Spin Orbit and Hyperfine Simulations with Two-Species Ultracold Atoms in a Ring

TL;DR

This paper models two-species ultracold atoms in a ring trap using a collective spin approach, revealing controllable spin-orbit and hyperfine interactions, and explores conditions for maximal entanglement for quantum information applications.

Contribution

It introduces a Hamiltonian framework that separates controllable linear and quadratic components, enabling simulation of spin-orbit and hyperfine interactions in ultracold atoms.

Findings

Complete set of commuting observables derived

Analytical spectra and density of states obtained

Conditions for maximal entanglement identified

Abstract

A collective spin model is used to describe two species of mutually interacting ultracold bosonic atoms confined to a toroidal trap. The system is modeled by a Hamiltonian that can be split into two components, a linear part and a quadratic part, which may be controlled independently. We show the linear component is an analog of a Zeeman Hamiltonian, and the quadratic component presents a macroscopic simulator for spin-orbit and hyperfine interactions. We determine a complete set of commuting observables for both the linear and quadratic Hamiltonians, and derive analytical expressions for their respective spectra and density of states. We determine the conditions for generating maximal entanglement between the two species of atoms with a view to applications involving quantum correlations among spin degrees of freedom, such as in the area of quantum information.