Simulating dynamical phases of chiral $p+ i p$ superconductors with a trapped ion magnet

TL;DR

This paper proposes using rotating trapped-ion crystals to simulate and study the dynamical phases of chiral p+ip superconductors, enabling exploration of topological properties and exotic spin textures.

Contribution

It introduces a method to simulate 2D p+ip superfluids with trapped ions, bridging quantum simulation and topological superconductivity research.

Findings

Mapping Cooper pairs to effective spins in ions

Inference of topological properties of dynamical phases

Potential to generate skyrmionic spin textures

Abstract

Two-dimensional $p+ i p$ superconductors and superfluids are systems that feature chiral behavior emerging from the Cooper pairing of electrons or neutral fermionic atoms with non-zero angular momentum. Their realization has been a longstanding goal because they offer great potential utility for quantum computation and memory. However, they have so far eluded experimental observation both in solid state systems as well as in ultracold quantum gases. Here, we propose to leverage the tremendous control offered by rotating two-dimensional trapped-ion crystals in a Penning trap to simulate the dynamical phases of two-dimensional $p+ip$ superfluids. This is accomplished by mapping the presence or absence of a Cooper pair into an effective spin-1/2 system encoded in the ions' electronic levels. We show how to infer the topological properties of the dynamical phases, and discuss the role of beyond mean-field corrections. More broadly, our work opens the door to use trapped ion systems to explore exotic models of topological superconductivity and also paves the way to generate and manipulate skyrmionic spin textures in these platforms.