A DENSITY-MATRIX TREATMENT OF STEP-WISE LASER EXCITATIONS OF ATOMS WITH DEGENERATE STATES IN HIGH COLLISIONAL MEDIA

A theory, based on the density-matrix formalism, for two-step excitation of atoms between three levels with arbitrary degeneracies in collision-dominated media by pulsed laser light of arbitrary bandwidth is presented. First, a general set of density-matrix equations is formulated within the rotating-wave approximation for a three level system, in which each level consists of an arbitrary number of sub-states. The system, composed of N2 equations (where N is the total number of sub-states of the atomic levels involved), is then reduced to six full time-dependent equations by a summation of the diagonal elements for each level and by an averaging of the non-diagonal elements for each transition. The high collisional rates are assumed to wash out all coherence between the sub-states within each level. It is assumed that the laser light is linearly polarized and has a Lorentzian shape (the finite bandwidths of the lasers are included as phase-fluctuations given by the phase-diffusion model). The equations are solved in the steady-state limit of the non-diagonal elements, yielding time dependent rate-equation-like population-transfer equations. An analytical solution in closed form of the full steady-state situation is also given.