, Germany, EU
³  School of Physics and Astronomy, Tel Aviv University - Tel Aviv, Israel
⁴  Department of Physics, Clarkson University - Potsdam NY, USA

Corresponding author: j.brand@massey.ac.nz

Received: 22 December 2007
Accepted: 25 June 2008

Abstract

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 () 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.