Pergamon Specrrochrmrco Acfo. Vol 49B. Nos 12-14. pp 1491-1505. 1994 CopyrIght 0 1994 Elsewer Science Ltd F’mted m Great Britam. All nghts reserved 05w547/94 s7.00 + 00 zyxwvutsrqp 0584-8547(94)ooo7&3 zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPO Full temporal density-matrix treatment of dual wavelength, arbitrary bandwidth, pulsed laser excitation of atoms with degenerate states in high collisional media* PETER LJUNGBERG, DENIS BouDREAut and OVE AXNER$ The Analytical Laser Spectroscopy Group, Department of Physics, Chalmers University of Technology and University of Giiteborg, S-412 96 Goteborg, Sweden zyxwvutsrqponmlkjihgfedcbaZ (Received 28 April 1994; accepted 11 July 1994) 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 N2 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. 1. INTRODUCTION DURING the last few years, it has become more and more apparent that the rate- equation formalism is unable to account for many phenomena connected with step- wise excitations of atoms in highly collisional media (e.g. excitation by pulsed laser systems with GHz laser bandwidths in flames where the collision rates are in the GHz range) [l-4]. For example, it has been shown experimentally that, for two-colour excitations of atoms in flames by the use of the Laser-Enhanced Ionization spectrometry (LEI) technique, a number of features originating from dynamic Stark effects and two-photon excitations can be observed-features for which the rate-equation formalism is clearly insufficient. Hence, that formalism cannot qualitatively describe many of the experimentally measured lineshapes that can be obtained at the light intensities that can easily be produced by modern pulsed dye-laser systems [3, 5, 61. Due to these inconsistencies between theory and experiment, a density-matrix formalism has recently been adapted to these types of atom-light systems, i.e. step- wise excitations of atoms in highly collisional media by pulsed laser systems with arbitrary bandwidths. The density-matrix formalism has in the past been used to describe excitation of atoms in collision-free environments by monochromatic, highly coherent light [7]. Special attention has been devoted to sodium, for example regarding electron-atom collisions [8] as well as the use of sodium guide stars for the adaptive correction of * This paper was published in the Special Honor Issue of Specfrochimica Acta Part B, dedicated to J. D. Winefordner. t On leave from Department of Chemistry, University of Florida, Gainesville, FL, 32611, USA. $ Author to whom all correspondence should be addressed. Now at Umei University, S-901 87 Umea, Sweden. 1491