Full temporal density-matrix treatment of dual wavelength, arbitrary bandwidth, pulsed laser excitation of atoms with degenerate states in high collisional media

Abstract

A full time-dependent theory, based on the Density-Matrix (D.M.) formalism, for two-step pulsed excitation of atoms in collision-dominated media by pulsed laser light of arbitrary bandwidth is presented. The atoms consist of three levels, of which each one, in turn, can consist of 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 fully time-dependent D.M. equations is formulated (the total number of equations is not more than 10, in contrast to the N 2 equations needed for a general set of D.M. equations, N being the total number of states within all three levels). The following approximations and assumptions have been made: the rotating-wave approximation; all individual transition probabilities between different states within a given pair of levels are the same (implying that the only input parameters for the transition probabilities are the spontaneous emission rates); all coherences 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 equations are then solved in the steady-state limit of the non-diagonal elements, yielding time-dependent rate-equation-like population transfer equations. A few fully time-dependent simulations of some typical cases are given.