Exact solution of the ion-laser interaction in all regimes

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. It is shown that in the trapped ion‐laser interaction all the regimes may be considered analytically. This applies not only for different laser intensities, but also away from resonance and from the Lamb‐Dicke regime. A dispersive Hamiltonian for the high intensity regime is found, that, being diagonal, allows for an easy calculation of the evolution operator.