An algorithm for the evaluation of induced transition probabilities for non-sinusoidal and sinusoidal applied fields with an application to Gaussian pulses

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Abstract
An efficient computational algorithm for evaluating the evolution operator, and related induced transition probabilities, for a multilevel system interacting with an amplitude-modulated sinusoidal field of arbitrary strength, modulating envelope, frequency and phase, is developed. The algorithm is based on the Riemann product integral representation of the evolution operator in conjunction with Frazer's method of mean coefficients and avoids the introduction of commonly used perturbative or rotating wave approximations. Model calculations for the interaction of a two-level system with a Gaussian pulse are presented and used to discuss the dependence of time-resolved and steady-state frequency sweep spectra on some of the pulse characteristics.