Mixed symmetry localized modes and breathers in binary mixtures of Bose-Einstein condensates in optical lattices

TL;DR

This paper investigates localized and breather modes in binary Bose-Einstein condensates within optical lattices, focusing on asymmetric configurations and their dynamics, using a systematic bifurcation approach.

Contribution

It introduces a systematic method for deriving localized and breather modes in binary BEC mixtures, considering asymmetries and symmetry properties of the coupled equations.

Findings

Diverse asymmetric localized modes identified.

Method for obtaining modes via bifurcation from the continuum spectrum.

Existence of breather modes in the system.

Abstract

We study localized modes in binary mixtures of Bose-Einstein condensates embedded in one-dimensional optical lattices. We report a diversity of asymmetric modes and investigate their dynamics. We concentrate on the cases where one of the components is dominant, i.e. has much larger number of atoms than the other one, and where both components have the numbers of atoms of the same order but different symmetries. In the first case we propose a method of systematic obtaining the modes, considering the "small" component as bifurcating from the continuum spectrum. A generalization of this approach combined with the use of the symmetry of the coupled Gross-Pitaevskii equations allows obtaining breather modes, which are also presented.