  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.
