Ultrafast pulse interactions with two-level atoms

An iterative predictor-corrector finite-difference time-domain method is used to solve the semiclassical Maxwell-Bloch system numerically without invoking any of the standard approximations such as the rotating-wave approximation. This approach permits a more exact study of self-induced transparency effects in a two-level atom. In addition to recovering the standard results, for instance, for π, 2π, and 4π pulses, several features in the results appear at the zeros of the driving pulse, where its time derivatives are maximum. Several ultrafast-pulse examples demonstrate that time-derivative-driven nonlinearities have a significant impact on the time evolution of a two-level atom system. Moreover, typical small-signal gain results are also obtained with our Maxwell-Bloch simulator. We illustrate that these time-derivative effects can be used to design an ultrafast, single-cycle pump pulse that completely inverts the two-level atom population. A pump-probe signal set is then used to illustrate gain in the probe signal.