Unconventional states of bosons with synthetic spin-orbit coupling

TL;DR

This paper explores unconventional Bose-Einstein condensates with synthetic spin-orbit coupling, revealing complex wavefunctions, topological spin textures, and novel vortex structures that challenge traditional bosonic ground state theories.

Contribution

It introduces the study of topological properties and vortex structures in bosonic condensates with spin-orbit coupling, extending understanding beyond the no-node theorem.

Findings

Landau-level-like quantization in harmonic traps

Spontaneous half-quantum vortex formation breaking time-reversal symmetry

Topological defects in quaternionic phase space

Abstract

Spin-orbit coupling with bosons gives rise to novel properties that are absent in usual bosonic systems. Under very general conditions, the conventional ground state wavefunctions of bosons are constrained by the "no-node" theorem to be positive-definite. In contrast, the linear-dependence of spin-orbit coupling leads to complex-valued condensate wavefunctions beyond this theorem. In this article, we review the study of this class of unconventional Bose-Einstein condensations focusing on their topological properties. Both the 2D Rashba and 3D $\vec{\sigma} \cdot \vec{p}$-type Weyl spin-orbit couplings give rise to Landau-level-like quantization of single-particle levels in the harmonic trap. The interacting condensates develop the half-quantum vortex structure spontaneously breaking time-reversal symmetry and exhibit topological spin textures of the skyrmion type. In particular, the 3D Weyl coupling generates topological defects in the quaternionic phase space as an SU(2) generalization of the usual U(1) vortices. Rotating spin-orbit coupled condensates exhibit rich vortex structures due to the interplay between vorticity and spin texture. In the Mott-insulating states in optical lattices, quantum magnetism is characterized by the Dzyaloshinskii-Moriya type exchange interactions.