Superfluid and magnetic states of an ultracold Bose gas with synthetic three-dimensional spin-orbit coupling in an optical lattice

TL;DR

This paper explores the phases and spin textures of ultracold bosonic atoms with synthetic 3D spin-orbit coupling in an optical lattice, revealing diverse superfluid and magnetic states including tunable Skyrmion crystals.

Contribution

It introduces a comprehensive study of superfluid and magnetic phases in a 3D spin-orbit coupled Bose gas, including the prediction of stable, tunable Skyrmion crystal states in an optical lattice.

Findings

Degenerate ground states depend on SO-coupling strengths.

Rich phase diagram with spiral, stripe, vortex, and Skyrmion textures.

Skyrmion crystals are stable and tunable along the z-axis.

Abstract

We study ultracold bosonic atoms with the synthetic three-dimensional spin-orbit (SO) coupling in a cubic optical lattice. In the superfluidity phase, the lowest energy band exhibits one, two or four pairs of degenerate single-particle ground states depending on the SO-coupling strengths, which can give rise to the condensate states with spin-stripes for the weak atomic interactions. In the deep Mott-insulator regime, the effective spin Hamiltonian of the system combines three-dimensional Heisenberg exchange interactions, anisotropy interactions and Dzyaloshinskii-Moriya interactions. Based on Monte Carlo simulations, we numerically demonstrate that the resulting Hamiltonian with an additional Zeeman field has a rich phase diagram with spiral, stripe, vortex crystal, and especially Skyrmion crystal spin-textures in each xy-plane layer. The obtained Skyrmion crystals can be tunable with square and hexagonal symmetries in a columnar manner along the z axis, and moreover are stable against the inter-layer spin-spin interactions in a large parameter region.