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Canadian Journal of Physics

Analytic expressions for fluorescence spectra and optical collision rates of collisionally perturbed atoms in a strong driving field

F. Schuller, Gerard Nienhuis

Published Feb 1, 1984• 6 citations
Publisher

Abstract

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.

DOI
10.1139/p84-029

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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.
The formal structure of the time dependence of the state of an atom in a perturber bath in an intense classical monochromatic radiation field is studied. The authors allow the cross sections of binary collisions to be affected by the radiation field. The result is used to derive an expression for the collision-broadened saturated fluorescence excitation spectrum and absorption rate in terms of a collisional relaxation operator. This operator can be related to the rate of collisionally aided radiative excitation.
An analysis is made of the spectrum of absorption of a weak probe electromagnetic by two-level atoms in a strong resonant laser field, undergoing collision with buffer gas atoms. The analysis is made using an approach that allows for the direct influence of a strong electromagnetic on the dynamics of an elastic collision between an active atom and a buffer gas atom. Rate equations are analyzed for a combined atom–strong electromagnetic field system (an atom dressed by the field) allowing for spontaneous and optical collisional transitions, and also for the interaction with the probe field. In the steady-state case, an expression is derived for the electric susceptibility of the medium at the small-signal frequency. This expression contains the rates of the optical collisional transitions that depend nontrivially on the parameters of the strong electromagnetic field. The phenomenological characteristics of optical collisional transitions generally used are only valid at low intensities and for small frequency detunings of the strong electromagnetic field, i.e., in the impact limit.
The authors derive an expression for the spectrum of fluorescence by a two-state atom in a perturber gas irradiated by nearly resonant monochromatic light of arbitrary intensity. The result is fully expressed in terms of the absorption profile that would be measured in a conventional low-intensity absorption experiment and of the rate of radiative and collisional transitions. The present result generalises previous work and the authors demonstrate that expressions obtained before in special cases are recovered by taking the appropriate limits.
A two-state atom in a perturber gas is irradiated by intense light with an arbitrary spectral profile. The authors derive a general expression for the fluorescence spectrum in terms of the conventional low-intensity absorption profile and the spectral density of the incident light. This result, which contains previous results as special limiting cases, describes the transition from the three-line fluorescence spectrum excited by intense monochromatic light and the power-broadened Lorentzian spectrum produced by broad-band excitation.
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.