Gauge-spin-space rotation invariant vortices in spin-orbit coupled Bose-Einstein condensates

TL;DR

This paper explores the ground states of spinor Bose-Einstein condensates with Rashba spin-orbit coupling, revealing vortex structures arising from spontaneous symmetry breaking and classifying lattice phases with topological properties.

Contribution

It introduces a symmetry-based classification of vortices and lattice phases in spin-orbit coupled Bose-Einstein condensates, including the identification of skyrmion crystal states.

Findings

Vortices result from spontaneous symmetry breaking into combined gauge, spin, and space rotations.

Certain lattice phases exhibit nontrivial topological charges, forming skyrmion crystals.

Ground states show vanishing topological charge per unit cell, with exceptions based on symmetry classification.

Abstract

We revisit ground states of spinor Bose-Einstein condensates with a Rashba spin-orbit coupling, and find that votices show up as a direct consequence of spontaneous symmetry breaking into a combined gauge, spin, and space rotation symmetry, which determines the vortex-core spin state at the rotating center. For the continuous combined symmetry, the total spin rotation about the rotating axis is restricted to $2\pi$, whereas for the discrete combined symmetry, we further need 2F quantum numbers to characterize the total spin rotation for the spin-$F$ system. For lattice phases we find that in the ground state the topological charge for each unit cell vanishes. However, we find two types of highly symmetric lattices with a nontrivial topological charge in the spin-$\frac{1}{2}$ system based on the symmetry classification, and show that they are skyrmion crystals.