Self-trapping under the two-dimensional spin-orbit-coupling and spatially growing repulsive nonlinearity

TL;DR

This paper introduces a method to create stable self-trapped modes in 2D and 1D spin-orbit-coupled Bose-Einstein condensates with spatially growing repulsive interactions, including exact solutions and stability analysis.

Contribution

It presents exact semi-vortex solutions and numerically finds various stable and unstable modes in spin-orbit-coupled BECs with spatially modulated nonlinearity.

Findings

Exact semi-vortex solutions for anti-Gaussian profiles.

Partially stable excited states of SVs and MMs.

Existence of semi-dipole solitons in 1D system.

Abstract

We elaborate a method for the creation of two- and one-dimensional (2D and 1D) self-trapped modes in binary spin-orbit (SO)-coupled Bose-Einstein condensates (BECs) with the contact repulsive interaction, whose local strength grows fast enough from the center to periphery. In particular, an exact semi-vortex (SV) solution is found for the anti-Gaussian radial-modulation profile. The exact modes are included in the numerically produced family of SV solitons. Other families, in the form of mixed modes(MMs), as well as excited state of SVs and MMs, are produced too. While the excited states are unstable in all previously studied models, they are partially stable in the present one. In the 1D version of the system, exact solutions for the counterpart of the SVs, namely, \textit{semi-dipole} solitons, are found too. Families of semi-dipoles, as well as the 1D version of MMs, are produced numerically.