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Physical Review A

Correlations between Doppler and pressure broadening for the resonance interaction

J. Cooper, Derek N. Stacey

Published Dec 1, 1975• 9 citations
Publisher

Abstract

The correlation between Doppler and collisional broadening has been considered in detail for radiation in which the lower level of the transition is broadened by the resonance interaction. It is found that rather than a single Voigt profile, the profile of the radiation is essentially a sum of Voigt profiles. Although the widths of these profiles vary by some 40%, the over-all line shape is very close to the single Voigt shape obtained when correlation effects are neglected.

DOI
10.1103/physreva.12.2438

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The correlation between Doppler and collisional broadening has been considered in detail for radiation in which the lower level of the transition is broadened by the resonance interaction. It is found that rather than a single Voigt profile, the profile of the radiation is essentially a sum of Voigt profiles. Although the widths of these profiles vary by some 40%, the over-all line shape is very close to the single Voigt shape obtained when correlation effects are neglected.
The Rautian-Sobelman approach describing the collision-Doppler shape of spectral line that takes into account both soft and hard velocity-changing collisions is extended to the case when correlation between Doppler and collision broadening as well as the dispersion line asymmetry should be considered. Numerical calculations show that speed-dependent effects can produce the additional line narrowing as well as broadening and also the line asymmetry. It is shown that speed-dependent profiles based on the soft and hard collision models differ much more one from another than those which omit the speed-dependent effects.
The effect of collisions on the resonance fluorescence spectrum of two-level atoms excited by monochromatic resonance radiation is studied. Analysis is performed for systems where the Doppler broadening is small compared to the collision frequency (high buffer gas pressures) and for the general case where collisions arbitrarily change the phase of the radiation-induced dipole moment (from completely interrupted to completely unaffected phase of the dipole moment). Both at a relatively low and at a high excitation radiation intensity, the resonance fluorescence spectrum is shown to depend on whether the two-level system is closed or open. This is especially true for the narrow unshifted Rayleigh scattering line. It is shown that, although the absorption line is homogeneously broadened, the resonance fluorescence spectrum exhibits a clearly pronounced anisotropy. In a direction close to the direction of propagation of the excitation radiation, the Rayleigh scattering line is maximally narrowed. Under certain conditions (that can easily be created in experiments), the width of this line is proportional to the diffusion coefficient of atoms interacting with the radiation.
The work of two previous papers is extended and a theory of pressure broadening is developed which treats the perturbers quantum mechanically and allows for inelastic collisions, degeneracy, and overlapping lines. The impact approximation is used. It consists in assuming that it takes, on the average, many collisions to produce an appreciable disturbance in the wave function of the atom, and it results in an isolated line having a Lorentz shape. Validity criteria are given. When the approximation is valid, it is allowable to replace the exact, fluctuating interaction of the perturbers with the atom by a constant effective interaction. The effective interaction is expressed in terms of the one-perturber quantum mechanical transition amplitudes on and near the energy shell and its close relationship to the scattering matrix is stressed. The calculation of the line shape in terms of the effective interaction is the same as when the perturbers move on classical paths. Results are written explicitly for isolated lines. If the interaction of the perturbers with the final state can be neglected, the shift and width are proportional to the real and imaginary part of the forward elastic scattering amplitude, respectively. By the optical theorem, the width can also be written in terms of the total cross section. When the interaction in the final state cannot be neglected, the shift and width are still given in terms of the elastic scattering amplitudes, in a slightly more complicated fashion. Finally, rules are given for taking into account rotational degeneracy of the radiating states.
The line shape of a Doppler-broadened transition is dramatically altered by the presence of a laser field resonating with a second Doppler-broadened transition sharing a common level: Two narrow resonances of different widths appear superimposed upon the broad background signal at frequencies symmetrically located about the corresponding line center. The effect has already found application in a number of seemingly different though intimately related studies, including high-resolution hfs and isotope-shift determinations. The theory of the effect is developed with reference to these applications. The treatment is formulated in terms of transition rates induced by two classical fields resonantly interacting with a pair of coupled Doppler-broadened transitions of arbitrary frequencies. The perturbation approach adopted is valid for one field fully saturating its transition; the resulting line-shape expression exhibits important power-broadening effects. This approach is equivalent to the familiar density-matrix formulation, which is also presented. Various features of the resulting expression are discussed in detail as they apply to two precision spectroscopic applications, mode crossing and spontaneous emission line narrowing. The connection with previous work is also discussed.