Effect of defects on the phonons and the effective spin-spin interactions of an ultracold Penning trap quantum simulator

TL;DR

This paper analyzes how inhomogeneities and defects in a Penning trap ionic crystal affect phonon modes and spin-spin interactions, showing small defect levels have minimal impact on experimental outcomes.

Contribution

It extends the analysis of normal modes in Penning trap crystals to include inhomogeneities and defects, providing insights relevant for current experimental setups.

Findings

Most properties are not strongly influenced by defects

Small defect levels (~15%) do not significantly affect phonon modes

Effective spin-spin interactions remain robust despite inhomogeneities

Abstract

We generalize the analysis of the normal modes for a rotating ionic Coulomb crystal in a Penning trap to allow for inhomogeneities in the system. Our formal developments are completely general, but we choose to examine a crystal of Be+ ions with BeH+ defects to compare with current experimental efforts. We examine the classical phonon modes (both transverse and planar) and we determine the effective spin-spin interactions when the system is driven by an axial spin-dependent optical dipole force. We examine situations with up to approximately 15% defects. We find that most properties are not strongly influenced by the defects, indicating that the presence of a small number of defects will not significantly affect experiments.