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Physical Review A

Elastic and inelastic collisional and radiative damping effects on saturated line shapes in the limit of well-separated spectral lines

B. R. Mollow

Published Mar 1, 1977• 80 citations
Publisher

Abstract

Resonant scattering of intense light is analyzed in the limit in which the separation of the spectral lines is large compared to their widths. The effect on the line intensities and widths of elastic and inelastic collisions in the impact approximation and of radiative damping is found. The limit of well-separated spectral lines allows simple solutions in a wide class of cases not easily treated outside this limit, in particular the case in which the upper laser-coupled state decays through a complicated cascade sequence to the lower laser-coupled ground state, or suffers collisional reorientation (depolarization) during the emission process.

DOI
10.1103/physreva.15.1023

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Resonant scattering of intense light is analyzed in the limit in which the separation of the spectral lines is large compared to their widths. The effect on the line intensities and widths of elastic and inelastic collisions in the impact approximation and of radiative damping is found. The limit of well-separated spectral lines allows simple solutions in a wide class of cases not easily treated outside this limit, in particular the case in which the upper laser-coupled state decays through a complicated cascade sequence to the lower laser-coupled ground state, or suffers collisional reorientation (depolarization) during the emission process.
The fluorescence spectrum from a multilevel system, in the presence of inelastic collisions which couple the upper states, is calculated in the impact limit. The results are expressed in terms of the collision rates (elastic and inelastic), the collision broadening rates, and the natural damping rates. The integrated intensities are also calculated, and the results are compared with the rate equation results. It is shown that the standard rate equation analysis of the experimental data is not valid when the lower state interaction is significant. The Doppler effect is also included in the general theory of the fluorescent line shapes, and the modification of the profile because of the velocity dependence of the collision rates is discussed.
The authors apply the dressed-atom model to evaluate the spectrum of nearly resonant light scattering from atoms in a perturber gas. The intensity of the monochromatic incident light may be sufficiently high to cause saturation effects, and the detuning from resonance may be large enough to invalidate the impact limit. The results for a two-state or a three-state atom, which are valid in the limit that the lines in the scattered spectrum are well separated, generalise previous work that assumed either the impact or the low-intensity limit.
The techniques of modern line-broadening theory are used to investigate the scattering of polarized radiation in the rest frame of an atom undergoing collisions. The formulation explicitly includes both elastic and inelastic (quenching) collisions. When the lower state has zero width, a form for the redistribution function similar to that of Zanstra is obtained, but with the redistribution in the neighborhood of the resonance line being caused solely by elastic collisions. In the limit of no collisions, but with both levels of finite lifetime, the result of `veisskopf and Woolley is obtained. The effect of level-degeneracy is also explicitly included; in this case the results are a function of the polarization of the light and the different relaxation rates for the multipolar components of the atomic states.
The evaluation of the binary-collision operator Phi ( omega ), pertaining to collisional redistribution of strong laser radiation, involves the computation of a time-ordered exponential, which only reduces to a scalar exponential in the medium-coupling limit. In this approximation one neglects the alteration of the collisional dynamics due to the presence of the laser field. A two-state atom is considered, for which the authors expand Phi ( omega ) in the ratio of the Rabi frequency Omega to the detuning from resonance. This parameter vanishes in the medium-coupling case, and is small for common gas-phase experiments. It is shown that the correction to medium coupling can again be expressed in a scalar function, which represents the temporal correlation between the interaction potential and the full time evolution during a single collision. The decay constants for collisional transitions between dressed states, which are germane to the width of the spectral lines, appear to be sensitive to the deviation from medium coupling. Quite remarkably, a non-vanishing collisional contribution survives in the limit Omega to 0 of Phi ( omega ).
The effects of phase-interrupting and velocity-changing collisions between active and perturber atoms on the spectral profile of a gas laser are studied. Exact analytical results for the density matrix are presented for the case of strong collisions in a unidirectional ring laser, and the laser intensity is then evaluated in the Doppler limit under the condition of self-consistency. The washout of the hole burning in the steady-state population difference and the broadening of the laser line shape are discussed. The results of the third-order perturbation theory are compared with the exact calculations valid for an arbitrarily intense pump.
A theoretical investigation is reported of the Raman scattering and fluorescence (doublet) spectra of three-level quantum systems subjected to a strong laser field reducing broadening of the spectral lines caused by adiabatic perturbations (elastic collisions). The dependences of the frequency shifts, widths, and integrated intensities of the spectral components of the doublet on the intensity and frequency of the laser field are derived allowing for the influence of this field on the collision dynamics.