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 A

Rayleigh component of the redistribution function

Dietrich Voslamber

Published Oct 1, 1986• 0 citations
Publisher

Abstract

A formal investigation of the redistribution of weak near-resonance radiation is presented for the case that the radiative transitions of the scattering atom occur between two well-separated groups of states. The lower states are assumed stable while the upper states are allowed to undergo arbitrary interactions with an environment. If the lower states are also degenerate, a Rayleigh component which is infinitesimally narrow in the atom's rest frame is shown to exist under extremely wide conditions and independent of the approximations made in previous work on redistribution. Like the absorption profile, the intensity of this component as a function of the detuning (Rayleigh response function) can be expressed in terms of the mean atomic time evolution operator projected on the upper-state manifold. As compared to the absorption profile, however, the Rayleigh response function is different in shape and may provide complementary information on the scattering medium.

DOI
10.1103/physreva.34.3521

Related papers

Redistribution of radiation by slowly perturbed atoms

Dietrich Voslamber

Redistribution of weak near-resonance radiation by perturbed two-state atoms is investigated without making the assumption of binary collisions. Perturbation of the atoms is assumed to occur as level fluctuations which obey a stationary stochastic process. The redistribution function is formally established in the atom's rest frame, neglecting lower-state broadening. The infinitesimally narrow Rayleigh component is shown to exist under a wide range of conditions, independently of the approximations made in binary-collision treatments. It is demonstrated that for slow perturbations of Rayleigh response function (intensity of the narrow component) is significantly different in shape from the absorption profile, even close to resonance. Slow perturbations also entail the occurrence of a broadened Rayleigh component in addition to the narrow Rayleigh component and the broadened fluorescence component. The redistribution function is evaluated for three special cases corresponding to small perturbations, very slow perturbations and perturbations obeying a Poisson step process.

Journal of Physics B Atomic and Molecular Physics•Oct 28, 1986•1 citation

Collisional redistribution of radiation. II. The effects of degeneracy on the equations of motion for the density matrix

Keith R. Burnett, J. Cooper

We apply the analysis of paper I to degenerate atomic systems and calculate the effect of correlations between an atom (the absorber) and perturbers in the binary-collision approximation. The result of our calculation is a generalized absorption profile that specifies the final state of the atom an absorption event. This profile is then related to the total intensities of Rayleigh scattering and fluorescence (redistributed radiation) from the atom. The profile is expressed in terms of collision operators that depend on the index of the multipole of the atom that is created. Some of the operators represent correlations between radiative and collisional events and cannot, except in certain limits, be expressed in terms of the usual line-broadening operators. This, of course, implies that one needs extra dynamical information, on top of that obtainable from ordinary absorption experiments, to be able to describe redistribution. Conversely, redistribution offers a probe of collisional dynamics, not given by absorption experiments, via the polarization of fluorescent light. We give practical expressions for the calculation of these operators and discuss their implications.

Physical Review A•Nov 1, 1980•65 citations

Collisional redistribution of radiation. II - The effects of degeneracy on the equations of motion for the density matrix. III - The equation of motion for the correlation function and the scattered spectrum

Keith R. Burnett, J. Cooper

The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.

Physical Review A•Nov 1, 1980•0 citations

The angular dependence of partially redistributed resonance radiation

R. J. Ballagh, J. Cooper

Explicit expressions for the angular distribution and frequency dependence of radiation scattered by a spatially degenerate atom undergoing collisions are derived using a previously developed formalism of the quantum theory of line broadening for an atom in its rest frame. Results valid in the impact regime for resonant scattering are presented for the cases of linear incident and scattered polarization circular incident and linear scattered polarization, and unpolarized incident radiation with no monitoring of the scattered polarization. These results relate to scattering involving a j - j + or - 1 - j atomic transition, with lower-state interactions neglected; the expressions obtained take a relatively simple form involving atomic multipolar relaxation rates of the order of k = 0 and k = 2. The angular distributions for each case are combined with the frequency dependences to yield a three-component frequency redistribution function for an s-p-s transition, the components being a coherent term, a frequency-redistributed term with the same angular dependence as the coherent term, and an isotropic frequency-redistributed term.

The Astrophysical Journal•Apr 1, 1977•32 citations

Redistribution of Resonance Radiation. I. The Effect of Collisions

A. Omont, E. W. Smith, Jon C. Cooper

The techniques of modern line-broadening theory are used to investigate the scattering of polarized radiation in the rest frame of an atom undergoing collisions. The formulation explicitly includes both elastic and inelastic (quenching) collisions. When the lower state has zero width, a form for the redistribution function similar to that of Zanstra is obtained, but with the redistribution in the neighborhood of the resonance line being caused solely by elastic collisions. In the limit of no collisions, but with both levels of finite lifetime, the result of `veisskopf and Woolley is obtained. The effect of level-degeneracy is also explicitly included; in this case the results are a function of the polarization of the light and the different relaxation rates for the multipolar components of the atomic states.

The Astrophysical Journal•Jul 1, 1972•250 citations

Role of collisional repopulation of atomic levels on coherent and redistributed components in resonant light scattering

J. Cooper, R. J. Ballagh

Resonant scattering (redistribution) of weak monochromatic light by atoms in the presence of collisions has been considered by Omont et al., who allowed for the broadening of both upper and lower levels of the transition. Mollow (who also has considered this problem for intense radiation) has shown that their results are applicable only if collisional repopulation of the levels (in contrast to collisional depopulation) is ignored. We here consider in detail the effect of repopulation. It leads, in the weak-field limit, to a true-coherent component ($\ensuremath{\delta}$-function spectrum) at the driving frequency, as well as a component at this frequency whose width is essentially the inelastic collisional rate of the lower state. An additional redistributed component due to repopulation of the upper level is also obtained.

Physical Review A•Sep 1, 1978•29 citations
A formal investigation of the redistribution of weak near-resonance radiation is presented for the case that the radiative transitions of the scattering atom occur between two well-separated groups of states. The lower states are assumed stable while the upper states are allowed to undergo arbitrary interactions with an environment. If the lower states are also degenerate, a Rayleigh component which is infinitesimally narrow in the atom's rest frame is shown to exist under extremely wide conditions and independent of the approximations made in previous work on redistribution. Like the absorption profile, the intensity of this component as a function of the detuning (Rayleigh response function) can be expressed in terms of the mean atomic time evolution operator projected on the upper-state manifold. As compared to the absorption profile, however, the Rayleigh response function is different in shape and may provide complementary information on the scattering medium.
Redistribution of weak near-resonance radiation by perturbed two-state atoms is investigated without making the assumption of binary collisions. Perturbation of the atoms is assumed to occur as level fluctuations which obey a stationary stochastic process. The redistribution function is formally established in the atom's rest frame, neglecting lower-state broadening. The infinitesimally narrow Rayleigh component is shown to exist under a wide range of conditions, independently of the approximations made in binary-collision treatments. It is demonstrated that for slow perturbations of Rayleigh response function (intensity of the narrow component) is significantly different in shape from the absorption profile, even close to resonance. Slow perturbations also entail the occurrence of a broadened Rayleigh component in addition to the narrow Rayleigh component and the broadened fluorescence component. The redistribution function is evaluated for three special cases corresponding to small perturbations, very slow perturbations and perturbations obeying a Poisson step process.
We apply the analysis of paper I to degenerate atomic systems and calculate the effect of correlations between an atom (the absorber) and perturbers in the binary-collision approximation. The result of our calculation is a generalized absorption profile that specifies the final state of the atom an absorption event. This profile is then related to the total intensities of Rayleigh scattering and fluorescence (redistributed radiation) from the atom. The profile is expressed in terms of collision operators that depend on the index of the multipole of the atom that is created. Some of the operators represent correlations between radiative and collisional events and cannot, except in certain limits, be expressed in terms of the usual line-broadening operators. This, of course, implies that one needs extra dynamical information, on top of that obtainable from ordinary absorption experiments, to be able to describe redistribution. Conversely, redistribution offers a probe of collisional dynamics, not given by absorption experiments, via the polarization of fluorescent light. We give practical expressions for the calculation of these operators and discuss their implications.
The effect of correlations between an absorber atom and perturbers in the binary-collision approximation are applied to degenerate atomic systems. A generalized absorption profile which specifies the final state of the atom after an absorption event is related to the total intensities of Rayleigh scattering and fluorescence from the atom. It is suggested that additional dynamical information to that obtainable from ordinary absorption experiments is required in order to describe redistributed atomic radiation. The scattering of monochromatic radiation by a degenerate atom is computed in a binary-collision approximation; an equation of motion is derived for the correlation function which is valid outside the quantum-regression regime. Solutions are given for the weak-field conditions in terms of generalized absorption and emission profiles that depend on the indices of the atomic multipoles.
Explicit expressions for the angular distribution and frequency dependence of radiation scattered by a spatially degenerate atom undergoing collisions are derived using a previously developed formalism of the quantum theory of line broadening for an atom in its rest frame. Results valid in the impact regime for resonant scattering are presented for the cases of linear incident and scattered polarization circular incident and linear scattered polarization, and unpolarized incident radiation with no monitoring of the scattered polarization. These results relate to scattering involving a j - j + or - 1 - j atomic transition, with lower-state interactions neglected; the expressions obtained take a relatively simple form involving atomic multipolar relaxation rates of the order of k = 0 and k = 2. The angular distributions for each case are combined with the frequency dependences to yield a three-component frequency redistribution function for an s-p-s transition, the components being a coherent term, a frequency-redistributed term with the same angular dependence as the coherent term, and an isotropic frequency-redistributed term.
The techniques of modern line-broadening theory are used to investigate the scattering of polarized radiation in the rest frame of an atom undergoing collisions. The formulation explicitly includes both elastic and inelastic (quenching) collisions. When the lower state has zero width, a form for the redistribution function similar to that of Zanstra is obtained, but with the redistribution in the neighborhood of the resonance line being caused solely by elastic collisions. In the limit of no collisions, but with both levels of finite lifetime, the result of `veisskopf and Woolley is obtained. The effect of level-degeneracy is also explicitly included; in this case the results are a function of the polarization of the light and the different relaxation rates for the multipolar components of the atomic states.
Resonant scattering (redistribution) of weak monochromatic light by atoms in the presence of collisions has been considered by Omont et al., who allowed for the broadening of both upper and lower levels of the transition. Mollow (who also has considered this problem for intense radiation) has shown that their results are applicable only if collisional repopulation of the levels (in contrast to collisional depopulation) is ignored. We here consider in detail the effect of repopulation. It leads, in the weak-field limit, to a true-coherent component ($\ensuremath{\delta}$-function spectrum) at the driving frequency, as well as a component at this frequency whose width is essentially the inelastic collisional rate of the lower state. An additional redistributed component due to repopulation of the upper level is also obtained.