Gap-Townes solitons and localized excitations in low dimensional Bose Einstein condensates in optical lattices

TL;DR

This paper investigates localized ground states in low-dimensional Bose-Einstein condensates within optical lattices, revealing unstable excitations akin to Townes solitons and exploring their stability, collapse prevention, and dissipative effects.

Contribution

It introduces the concept of gap-Townes solitons in a quintic nonlinear Schrödinger framework and analyzes their role in the stability and delocalization of BEC in optical lattices.

Findings

Existence of unstable localized excitations near band edges.

Gap solitons can prevent collapse in low-dimensional BEC.

Dissipative effects influence soliton stability and dynamics.

Abstract

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 Schr\"odinger 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 Schr\"odinger 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.