Numerical Simulations of 3D Ion Crystal Dynamics in a Penning Trap using the Fast Multipole Method

TL;DR

This paper presents a fast, scalable simulation method for 3D ion crystals in a Penning trap, demonstrating efficient laser cooling and potential for quantum science applications.

Contribution

Develops a novel molecular dynamics simulation using the fast multipole method to efficiently model large 3D ion crystals with laser cooling.

Findings

Simulation time scales linearly with ion number

Ions can be cooled to millikelvin temperatures within milliseconds

3D ion crystals are promising for quantum science experiments

Abstract

We simulate the dynamics, including laser cooling, of 3D ion crystals confined in a Penning trap using a newly developed molecular dynamics-like code. The numerical integration of the ions' equations of motion is accelerated using the fast multipole method to calculate the Coulomb interaction between ions, which allows us to efficiently study large ion crystals with thousands of ions. In particular, we show that the simulation time scales linearly with ion number, rather than with the square of the ion number. By treating the ions' absorption of photons as a Poisson process, we simulate individual photon scattering events to study laser cooling of 3D ellipsoidal ion crystals. Initial simulations suggest that these crystals can be efficiently cooled to ultracold temperatures, aided by the mixing of the easily cooled axial motional modes with the low frequency planar modes. In our simulations of a spherical crystal of 1,000 ions, the planar kinetic energy is cooled to several millikelvin in a few milliseconds while the axial kinetic energy and total potential energy are cooled even further. This suggests that 3D ion crystals could be well-suited as platforms for future quantum science experiments.