Coherent control of atomic excitation using off-resonant strong few-cycle pulses

We study the dynamics of a two-level system driven by an off-resonant few-cycle pulse which has a phase jump $\phi$ at $t=t_{0}$, in contrast to many cycle pulses, under non rotating-wave approximation (NRWA). We give a closed form analytical solution for the evolution of the probability amplitude $|C_{a} (t)|$ for the upper level. Using the appropriate pulse parameters like phase-jump $\phi$, jump time $t_{0}$, pulse width $\tau$, frequency $\nu$ and Rabi frequency $\Omega_{0}$ the population transfer, after the pulse is gone, can be optimized and for the pulse considered here, enhancement of $10^{6}-10^{8}$ factor was obtained.