Solitons in quasi one-dimensional Bose-Einstein condensates with competing dipolar and local interactions

TL;DR

This paper investigates the existence, stability, and interactions of one-dimensional matter-wave solitons in Bose-Einstein condensates with competing dipolar and local interactions, revealing conditions for stable solitons and their collision behaviors.

Contribution

It introduces new families of solitons supported by competing interactions and analyzes their stability and dynamics in free space and optical lattice environments.

Findings

Stable soliton families exist with weak local attraction and fixed dipole-dipole repulsion.

Gap solitons require sufficiently strong contact repulsion or not too strong attraction.

Collision behaviors depend on local interactions, with merging, passing, or bouncing observed.

Abstract

We study families of one-dimensional matter-wave bright solitons supported by the competition of contact and dipole-dipole (DD) interactions of opposite signs. Soliton families are found, and their stability is investigated in the free space, and in the presence of an optical lattice (OL). Free-space solitons may exist with an arbitrarily weak local attraction if the strength of the DD repulsion is fixed. In the case of the DD attraction, solitons do not exist beyond a maximum value of the local-repulsion strength. In the system which includes the OL, a stability region for \textit{subfundamental solitons} (SFSs) is found in the second finite bandgap. For the existence of gap solitons (GSs) under the attractive DD interaction, the contact repulsion must be strong enough. In the opposite case of the DD repulsion, GSs exist if the contact attraction is not too strong. Collisions between solitons in the free space are studied too. In the case of the local attraction, they merge or pass through each other at small and large velocities, respectively. In the presence of the local repulsion, slowly moving solitons bounce from each other.