New results for transition probabilities in two-level systems: The large-detuning regime

Abstract

The problem of calculating transition probabilities in two-level systems is studied in the limit where the detuning is large compared to the inverse duration of the interaction. Coupling potentials whose Fourier transforms $\tilde{V}\left(\omega \right)$ are of the form $f\left(\omega \right)e^{-\left(\right|b\omega \mathrm{}\left|\right)\mathrm{}}$ for large frequencies give rise to solutions which may be classified into families according to the form of $f\left(\omega \right)$. Within each family transition probabilities may be calculated from formulas that differ only in the numerical value of a scaling parameter. In cases where the coupling function has a pole in the complex time plane, the families are identified with the order of this singularity. In particular, for poles of first order, a connection with the Rosen-Zener solution can be made. The analysis is performed via high-order perturbation expansions which are shown to always converge for two-level systems driven by coupling potentials of finite pulse area.