Vortical and fundamental solitons in dipolar Bose-Einstein condensates trapped in isotropic and anisotropic nonlinear potentials

TL;DR

This paper predicts and analyzes stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates with complex trapping potentials, extending the understanding of self-trapped modes in anisotropic and long-range interacting systems.

Contribution

It introduces the existence and stability analysis of vortical and fundamental solitons in dipolar BECs with anisotropic nonlinear pseudopotentials using variational and numerical methods.

Findings

Fundamental solitons and vortices with =1 are stable within certain eccentricity limits.

Vortices with =2 are stable only in isotropic models.

Stable modes exist up to critical anisotropy levels, depending on vorticity.

Abstract

We predict the existence of stable fundamental and vortical bright solitons in dipolar Bose-Einstein condensates (BECs) with repulsive dipole-dipole interactions (DDI). The condensate is trapped in the 2D plane with the help of the repulsive contact interactions whose local strength grows $\sim r^{4}$ from the center to periphery, while dipoles are oriented perpendicular to the self-trapping plane. The confinement in the perpendicular direction is provided by the usual harmonic-oscillator potential. The objective is to extend the recently induced concept of the self-trapping of bright solitons and solitary vortices in the pseudopotential, which is induced by the repulsive local nonlinearity with the strength growing from the center to periphery, to the case when the trapping mechanism competes with the long-range repulsive DDI. Another objective is to extend the analysis for elliptic vortices and solitons in an anisotropic nonlinear pseudopotential. Using the variational approximation (VA) and numerical simulations, we construct families of self-trapped modes with vorticities $\ell =0$ (fundamental solitons), $\ell =1$, and $\ell =2$. The fundamental solitons and vortices with $\ell =1$ exist up to respective critical values of the eccentricity of the anisotropic pseudopotential, being stable in the entire existence regions. The vortices with $\ell =2$ are stable solely in the isotropic model.