Quantum Simulation and Phase Diagram of the Transverse Field Ising Model with Three Atomic Spins

TL;DR

This paper demonstrates a quantum simulation of the transverse field Ising model using three trapped atomic spins, revealing a phase diagram and showcasing scalability for larger systems to study phase transitions.

Contribution

It introduces a method to simulate the Ising model with trapped ions and explores the phase diagram, enabling studies of larger systems where classical theory is limited.

Findings

Direct measurement of ground states across various fields.

Mapping of magnetic order phase diagram.

Scalability potential for larger ion systems.

Abstract

We perform a quantum simulation of the Ising model with a transverse field using a collection of three trapped atomic ion spins. By adiabatically manipulating the Hamiltonian, we directly probe the ground state for a wide range of fields and form of the Ising couplings, leading to a phase diagram of magnetic order in this microscopic system. The technique is scalable to much larger numbers of trapped ion spins, where phase transitions approaching the thermodynamic limit can be studied in cases where theory becomes intractable.