Large, 3D trapped ion crystals offer improved sensitivity in quantum sensing protocols, and are expected to be implemented as platforms in near-future experiments. However, numerical techniques used to study the laser cooling of such crystals are inefficient as the number of ions,
N, in the crystal increases. Here we develop a powerful numerical framework to simulate laser cooling of up to
105 ions stored in a Penning trap. We apply this framework to characterize and optimize the cooling of ellipsoidal 3D crystals. We document new pathways to enhanced cooling based on the addition of an axial component to the potential energy-dominated
E×B modes. Furthermore, we observe greatly enhanced cooling of the perpendicular kinetic energy to below 1 mK in prolate ion crystals, enabling a simplified cooling beam setup for such crystals. We propose specific values of trap and laser beam parameters which lead to optimal cooling in a variety of examples. This work illustrates the feasibility of preparing large 3D crystals for high-sensitivity quantum science protocols, motivating their use in future experiments.
Motional modes of trapped-ion crystals in Penning traps can now be cooled to near their ground states via electromagnetically induced transparency (EIT) cooling. Numerical simulations are valuable tools for interpreting EIT cooling results and optimizing experimental protocols, but existing molecular dynamics codes are limited to the simulation of Doppler cooling. In this work, we fill this gap by implementing a semiclassical model of EIT cooling in a novel MD code. By simultaneously evolving the ions' internal quantum states and classical motion, we are able to calculate the instantaneous EIT laser forces acting on the ions. We first validate our code by comparing the single-ion cooling rate to fully quantum simulation results. Next, we analyze cooling of the drumhead modes in planar ion crystals, quantifying the effects of planar ion motion and a finite laser beam width. Finally, we demonstrate efficient EIT cooling of the axial modes in 3D ellipsoidal crystals containing up to 500 ions. Such crystals are a promising platform for future quantum sensing experiments with enhanced sensitivity. We find that the mode spectra of 3D crystals can be engineered to enable sympathetic cooling of the low-frequency
E×B modes. This numerical framework provides a powerful tool for modeling sub-Doppler cooling techniques and for optimizing future quantum sensing and quantum information experiments.
A direct numerical simulation of many interacting ions in a Penning trap with a rotating wall is presented. The ion dynamics is modeled classically. Both axial and planar Doppler laser cooling processes are modeled using stochastic momentum impulses based on two-level atomic scattering rates. The plasmas being modeled are ultracold two-dimensional crystals made up of hundreds of ions. We compare Doppler cooled results directly to a previous linear eigenmodes analysis. Agreement in both frequency and mode structure is obtained. Additionally, when Doppler laser cooling is applied, the laser cooled steady state plasma axial temperature agrees with the Doppler cooling limit. Numerical simulations using the approach described and benchmarked here will provide insights into the dynamics of large trapped-ion crystals, improving their performance as a platform for quantum simulation and sensing.