Quantum simulation of superexchange magnetism in linear ion crystals

TL;DR

This paper demonstrates how linear ion crystals can simulate Heisenberg spin models through laser-induced interactions, enabling controlled quantum magnetism studies with tunable parameters.

Contribution

It introduces a method to realize superexchange interactions in trapped ions, simulating quantum magnetism with adjustable coupling strengths.

Findings

Superexchange interactions induce Heisenberg-type spin couplings.

Laser-ion interactions create localized phonon and atom excitations.

Tunable parameters allow control over simulated magnetic properties.

Abstract

We present a system for the simulation of Heisenberg models with spins $s=\frac{1}{2}$ and $s=1$ with a linear crystal of trapped ions. We show that the laser-ion interaction induces a Jaynes-Cummings-Hubbard interaction between the atomic V-type level structure and the two phonon species. In the strong-coupling regime the collective atom and phonon excitations become localized at each lattice site and form an effective spin system with varying length. We show that the quantum-mechanical superexchange interaction caused by the second-order phonon hopping processes creates a Heisenberg-type coupling between the individual spins. Trapped ions allow to control the superexchange interactions by adjusting the trapping frequencies, the laser intensity, and the detuning.