Symmetry breaking in a localized interacting binary BEC in a bi-chromatic optical lattice

TL;DR

This paper investigates how interactions cause symmetry breaking in localized two-component Bose-Einstein condensates within a bi-chromatic optical lattice, using numerical simulations and variational analysis to explore stability and different localized states.

Contribution

It provides a detailed numerical study of symmetry breaking phenomena in binary BECs in quasi-periodic potentials, highlighting the effects of inter- and intra-species interactions on localization.

Findings

Symmetry breaking occurs due to inter- and intra-species interactions.

Localized states can have either symmetric or asymmetric density profiles.

Symmetry-broken states remain stable under small perturbations.

Abstract

By direct numerical simulation of the time-dependent Gross-Pitaevskii equation using the split-step Fourier spectral method we study different aspects of the localization of a cigar-shaped interacting binary (two-component) Bose-Einstein condensate (BEC) in a one-dimensional bi-chromatic quasi-periodic optical-lattice potential, as used in a recent experiment on the localization of a BEC [Roati et al., Nature 453, 895 (2008)]. We consider two types of localized states: (i) when both localized components have a maximum of density at the origin x=0, and (ii) when the first component has a maximum of density and the second a minimum of density at x=0. In the non-interacting case the density profiles are symmetric around x=0. We numerically study the breakdown of this symmetry due to inter-species and intra-species interaction acting on the two components. Where possible, we have compared the numerical results with a time-dependent variational analysis. We also demonstrate the stability of the localized symmetry-broken BEC states under small perturbation.