Dimers and discrete breathers in Bose-Einstein condensates in a quasi-periodic potential

TL;DR

This paper investigates nonlinear localized modes, including dimers and breathers, in a quasi-periodic Bose-Einstein condensate, revealing their stability and dynamics beyond the tight-binding approximation.

Contribution

It introduces a discrete model for BECs in quasi-periodic potentials that captures nonlinear modes and breathers without relying on the tight-binding approximation.

Findings

Breathers are stable for negative scattering lengths.

Localization and stable propagation occur for positive scattering lengths at moderate nonlinearities.

Solutions include families of nonlinear modes with no linear limit.

Abstract

A quasi-one-dimensional Bose-Einstein condensate loaded into a quasi-periodic potential created by two sub-lattices of comparable amplitudes and incommensurate periods is considered. Although the conventional tight-binding approximation is not applicable in this setting, the description can still be reduced to a discrete model that accounts for the modes below the mobility edge. In the respective discrete lattice, where no linear hopping exists, solutions and their dynamics are governed solely by nonlinear interactions. Families of nonlinear modes, including those with no linear limit, are described with a special focus on dimers, which correspond to breather solutions of the Gross-Pitaevskii equation with a quasi-periodic potential. The breathers are found to be stable for negative scattering lengths. Localization and stable propagation of breathers are also observed for positive scattering lengths at relatively weak and moderate nonlinearities.