Bound solitonic states in trapped multidimensional Bose-Einstein condensates

TL;DR

This paper investigates the existence, stability, and dynamics of multidimensional bound solitonic states, including dark solitons and vortex configurations, in harmonically-trapped Bose-Einstein condensates, revealing their bifurcations and instabilities.

Contribution

It provides a detailed analysis of stable and unstable bound solitonic states and vortex structures in 3D Bose-Einstein condensates, including bifurcation scenarios and dynamical behaviors.

Findings

Static bound dark solitons are stable in elongated condensates within certain interaction ranges.

Beyond this range, snaking instability causes decay into vortex states.

High chemical potential leads to complex vortex configurations like chains and vortex rings.

Abstract

We report on the existence and stability of multidimensional bound solitonic states in harmonically-trapped scalar Bose-Einstein condensates. Their equilibrium separation, as a measure of the strength of the soliton-soliton or the solitonic vortex-vortex interaction, is provided for varying chemical potential $\mu$. Static bound dark solitons are shown to be dynamically stable in elongated condensates within a range of intermediate (repulsive) interparticle-interaction strength. Beyond this range the snaking instability manifests during the time evolution of the planar solitons and produces the decay into non-stationary vortex states. A subsequent dynamical recurrence of solitons and vortices can be observed at low $\mu$. At equilibrium, the bifurcations of bound dark solitons are bound solitonic vortices. Among them, both two-open and two-ring vortex lines are demonstrated to exist with both counter- and co-rotating steady velocity fields. The latter flow configurations evolve, for high chemical potential, into a stationary 3D-chain-shaped vortex and a three vortex-antivortex-vortex ring sequence that arrest the otherwise increasing angular or linear momentum respectively. As a common feature to the bifurcated vortex states, their excitation spectra present unstable modes with associated oscillatory dynamics.