Bessel Vortices in Spin-Orbit-Coupled Binary Bose-Einstein Condensates with Zeeman Splitting

TL;DR

This paper analyzes stationary solutions in 2D spin-orbit-coupled Bose-Einstein condensates with Zeeman splitting, revealing exact solutions, ground states, and skyrmion structures using analytical methods and neural networks.

Contribution

It introduces exact solutions for linear systems and constructs ground states of nonlinear BECs with neural networks, highlighting skyrmion formation in specific vortex states.

Findings

Exact solutions for linear BEC systems with spin-orbit coupling.

Ground states exhibit skyrmion structures in certain vortex configurations.

Neural networks effectively determine the nonlinear ground states.

Abstract

We present an analysis of stationary solutions for two-dimensional (2D) Bose-Einstein condensates (BECs) with the Rashba spin-orbit (SO) coupling and Zeeman splitting. By introducing the generalized momentum operator, the linear version of the system can be solved exactly. The solutions are semi-vortices of the Bessel-vortex (BV) and modified Bessel-vortex (MBV) types, in the presence of the weak and strong Zeeman splitting, respectively. The ground states (GSs) of the full nonlinear system are constructed with the help of a specially designed neural network (NN). The GS of the mixed-mode type appears as cross-attraction interaction increases. The spin texture of the GS is produced in detail. It exhibits the Neel skyrmion structure for the semi-vortex GS of the BV type, and the respective skyrmion number is found in an analytical form. On the other hand, GSs of the MBV and mixed-mode types do not form skyrmions.