The effects of multifrequency-mode laser radiation on polarization-spectroscopy signal generation are investigated by direct numerical integration of the time-dependent density-matrix equations. The numerical solution of the density-matrix equations allows us to incorporate a physically reasonable model for pulsed dye-laser radiation in our analysis of the laser–resonance interaction. The laser radiation is modeled as the sum of electric fields from a finite number of modes that are assumed to have random pulse-to-pulse phases and exponentially distributed amplitudes. Calculations are performed for a homogeneously broadened resonance (only collisional broadening) and for a resonance that is both collision and Doppler broadened. The effect of the multimode laser radiation on polarization-spectroscopy line shapes and saturation curves is investigated for different values of the laser bandwidth and mode spacing and resonance collision and Doppler widths. The saturation parameter for the resonance is strongly dependent on the ratio of the laser bandwidth to the resonance collision width when the laser bandwidth is greater than the collision width. The pulse-to-pulse fluctuations in polarization-spectroscopy signal levels are found to decrease substantially for saturating pump intensities. The inclusion of the multimode laser structure into our density-matrix equations represents a significant advance in modeling the nonlinear interaction of laser radiation with atomic or molecular resonances.
Elastic and depolarizing collisions between excited ytterbium atoms (6s6p
3P1 level) and noble gases (He, Ne, and Xe) are investigated using a stimulated-photon-echo technique. The method is sensitive to collisional velocity changes concerning both the total population ${\ensuremath{\rho}}^{0}$ and the alignment ${\ensuremath{\rho}}^{2}$ of the level. More specifically, it enables us to compare precisely the velocity changes associated with elastic scattering and with alignment-preserving scattering. This represents an improvement with regard to previous works. A detailed theoretical discussion of depolarizing collisions in laser spectroscopy is presented. A simplified density-matrix equation is derived under appropriate approximations. Stimulated photon-echo data for elastic scattering are interpreted within the limits of small-angle scattering in a long-range van der Waals potential; total elastic scattering cross sections are derived from comparison between experiment and calculation: ${\mathit{\ensuremath{\sigma}}}_{\mathrm{He}}^{\mathrm{el}}$=220(20) A
˚2, ${\mathit{\ensuremath{\sigma}}}_{\mathrm{Ne}}^{\mathrm{el}}$=320(20) A
˚2, ${\mathit{\ensuremath{\sigma}}}_{\mathrm{Xe}}^{\mathrm{el}}$=1240(60) A
˚2. Total rates for destruction of alignment are measured in an auxiliary standard photon-echo experiment; the corresponding cross sections are ${\mathit{\ensuremath{\sigma}}}_{\mathrm{He}}^{(2)}$=94(3) A
˚2, ${\mathit{\ensuremath{\sigma}}}_{\mathrm{Ne}}^{(2)}$=123(7) A
˚2, ${\mathit{\ensuremath{\sigma}}}_{\mathrm{Xe}}^{(2)}$=300(20) A
˚2. Stimulated photon-echo data for depolarizing collisions are successfully compared with a calculation that we develop starting from a long-range anisotropic model potential.
A quantum-mechanical unified theory of foreign-gas pressure broadening of atomic lines which includes the impact and statistical theories and duration-of-collision effects is developed. The model consists of an absorber atom with two internal states
u (upper) and
l (lower) interacting with a structureless perturber gas via two spherical pairwise additive potentials
Vu(r) and
Vl(r), e.g., a simple model of an alkali-atom line perturbed by a rare gas. The dipolemoment correlation function is analyzed in the time domain using Liouville (tetradic) techniques. The correlation function reduces exactly to a two-body form $\ensuremath{\varphi}(t)$ containing the proper thermal weight factors. Detailed balance is obeyed and no $|\frac{\ensuremath{\hbar}(\ensuremath{\omega}\ensuremath{-}{\ensuremath{\omega}}_{0})}{\mathrm{kT}}|<1$ restriction is required. The impact theory follows from a long-time analysis of $\ensuremath{\varphi}(t)$. Sum rules or spectral moments are used to study short-time behavior revealing conventional statistical-theory effects (including satellite bands) and the important duration-of-collision effects which link the statistical and impact regimes. The sum rules are expressed as quadratures involving potential functions and the quantum-mechanical radial distribution function. Unified methods for calculating the total line shapes are suggested: (1) Pad\'e approximants (ratios of polynomials) can be used to interpolate from the known short-time behavior to the known long-time beahvior; this requires the least computational effort; (2) exact results for this model may be obtained numerically from the overlap integrals of radial wave functions (Franck-Condon factors) for the two potentials
Vu and
Vl; (3) classical phase (trajectory) expressions are given which are reasonable approximations in both the impact and statistical limits. A number of related topics are discussed including diabatic effects, collision-induced absorption, non-Lorentzian wings of molecular vibration-rotation bands, and the Condon approximation for the dipole-moment transition strength vs
r. The use of line shapes to probe atomic interactions, especially in excited states, is emphasized and the suggestion made that experiments be done over as wide a temperature range as possible with the measured line shapes in computer-readable form. The entire line-shape problem is described as the study of the spectrum of an atom-perturber "quasimolecule" (with primarily unbound states).