Gap-type dark localized modes in a Bose-Einstein condensate with optical lattices

TL;DR

This paper theoretically and numerically investigates the formation, stability, and properties of gap-type dark localized modes, including solitons and vortices, in Bose-Einstein condensates within optical lattices, predicting their existence in one and two dimensions.

Contribution

It introduces the first theoretical prediction of stable dark gap solitons and clusters in BECs with optical lattices, including their vortical counterparts in two dimensions.

Findings

Prediction of stable dark gap solitons and clusters in 1D and 2D.

Identification of stability regions via linear stability analysis.

Existence of vortical dark gap modes in two dimensions.

Abstract

Bose-Einstein condensate (BEC) exhibits a variety of fascinating and unexpected macroscopic phenomena, and has attracted sustained attention in recent years--particularly in the field of solitons and associated nonlinear phenomena. Meanwhile, optical lattices have emerged as a versatile toolbox for understanding the properties and controlling the dynamics of BEC, among which the realization of bright gap solitons is an iconic result. However, the dark gap solitons are still experimentally unproven, and their properties in more than one dimension remain unknown. In light of this, we describe, numerically and theoretically, the formation and stability properties of gap-type dark localized modes in the context of ultracold atoms trapped in optical lattices. Two kinds of stable dark localized modes--gap solitons and soliton clusters--are predicted in both the one- and two-dimensional geometries. The vortical counterparts of both modes are also constructed in two dimensions. A unique feature is the existence of a nonlinear Bloch-wave background on which all above gap modes are situated. By employing linear-stability analysis and direct simulations, stability regions of the predicted modes are obtained. Our results offer the possibility of observing dark gap localized structures with cutting-edge techniques in ultracold atoms experiments and beyond, including in optics with photonic crystals and lattices.