Ultra-short strong excitation of two-level systems

We present a model describing the use of ultra-short strong pulses to control the population of the excited level of a two-level quantum system. In particular, we study an off-resonance excitation with a few cycles pulse which presents a smooth phase jump i.e. a change of the pulse׳s phase which is not step-like, but happens over a finite time interval. A numerical solution is given for the time-dependent probability amplitude of the excited level. The control of the excited level׳s population is obtained acting on the shape of the phase transient, and other parameters of the excitation pulse.