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Localization of Bose-Einstein condensates in optical lattices

Franzosi, Roberto and Giampaolo, Salvatore and Illuminati, Fabrizio and Livi, Roberto and Oppo, Gian-Luca and Politi, Antonio (2011) Localization of Bose-Einstein condensates in optical lattices. Central European Journal of Physics, 9 (5). pp. 1248-1254. ISSN 1895-1082

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The dynamics of repulsive bosons condensed in an optical lattice is effectively described by the Bose-Hubbard model. The classical limit of this model, reproduces the dynamics of Bose-Einstein condensates, in a periodic potential, and in the superfluid regime. Such dynamics is governed by a discrete nonlinear Schrödinger equation. Several papers, addressing the study of the discrete nonlinear Schrödinger dynamics, have predicted the spontaneous generation of (classical) breathers in coupled condensates. In the present contribute, we shall focus on localized solutions (quantum breathers) of the full Bose-Hubbard model. We will show that solutions exponentially localized in space and periodic in time exist also in absence of randomness. Thus, this kind of states, reproduce a novel quantum localization phenomenon due to the interplay between bounded energy spectrum and non-linearity.