5.3 Density matrix for a two-level atom 163 and (5.2.5). The resulting equations are Paa = -YaPaa + + [80 abEpba - C.c.], (5.3.22) N . Pbb = - ybpbb - [80 ab EPba - C.C.], (5.3.23) Pab = -(iw + Vab)Pab - # 8 abE(Paa - Pbb), (5.3.24) where yab = (Va + 1b)/2 with ya and yb defined by Eq. (5.3.10) and E(t) is given by Eq. (5.2.6). In the rotating-wave approximation, cos(vt) is replaced by exp(-ivt)/2 in Eqs. (5.3.22)-(5.3.24)