Three-Dimensional Spin-Orbit Coupling in a Trap

TL;DR

This paper studies a trapped atom with three-dimensional Weyl spin-orbit coupling, revealing a dimensional reduction at low energies and detailed properties of the ground state including spin textures.

Contribution

It introduces a numerical scheme leveraging angular momentum conservation and characterizes the spectral transition from Landau-like levels to harmonic oscillator behavior.

Findings

At large spin-orbit coupling, the system reduces from 3D to 1D at low energies.

The spectrum transitions from Landau levels to harmonic oscillator levels at high energies.

The ground state exhibits spin textures with oscillations determined by the spin-orbit length.

Abstract

We investigate the properties of an atom under the influence of a synthetic three-dimensional spin-orbit coupling (Weyl coupling) in the presence of a harmonic trap. The conservation of total angular momentum provides a numerically efficient scheme for finding the spectrum and eigenfunctions of the system. We show that at large spin-orbit coupling the system undergoes dimensional reduction from three to one dimension at low energies, and the spectrum is approximately Landau level-like. At high energies, the spectrum is approximately given by the three-dimensional isotropic harmonic oscillator. We explore the properties of the ground state in both position and momentum space. We find the ground state has spin textures with oscillations set by the spin-orbit length scale.