FULL TEMPORAL DENSITY-MATRIX TREATMENT OF DUAL-WAVELENGTH, ARBITRARY BANDWIDTH, PULSED-LASER EXCITATION OF ATOMS WITH DEGENERATE STATES IN HIGH COLLISIONAL MEDIA

A full time-dependent theory, based on the Density-Matrix (D.M.) forma lism, for two-step pulsed excitation of atoms in collision-dominated m edia by pulsed laser light of arbitrary bandwidth is presented. The at oms consist of three levels, of which each one, in turn, can consist o f an arbitrary number of degenerate states. The atoms are exposed both to quenching collisions as well as elastic collisions. From a general set of density-matrix equations a more manageable, reduced set of ful ly time-dependent D.M. equations is formulated (the total number of eq uations is not more than in, in contrast to the N-2 equations needed f or a general set of D.M. equations, N being the total number of states within all three levels). The following approximations and assumption s have been made: the rotating-wave approximation; all individual tran sition probabilities between different states within a given pair of l evels are the same (implying that the only input parameters for the tr ansition probabilities are the spontaneous emission rates); all cohere nces between different states within each level are washed out by the high collisional rates; and the laser light is linearly polarized with an arbitrary bandwidth of Lorentzian shape. The full time-dependent e quations are then solved in the steady-state limit of the non-diagonal elements, yielding time-dependent rate-equation-like population trans fer equations. A few fully time-dependent simulations of some typical cases are given.