Three-dimensional gap solitons in Bose-Einstein condensates supported by one-dimensional optical lattices

TL;DR

This paper investigates 3D gap solitons in Bose-Einstein condensates within 1D optical lattices, revealing their structures, stability, and potential for experimental realization under realistic conditions.

Contribution

It introduces the existence and stability of 3D gap solitons with complex radial structures and vorticity in BECs, extending understanding beyond previous 1D or simplified models.

Findings

Stable fundamental and vortex gap solitons exist in 3D BECs with optical lattices.

Gap solitons exhibit nontrivial radial structures aligned with linear spectral bands.

Potential for experimental generation of robust 3D gap solitons is demonstrated.

Abstract

We study fundamental and compound gap solitons (GSs) of matter waves in one-dimensional (1D) optical lattices (OLs) in a three-dimensional (3D) weak-radial-confinement regime, which corresponds to realistic experimental conditions in Bose-Einstein condensates (BECs). In this regime GSs exhibit nontrivial radial structures. Associated with each 3D linear spectral band exists a family of fundamental gap solitons that share a similar transverse structure with the Bloch waves of the corresponding linear band. GSs with embedded vorticity $m$ may exist \emph{inside} bands corresponding to other values of $m$. Stable GSs, both fundamental and compound ones (including vortex solitons), are those which originate from the bands with lowest axial and radial quantum numbers. These findings suggest a scenario for the experimental generation of robust GSs in 3D settings.