Here we use perturbation techniques based on the averaging method to investigate Rabi oscillations in cw and pulse-driven two-level systems (TLS's). By going beyond the rotating-wave approximation, especifically to second-order in perturbation, we obtain the Bloch-Siegert shift of the TLS resonant frequency, in which the resonant frequency increases with the driving field amplitude. This frequency shift implies that short resonant
π-pulses in which the Rabi frequency is approximately 40\% or higher of the transition frequency do not achieve complete inversion in TLS's. Hence, guided by analytical results based on the averaging technique, we propose two methods for obtaining population inversions in the TLS driven by short
π-pulses: one with chirping and the other with pulse shaping and near resonance blue-shifted detuning. Both methods minimize dephasing due to the Bloch-Siegert shift, reduce the dependance of the excitation of the TLS on the pulse phase, and are very effective in achieving complete population inversions.
Abstract Developing an analytical theory for atomic coherence driven by ultrashort laser pulses has proved to be challenging due to the breakdown of the rotating wave approximation (RWA). In this paper, we present an approximate analytical solution 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, a closed-form solution for Gaussian pulses is explicitly given, and the result is used to analyse the impact of carrier envelope phase on atomic population ratios. 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. The work lays out feasible theoretical paths toward analytically describing two-level atoms driven by ultrashort pulses.