Pseudospin and spin-spin interactions in ultra-cold alkali atoms

TL;DR

This paper models ultra-cold alkali atoms as spin-1/2 particles with effective spin-spin interactions, analyzing how external magnetic fields influence these interactions and mapping the system to well-known spin models.

Contribution

It introduces a detailed description of spin-dependent interactions in ultra-cold alkali atoms, including their dependence on magnetic fields and their mapping to classical spin models.

Findings

Calculated spin-spin interaction parameters as a function of magnetic field.

Demonstrated mapping of cold atom systems to Ising and XY spin models.

Showed the advantage of the spin-spin interaction form in modeling.

Abstract

Ultra-cold alkali atoms trapped in two distinct hyperfine states in an external magnetic field can mimic magnetic systems of spin 1/2 particles. We describe the spin-dependent effective interaction as a spin-spin interaction. As a consequence of the zero-range, the interaction of spin 1/2 bosons can be described as an Ising or, alternatively, as an XY-coupling. We calculated the spin-spin interaction parameters as a function of the external magnetic field in the Degenerate Internal State (DIS) approximation. We illustrate the advantage of the spin-spin interaction form by mapping the system of N spin 1/2 bosons confined by a tight trapping potential on that of N spin 1/2 spins coupled via an infinite range interaction.