Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review

The Effect of Collisions upon the Doppler Width of Spectral Lines

Robert Henry Dicke

Published Jan 15, 1953• 1,491 citations
Publisher

Abstract

Quantum mechanically the Doppler effect results from the recoil momentum changing the translational energy of the radiating atom. The assumption that the recoil momentum is given to the radiating atom is shown to be incorrect if collisions are taking place. If the collisions do not cause broadening by affecting the internal state of the radiator, they result in a substantial narrowing of the Doppler broadened line.

DOI
10.1103/physrev.89.472

Related papers

Effect of collisions on the resonance fluorescence spectrum

А. И. Пархоменко, Anatolii M. Shalagin

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.

Journal of Experimental and Theoretical Physics•May 1, 2008•1 citation

Combined Doppler and Collision Broadening*

Joel I. Gersten, Henry M. Foley

The combined effect of Doppler and collision broadening of spectral lines is studied by means of the statistical correlation function for the time-varying amplitude of classical oscillators. It is shown that at high pressures (mean-free path smaller than wavelength) the line shape is lorentzian with a width which is the sum of the conventional collision broadening and a Doppler contribution which decreases with increasing pressure, consistent with Dicke’s result.

Journal of the Optical Society of America•Jul 1, 1968•77 citations

The spectra of radiation redistribution in the presence of velocity-changing collisions

S Kryszewski, Gerard Nienhuis

The authors present an approach that allows the study of the influence of velocity-changing collisions (VCC) on the spectrum of resonance fluorescence. They give a theoretical framework yielding general, though quite complicated results. Working in the dressed-atom basis and describing the VCC by a strong-collision model, they focus their attention on the particular case of well separated spectral lines, which leads to relatively simple expressions. The results allow the authors to compare the effects of Doppler shifts and VCC on the profiles of the central line and on the spectra sidebands. They predict that VCC cause a narrowing of the spectral lines, which they attribute to Dicke narrowing. This prediction is also confirmed by numerical results. The adopted method of dealing with VCC in terms of collision operators can be applied to a larger class of collision models than just the strong-collision model used here.

Journal of Physics B Atomic Molecular and Optical Physics•Sep 28, 1991•2 citations

Shapes of pressure- and Doppler-broadened spectral lines in the core and near wings

R. Ciuryło

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.

Physical Review A•Aug 1, 1998•151 citations

Theory of Dicke narrowing in coherent population trapping

Ofer Firstenberg, M. Shuker, Amit Ben-Kish +3 more

The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.

arXiv:quant-ph/0701008•Physical Review A•Jul 19, 2007•39 citations

Polarization of Resonance Radiation and Breadth of Spectral Lines

A. Ellett

Observations of the polarization of the D line resonance radiation of sodium indicate that the transition probabilities for the various components of the Zeeman pattern are substantially in agreement with the predictions of the so-called sum rule. Observations in relatively strong fields show the effect of non-uniform distribution of intensity in the exciting spectral line. The assumption that the distribution of energy in the exciting line is due practically entirely to Doppler effect leads to equations for the variation of polarization with field strength which are well verified experimentally. Any broadening of the line by collision or by a coupling effect is evidently quite small in comparison with the Doppler breadth.

Proceedings of the Iowa Academy of Science•Jan 1, 1927•0 citations
Quantum mechanically the Doppler effect results from the recoil momentum changing the translational energy of the radiating atom. The assumption that the recoil momentum is given to the radiating atom is shown to be incorrect if collisions are taking place. If the collisions do not cause broadening by affecting the internal state of the radiator, they result in a substantial narrowing of the Doppler broadened line.
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 authors present an approach that allows the study of the influence of velocity-changing collisions (VCC) on the spectrum of resonance fluorescence. They give a theoretical framework yielding general, though quite complicated results. Working in the dressed-atom basis and describing the VCC by a strong-collision model, they focus their attention on the particular case of well separated spectral lines, which leads to relatively simple expressions. The results allow the authors to compare the effects of Doppler shifts and VCC on the profiles of the central line and on the spectra sidebands. They predict that VCC cause a narrowing of the spectral lines, which they attribute to Dicke narrowing. This prediction is also confirmed by numerical results. The adopted method of dealing with VCC in terms of collision operators can be applied to a larger class of collision models than just the strong-collision model used here.
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 Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.
Observations of the polarization of the D line resonance radiation of sodium indicate that the transition probabilities for the various components of the Zeeman pattern are substantially in agreement with the predictions of the so-called sum rule. Observations in relatively strong fields show the effect of non-uniform distribution of intensity in the exciting spectral line. The assumption that the distribution of energy in the exciting line is due practically entirely to Doppler effect leads to equations for the variation of polarization with field strength which are well verified experimentally. Any broadening of the line by collision or by a coupling effect is evidently quite small in comparison with the Doppler breadth.