Localized gap soliton trains of Bose-Einstein condensates in an optical lattice

TL;DR

This paper presents an analytical study of localized gap soliton trains in Bose-Einstein condensates within optical lattices, revealing controllable soliton properties and agreement with experimental results.

Contribution

It introduces a systematic analytical approach to understand linear and nonlinear excitations, identifying stable and unstable solitons, and predicts the formation of soliton trains in experiments.

Findings

Fundamental solitons are stable and localized.

Pinning position and amplitude are controllable via lattice parameters.

Predicted formation of soliton trains with increased condensate length.

Abstract

We develop a systematic analytical approach to study the linear and nonlinear solitary excitations of quasi-one-dimensional Bose-Einstein condensates trapped in an optical lattice. For the linear case, the Bloch wave in the $nth$ energy band is a linear superposition of Mathieu's functions $ce_{n-1}$ and $se_n$; and the Bloch wave in the $nth$ band gap is a linear superposition of $ce_n$ and $se_n$. For the nonlinear case, only solitons inside the band gaps are likely to be generated and there are two types of solitons -- fundamental solitons (which is a localized and stable state) and sub-fundamental solitons (which is a lacalized but unstable state). In addition, we find that the pinning position and the amplitude of the fundamental soliton in the lattice can be controlled by adjusting both the lattice depth and spacing. Our numerical results on fundamental solitons are in quantitative agreement with those of the experimental observation [Phys. Rev. Lett. {\bf92}, 230401 (2004)]. Furthermore, we predict that a localized gap soliton train consisting of several fundamental solitons can be realized by increasing the length of the condensate in currently experimental conditions.