Equilibration of the planar modes of ultracold two dimensional ion crystals in a Penning trap

TL;DR

This study uses numerical simulations to analyze how ultracold 2D ion crystals in a Penning trap equilibrate their planar modes, revealing exponential suppression of equilibration rates and implications for quantum information applications.

Contribution

It provides a detailed eigenmode analysis of in-plane mode equilibration, highlighting the exponential suppression of the rate and effects of trap parameters on stability and cooling strategies.

Findings

Equilibration rate is exponentially suppressed with increasing frequency ratio.

Predicted equilibration times are much longer than experimental timescales.

Increasing rotating wall strength enhances crystal stability.

Abstract

Planar thermal equilibration is studied using direct numerical simulations of ultracold two-dimensional (2D) ion crystals in a Penning trap with a rotating wall. The large magnetic field of the trap splits the modes that describe in-plane motion of the ions into two branches: High frequency cyclotron modes dominated by kinetic energy and low frequency $\mathbf{E \times B}$ modes dominated by potential energy associated with thermal position displacements. Using an eigenmode analysis we extract the equilibration rate between these two branches as a function of the ratio of the frequencies that characterize the two branches and observe this equilibration rate to be exponentially suppressed as the ratio increases. Under experimental conditions relevant for current work at NIST, the predicted equilibration time is orders of magnitude longer than any relevant experimental timescales. We also study the coupling rate dependence on the thermal temperature and the number of ions. Besides, we show how increasing the rotating wall strength improves crystal stability. These details of in-plane mode dynamics help set the stage for developing strategies to efficiently cool the in-plane modes and improve the performance of single-plane ion crystals for quantum information processing.