Vortex solitons in two-dimensional spin-orbit coupled Bose-Einstein condensates: effects of the Rashba-Dresselhaus coupling and the Zeeman splitting

TL;DR

This paper investigates two-dimensional spin-orbit coupled Bose-Einstein condensate solitons, analyzing how Rashba-Dresselhaus coupling and Zeeman splitting influence their existence, stability, and properties through analytical and numerical methods.

Contribution

It introduces the first comprehensive analysis of 2D vortex solitons in spin-orbit coupled BECs, highlighting the effects of Rashba-Dresselhaus coupling and Zeeman splitting on soliton stability and structure.

Findings

Stable semi-vortex and mixed-mode solitons exist in free space.

Dresselhaus SOC has a destructive effect on vortex solitons.

Zeeman splitting converts mixed-mode states into semi-vortex states.

Abstract

We present an analysis of two-dimensional (2D) matter-wave solitons, governed by the pseudo-spinor system of Gross-Pitaevskii equations with self- and cross-attraction, which includes the spin-orbit coupling (SOC) in the general Rashba-Dresselhaus form, and, separately, the Rashba coupling and the Zeeman splitting. Families of semi-vortex (SV) and mixed-mode (MM) solitons are constructed, which exist and are stable in free space, as the SOC terms prevent the onset of the critical collapse and create the otherwise missing ground states in the form of the solitons. The Dresselhaus SOC produces a destructive effect on the vortex solitons, while the Zeeman term tends to convert the MM states into the SV ones, which eventually suffer delocalization. Existence domains and stability boundaries are identified for the soliton families. For physically relevant parameters of the SOC system, the number of atoms in the 2D solitons is limited by $\sim 1.5\times 10^{4}$. The results are obtained by means of combined analytical and numerical methods.