Coherent excitation of a two-state system by a linearly chirped Gaussian pulse

This work presents an analytic description of coherent excitation of a two-state quantum system by an external field with a Gaussian temporal shape and a linear frequency sweep. A very accurate analytic approximation to the transition probability in terms of the Lambert function is derived by using the Dykhne-Davis-Pechukas approach. This approximation provides analytic expressions for the frequency and the amplitude of the probability oscillations and for the ranges of interaction parameters where high transition probability is obtained.