Magnetic and nematic phases in a Weyl type spin-orbit-coupled spin-1 Bose gas

TL;DR

This study investigates the magnetic and nematic phases in a spin-1 Bose gas with Weyl-type spin-orbit coupling, revealing how spin-orbit interaction modifies phase boundaries and induces complex spin textures.

Contribution

It introduces a variational approach to analyze phase behavior in spin-1 Bose gases with Weyl spin-orbit coupling, highlighting the impact on phase boundaries and spin textures.

Findings

Magnetic phase exhibits phase separation and skyrmion-like textures.

Nematic phase shows miscible density and uniaxial nematic order.

Spin-orbit coupling shifts the phase boundary between magnetic and nematic phases.

Abstract

We present a variational study of the spin-1 Bose gases in a harmonic trap with three-dimensional spin-orbit coupling of Weyl type. For weak spin-orbit coupling, we treat the single-particle ground states as the form of perturbational harmonic oscillator states in the lowest total angular momentum manifold with $j=1, m_j=1,0,-1$. When the two-body interaction is considered, we set the trail order parameter as the superposition of three degenerate single-particle ground-states and the weight coefficients are determined by minimizing the energy functional. Two ground state phases, namely the magnetic and the nematic phases, are identified depending on the spin-independent and the spin-dependent interactions. Unlike the non-spin-orbit-coupled spin-1 Bose-Einstein condensate for which the phase boundary between the magnetic and the nematic phase lies exactly at zero spin-dependent interaction, the boundary is modified by the spin-orbit-coupling. We find the magnetic phase is featured with phase-separated density distributions, 3D skyrmion-like spin textures and competing magnetic and biaxial nematic orders, while the nematic phase is featured with miscible density distributions, zero magnetization and spatially modulated uniaxial nematic order. The emergence of higher spin order creates new opportunities for exploring spin-tensor-related physics in spin-orbit coupled superfluid.