Multidimensional solitons in a low-dimensional periodic potential

TL;DR

This paper predicts stable, mobile 2D and 3D solitons in a self-attractive BEC with a mixed potential, demonstrating their dynamics, interactions, and stability properties through variational approximation and simulations.

Contribution

It introduces the first prediction of mobile 2D and 3D solitons in BECs within a mixed potential landscape, including their collision behaviors and bound states.

Findings

Stable 2D and 3D solitons exist in the specified potential.

Head-on collisions can cause fusion or bound states.

Mobility of solitons along the uniform direction is demonstrated.

Abstract

Using the variational approximation(VA) and direct simulations, we find stable 2D and 3D solitons in the self-attractive Gross-Pitaevskii equation (GPE) with a potential which is uniform in one direction ($z$) and periodic in the others (but the quasi-1D potentials cannot stabilize 3D solitons). The family of solitons includes single- and multi-peaked ones. The results apply to Bose-Einstein condensates (BECs) in optical lattices (OLs), and to spatial or spatiotemporal solitons in layered optical media. This is the first prediction of {\em mobile} 2D and 3D solitons in BECs, as they keep mobility along $z$. Head-on collisions of in-phase solitons lead to their fusion into a collapsing pulse. Solitons colliding in adjacent OL-induced channels may form a bound state (BS), which then relaxes to a stable asymmetric form. An initially unstable soliton splits into a three-soliton BS. Localized states in the self-repulsive GPE with the low-dimensional OL are found too.