2005/04/30 by Fatkhulla Kh. Abdullaev, Mario Salerno · 1 citation
Physics and Astronomy · #cond-mat.other
paper · pdf · doi:10.1103/physreva.72.033617
published as Phys. Rev. A 72 (2005) 033617
arxiv created 2005/11/05 · arxiv updated 2009/12/01
We discuss localized ground states of Bose-Einstein condensates in optical lattices with attractive and repulsive three-body interactions in the framework of a quintic nonlinear Schrödinger equation which extends the Gross-Pitaevskii equation to the one dimensional case. We use both a variational method and a self-consistent approach to show the existence of unstable localized excitations which are similar to Townes solitons of the cubic nonlinear Schrödinger equation in two dimensions. These solutions are shown to be located in the forbidden zones of the band structure, very close to the band edges, separating decaying states from stable localized ones (gap-solitons) fully characterizing their delocalizing transition. In this context usual gap solitons appear as a mechanism for arresting collapse in low dimensional BEC in optical lattices with attractive real three-body interaction. The influence of the imaginary part of the three-body interaction, leading to dissipative effects on gap solitons and the effect of atoms feeding from the thermal cloud are also discussed. These results may be of interest for both BEC in atomic chip and Tonks-Girardeau gas in optical lattices.