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Journal of Physics B Atomic and Molecular Physics

Redistribution of radiation by slowly perturbed atoms

Dietrich Voslamber

Published Oct 28, 1986• 1 citation
Publisher

Abstract

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.

DOI
10.1088/0022-3700/19/20/007

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Journal of Experimental and Theoretical Physics•May 1, 2008•1 citation
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.
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.
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.
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 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 authors incorporate in the theory of collisional redistribution of resonance radiation the effect of a finite bandwidth of the intense incident radiation. The phase of the radiation is treated as a process with independent increments, which contains the phase-diffusion model as a special case. These phase fluctuations give rise to effective decay operators affecting the evolution of the density matrix and the regression of the correlation function. For a two-level atom suffering binary collisions the combined effect of collisions and phase fluctuations on the fluorescence spectrum is evaluated in several limiting cases of practical interest.
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.