Laser cooling trapped-ion crystal modes beyond the Lamb-Dicke regime

TL;DR

This paper introduces a non-perturbative semiclassical method to accurately predict laser cooling dynamics of trapped-ion crystals beyond the Lamb-Dicke regime, enabling better modeling of high-energy phenomena.

Contribution

A novel semiclassical approach that models energy-dependent cooling dynamics of trapped ions beyond the Lamb-Dicke approximation, validated against quantum simulations and experiments.

Findings

Accurately predicts cooling rates over a wide energy range.

Reveals breakdown of EIT cooling at high energies.

Enables efficient modeling of multi-mode, high-temperature ion cooling.

Abstract

Laser cooling methods for trapped ions are most commonly studied at low energies, i.e., in the Lamb-Dicke regime. However, ions in experiments are often excited to higher energies for which the Lamb-Dicke approximation breaks down. Here we construct a non-perturbative, semiclassical method for predicting the energy-dependent cooling dynamics of trapped-ion crystals with potentially many internal levels and motional modes beyond the Lamb-Dicke regime. This method allows accurate and efficient modeling of a variety of interesting phenomena, such as the breakdown of EIT cooling at high energies and the simultaneous cooling of multiple high-temperature modes. We compare its predictions both to fully-quantum simulations and to experimental data for a broadband EIT cooling method on a Raman $S$-$D$ transition in $^{138}$Ba${^+}$. We find the method can accurately predict cooling rates over a wide range of energies relevant to trapped ion experiments. Our method complements fully quantum models by allowing for fast and accurate predictions of laser-cooling dynamics at much higher energy scales.