Approximate solutions of the generalized Bloch equation with damping terms

Approximate solutions of the feneralized Bloch equations which describe a two-level system interacting with a strong no-rotating field are presented. The approximation is based on an iterative method. The accuracy of solutions is discussed by comparing them with the numerically intefrated solutions. It is shown that the first order iterative solutions have sufficiently good accuracy. Several valuable conclusions on the time-dependence of the occupation probability, the multi-photon absorption, and the Bloch-Siegert shift are drawn.