Populating Excited States of Incoherent Atoms Using Coherent Light

Abstract

This paper deals with the equations of motion of the density matrix of a two-level atom in the presence of an intense multimode radiation field characterizing a multimode laser. Using a simplified treatment of line broadening which does not include correlations between momentum-changing collisions and pressure-broadening collisions, we obtain expressions which show the effect of pressure, laser-pulse length, and intensity on the excitation. We obtain analytic expressions in limiting cases of the pressure which allow prediction of the degree of excitation from a given laser pulse. In our treatment the phase relaxation time of the atoms is assumed to be fast enough so that coherence effects among the atoms can be ignored. Treating the velocity of the atoms statistically, we solve for three cases: constant velocity, velocity changes that are fast compared to the excitation time but slow compared to the dephasing time, and velocity changes that are fast compared to all other processes. The three cases yield the same formal equation for the two-body process of absorption of photons by incoherent atoms; however, the cross sections differ and are calculated explicitly for each case. Also discussed are the range of laboratory conditions and the relationship between these laboratory conditions and the various cases considered to demonstrate that under most circumstances this simple photon-absorption picture is applicable, provided the cross section is calculated correctly.