Exact solution of the ion-laser interaction in all regimes

TL;DR

This paper presents an exact analytical solution for the trapped ion-laser interaction across all regimes, including various laser intensities, detunings, and the Lamb-Dicke regime, by deriving a dispersive Hamiltonian for high intensities.

Contribution

It provides a comprehensive analytical framework for solving the ion-laser interaction in all regimes, extending beyond previous approximations.

Findings

Derived a dispersive Hamiltonian for high intensity regimes

Solved the ion-laser interaction analytically outside the Lamb-Dicke regime

Unified treatment of different laser intensities and detunings

Abstract

We show that in the trapped ion-laser interaction all the regimes may be considered analytically. We may solve not only for different laser intensities, but also away from resonance and from the Lamb-Dicke regime. It is found a dispersive Hamiltonian for the high intensity regime, that, being diagonal, its evolution operator may be easily calculated.