Proposal for realizing Heisenberg-type quantum-spin models in Rydberg-atom quantum simulators

TL;DR

This paper proposes a method to realize Heisenberg-type quantum spin models using Rydberg-atom quantum simulators by tuning magnetic fields, enabling exploration of quantum many-body phenomena without Floquet engineering.

Contribution

It introduces a way to implement Heisenberg-type models in Rydberg atoms through magnetic field tuning, avoiding complex Floquet techniques.

Findings

Anisotropy of the XXZ model can be controlled by magnetic fields.

Effective spin models can be realized without Floquet engineering.

Guidance provided for future Rydberg atom quantum simulation experiments.

Abstract

We investigate the magnetic-field dependence of the interaction between two Rydberg atoms, $|nS_{1/2}, m_J\rangle$ and $|(n+1)S_{1/2}, m_J\rangle$. In this setting, the effective spin-1/2 Hamiltonian takes the form of an {\it XXZ} model. We show that the anisotropy parameter of the {\it XXZ} model can be tuned by applying a magnetic field and, in particular, that it changes drastically near the F\"orster resonance points. Based on this result, we propose experimental realizations of spin-1/2 and spin-1 Heisenberg-type quantum spin models in Rydberg atom quantum simulators, without relying on Floquet engineering. Our results provide guidance for future experiments of Rydberg atom quantum simulators and offer insight into quantum many-body phenomena emerging in the Heisenberg model.