Localization by entanglementJ. Brand1, S. Flach2, V. Fleurov2, 3, L. S. Schulman2, 4 and D. Tolkunov4
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
received 22 December 2007; accepted in final form 25 June 2008; published August 2008
published online 5 August 2008
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.
03.75.Gg - Entanglement and decoherence in Bose-Einstein condensates.
05.45.-a - Nonlinear dynamics and chaos.
11.15.Kc - General theory of fields and particles: Classical and semiclassical techniques.
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