Approximate solutions for the ion-laser interaction in the high intensity regime: Matrix method perturbative analysis

TL;DR

This paper derives an explicit second-order perturbative solution for a trapped-ion interacting with a laser in the high intensity regime, confirming previous results and providing analytical insights into the ion-laser dynamics.

Contribution

It introduces a matrix method-based perturbative approach with normalization for analyzing ion-laser interactions in the strong excitation regime, offering a new analytical tool.

Findings

The second-order perturbative solution matches previous numerical results.

The matrix method provides a clear analytical framework for high-intensity ion-laser interactions.

Normalized solutions improve the accuracy of excited state probability predictions.

Abstract

We provide an explicit expression for the second-order perturbative solution of a single trapped-ion interacting with a laser field in the strong excitation regime. From the perturbative analytical solution, based on a matrix method and a final normalization of the perturbed solutions, we show that the probability to find the ion in its excited state fits well with former results.