Laser Cooling Trapped-Ion Crystal Modes Beyond the Lamb-Dicke Regime

We utilize a semiclassical framework to explore the cooling dynamics of trapped ion crystals with potentially many internal levels and motional modes. The framework is non-perturbative in the Lamb-Dicke parameter η, thereby capturing dynamics beyond the Lamb-Dicke regime, and removes much of the computational complexity required by a fully quantum treatment. We present a generalized method to analyze laser cooling by calculating crystal mode cooling rates as a function of energy, and apply this to a variety of interesting scenarios, including the capture range for EIT cooling and the simultaneous cooling of multiple high-temperature modes. At high energies, the model predicts cooling rates to be strongly dependent on the instantaneous motional energy of the ion crystal modes. We present numerical evidence that the predicted cooling rates quantitatively agree with a fully quantum model over the range of energies relevant to most trapped ion experiments, and also compare the predictions of the model to experimental data, finding excellent agreement. Our method complements Lamb-Dicke regime models by extending accurate and fast predictions of laser cooling dynamics to far higher energies.