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Physical Review A

Nonimpact theory of resonance Raman line shapes in strong radiation fields

Shaul Mukamel, Danielle Grimbert, Yitzhak Rabin

Published Jul 1, 1982• 17 citations
Publisher

Abstract

We develop an expansion for the resonance Raman line shape of a three-level system $|a〉$, $|b〉$, and $|c〉$ in an arbitrary strong radiation field, being perturbed by dephasing collisions with foreign gas particles. The microscopic information relevant to the line broadening is expresssed in terms of a hierarchy of $n$-time correlation functions of the transition dipole operator ($n=2,4,6,\dots{}$). To lowest order ($n=2$) the spectrum is expressed in terms of the three ordinary line-shape functions corresponding to the $\mathrm{ab}$, $\mathrm{bc}$, and $\mathrm{ac}$ transitions. The present theory is not restricted to the impact limit and, depending on the collision time scale, may yield very different results from the well-known impact spectra. Explicit calculations of the predicted spectra are presented for a model system.

DOI
10.1103/physreva.26.341

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We develop an expansion for the resonance Raman line shape of a three-level system ∣a〉|a〉∣a〉, ∣b〉|b〉∣b〉, and ∣c〉|c〉∣c〉 in an arbitrary strong radiation field, being perturbed by dephasing collisions with foreign gas particles. The microscopic information relevant to the line broadening is expresssed in terms of a hierarchy of nnn-time correlation functions of the transition dipole operator (n=2,4,6,…n=2,4,6,\dots{}n=2,4,6,…). To lowest order (n=2n=2n=2) the spectrum is expressed in terms of the three ordinary line-shape functions corresponding to the ab\mathrm{ab}ab, bc\mathrm{bc}bc, and ac\mathrm{ac}ac transitions. The present theory is not restricted to the impact limit and, depending on the collision time scale, may yield very different results from the well-known impact spectra. Explicit calculations of the predicted spectra are presented for a model system.
We develop an expansion for the absorption line shape of a two-level system in a strong radiation field being perturbed by dephasing collisions with a thermal bath of foreign atoms. We assume that the bath atoms do not interact with the radiation field and with each other. The microscopic information relevant for line broadening in a strong field is expressed in terms of a hierarchy of dipole correlation functions. The latter may be calculated with the use of the Franck-Condon factors for the nuclear wave functions. The present theory reduces in the weak-field limit to the well-known linear unified theory of line broadening and in the impact limit we recover the Karplus-Schwinger formula.
A non-Markovian microscopic theory for the spontaneous emission spectrum of a two-level atom driven by a strong laser field and undergoing dephasing via the interaction with a thermal bath is developed. The present theory is valid for an arbitrary correlation time scale of the bath relative to the linewidth and interpolates from the Markovian to the static limits. Model calculations using the stochastic line-shape function of Kubo show how the characteristic triplet spectrum is modified by the interaction with the bath. The present results generalize our previous studies of resonance Raman scattering in a three-level system in a strong radiation field.
The influence of phase memory effects on the spectrum of resonance Raman scattering by three-level atoms with the Λ configuration of levels experiencing collisions with buffer gas atoms in a strong monochromatic radiation field is studied theoretically. Systems with a small Doppler broadening compared to the collision frequency (large buffer gas pressures) are analysed in the general case of an arbitrary change (from complete change to complete preservation) in the phase memory at any of three transitions in the Λ system. It is shown that in the absence of the collision relaxation of the low-frequency coherence at the transitions between two lower levels of the Λ system, the radiation scattering spectrum has a spectrally narrow component at the Raman frequency, which, despite the homogeneous broadening of the absorption line, exhibits a strongly pronounced anisotropy. In the direction, close to the propagation direction of exciting radiation, this line maximally narrows down. It is significant that upon optical pumping to the level unaffected by a strong field the resonance Raman spectrum noticeably differs from the spectrum in the case of the probe field. A simple expression is proposed for calculating the degree of the phase memory preservation in collisions from the relative amplitude of the Raman resonance.
An expansion is presented for the absorption lineshape of a two-level system in a strong radiation field being perturbed by dephasing collisions, within the binary collision approximation. No dynamical assumptions regarding the time scale of the collisions (relative to the broadening) need to be made and the present theory interpolates smoothly between the impact and the quasistatic limits. The present solution reduces in weak radiation fields to the linear unified theory of spectral lineshapes and in the impact limit (fast collisions) the authors recover the Karplus-Schwinger formula. The only molecular information necessary for the exact evaluation of the absorption lineshape in a strong field is the same single-particle correlation function g( tau ) which appears in the linear (weak field) unified theory.
A method is developed for calculating the cross section for line broadening in the limiting case in which important collisions may be considered to occur very rapidly with respect to the periods corresponding to the transitions in question. This method is essentially an extension of the familiar "sudden" approximation; reference is made throughout to the particular example of optical double resonance only for definiteness and because there are available experimental results for comparison with the theory. Assuming the impact model and considering the case when the energy levels in question are well resolved with respect to their width, an exact expression is found for resonant self-broadening in the usual weak rf field limit of interest in double resonance. For the case of very small oscillator strengths for the optical transition (intercombination lines), the resonant broadening becomes sufficiently small so that second-order, intermediate-state processes dominate, and approximations must be made to effect sums over intermediate states. Here the broadening is of the same sort as foreign gas broadening, and in many cases of interest, the approximations can be made in a sufficiently realistic manner to obtain useful expressions for the broadening. It is shown that the resonant cross section and this "second-order" cross section are not additive, but that the one which is larger dominates the total cross sections very strongly. Finally, we evaluate explicitly the self-broadening and foreign gas broadening (by the noble gases) of double resonance lines in the group II metals and the self-broadening in the optical spectrum of helium. In all cases our theoretical predictions are in good agreement with measurements which have been made.
A new approach is suggested for dealing with the many-body aspects of resonance broadening of spectral lines in gases. A Liouville-space formalism is used in which the absorption by NNN identical molecules undergoing resonance-exchange collisions is described by an NNN-dimensional projection operator in Liouville space. In the impact approximation, under conditions in which the Doppler shift of resonance frequencies can be neglected, it is shown that the effect of resonance collisions is to modify the linewidth expression obtained by ordinary foreign-gas-type theories. The shape of isolated lines remains, however, Lorentzian. Only a combined effect of Doppler and collision broadening causes appreciable deviations from the Lorentzian shape near the line center, but these deviations are not peculiar to resonance broadening.