Few-cycle excitation of atomic coherence: A closed-form analytical solution beyond the rotating-wave approximation

Developing an analytical theory for atomic coherence driven by ultrashort laster pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate, closed-form solution to the Schrodinger equation that describes a two-level atom under the excitation of a far-off-resonance, few-cycle pulse of arbitrary shape without invoking the RWA. As an example of its applicability, an analytical solution for Gaussian pulses is explicitly given. Comparisons with numerical solutions validate the accuracy our solution within the scope of the approximation. Finally, we outline an alternative approach that can lead to a more accurate solution by capturing the nonlinear behaviors of the system.