Quantum simulation with Rydberg ions in a Penning trap

TL;DR

This paper proposes a novel quantum simulation platform using Rydberg ions in a Penning trap, enabling strong, long-range interactions for studying complex many-body spin phenomena over extended timescales.

Contribution

It introduces a new method for simulating 2D spin systems with enhanced interaction strengths using Rydberg ions in a Penning trap, surpassing traditional approaches.

Findings

Achievable spin-spin interactions of MHz strength under realistic conditions.

Demonstration of entanglement in a three-ion frustrated spin system.

Potential to explore slow and collective relaxation phenomena.

Abstract

Quantum simulation of interacting many-body spin systems is routinely performed with cold trapped ions, and systems with hundreds of spins have been studied in one and two dimensions. In the most common realizations of these platforms, spin degrees of freedom are encoded in low-lying electronic levels, and interactions among the spins are mediated through crystal vibrations. Here we propose a new approach which enables the quantum simulation of two-dimensional spin systems with interaction strengths that are increased by orders of magnitude. This, together with the unprecedented longevity of trapped ions, opens an avenue for the exploration of phenomena that take place on long timescales, e.g., slow and collective relaxation in frustrated and kinetically constrained systems. Our platform makes use of the strong dipolar interactions among electronic Rydberg states and planar confinement provided by a Penning trap. We investigate how the strong electric and magnetic fields that form this trap affect the properties of the Rydberg states and show that spin-spin interaction strengths on the order of MHz are achievable under experimentally realistic conditions. As a brief illustration of the capabilities of this quantum simulator, we study the entanglement in a frustrated spin system realized by three ions.