  Using the Magnus expansion to the fourth order, we obtain analytic
expressions for the atomic state of a two-level system driven by a laser pulse
of arbitrary shape with small pulse area. We also determine the limitation of
our obtained formulas due to limited range of convergence of the Magnus series.
We compare our method to the recently developed method of Rostovtsev et al.
(PRA 2009, 79, 063833) for several detunings. Our analysis shows that our
technique based on the Magnus expansion can be used as a complementary method
to the one in PRA 2009.
