Rotating nonlinear states in trapped binary Bose-Einstein condensates under the action of the spin-orbit coupling

TL;DR

This paper systematically analyzes rotating patterns in two-component Bose-Einstein condensates with spin-orbit coupling, revealing novel vortex chain structures and pattern transitions influenced by rotation speed and nonlinear interactions.

Contribution

It introduces new vortex chain configurations and pattern transitions in spin-orbit coupled BECs, especially under repulsive interactions, expanding understanding of their nonlinear rotating states.

Findings

Revealed chain and star-shaped vortex patterns at various rotation speeds.

Identified instability and transition mechanisms between different vortex configurations.

Compared energies to explain pattern stability and transitions.

Abstract

We report results of systematic analysis of confined steadily rotating patterns in the two-component BEC including the spin-orbit coupling (SOC) of the Rashba type, which acts in the interplay with the attractive or repulsive intra-component and inter-component nonlinear interactions and confining potential. The analysis is based on the system of the Gross-Pitaevskii equations (GPEs) written in the rotating coordinates. The resulting GPE system includes effective Zeeman splitting. In the case of the attractive nonlinearity, the analysis, performed by means of the imaginary-time simulations, produces deformation of the known two-dimensional SOC solitons (semi-vortices and mixed-modes). Essentially novel findings are reported in the case of the repulsive nonlinearity. They demonstrate patterns arranged as chains of unitary vortices which, at smaller values of the rotation velocity Omega, assume the straight (single-string) form. At larger Omega, the straight chains become unstable, being spontaneously replaced by a trilete star-shaped array of vortices. At still large values of Omega, the trilete pattern rebuilds itself into a star-shaped one formed of five and, then, seven strings. The transitions between the different patterns are accounted for by comparison of their energy. It is shown that the straight chains of vortices, which form the star-shaped structures, are aligned with boundaries between domains populated by plane waves with different wave vectors. A transition from an axisymmetric higher-order (multiple) vortex state to the trilete pattern is investigated too.