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Journal of Physics B Atomic and Molecular Physics

Unified theory for collisional dephasing in strong radiation fields. A generalisation of the Karplus-Schwinger formula

Yitzhak Rabin

Published Jun 14, 1980• 6 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/13/11/002

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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.
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.
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 have studied the problem of a collisionally perturbed two-level atom in an intense driving field by developing a method which allows us to calculate the field-dependent collision operator in terms of the low intensity field-independent line-broadening function arising in the usual unified theory of pressure broadening. Our relations are exact to all orders in the field in the limiting case of weak collisions, but they are exact also in the complementary case of strong collisions and weak fields. We apply our results to derive explicit expressions for the rate of optical collisions, the fluorescence spectrum in the case of well-separated components, and the absorption during an adiabatic square pulse.
Perturbation theory is applied to the interaction between a binary collisional system and a weak radiation field to obtain the rate of induced absorption or the line profile of an optically allowed transition at low density. The collisional system wave functions are not affected by the radiation field and appropriate different expansions of these functions must be used for the two electron-atom or atom-atom systems under study. Unified expressions of the profile are given which converges to the impact limit at small detunings. The semi-classical approach of the collisional problem is given to underline the correspondence with the usual autocorrelation formalism. Both approaches break down for large detunings where a quantum collisional theory must be used.
The author derives an expression for the spectrum of the radiation scattered by an atom that suffers binary collisions in the weak-field limit. The frequency of the incident radiation is in near-resonance with a multiplet transition. The authors accounts for strong atom-perturber correlations that are induced when the incident or the detected frequency is in the far wing of an absorption line. For an isolated transition between two degenerate atomic levels the model picture of quasistatic absorption followed by adiabatic reorientation of the excited state predicts a redistributed fluorescence line with a polarisation that is determined by geometrical factors.
Lineshapes of three-level resonance Raman scattering and two-level resonance fluorescence, homogeneously broadened by collisions, in the presence of arbitrarily strong coherent radiation, are studied by means of a tetradic (density-matrix) scattering theory. In the case of medium coupling strength V L to the radiation field (where T 2 -1 <or=V L << tau c -1 , with T 2 and tau c being the coherence damping and collision times, respectively) the Mollow lineshape (1977) for resonance fluorescence is rederived, with proper T 2 and population cross-relaxation effects included. In particular it is shown that relaxation through intermediate non-resonant levels can considerably alter the lineshape in resonance fluorescence. In the case of strong coupling (V L >or approximately= tau c -1 ) the collision rates are modified by the applied field (optical collisions). It is shown that, whereas in self attenuation spectra optical collision rates can be obtained only from line intensity or line wing measurements, in resonance scattering these rates are directly obtained from linewidth measurements.