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Journal of Physics B Atomic and Molecular Physics

Collisional redistribution of intense phase-fluctuation radiation

Henk F. Arnoldus, Gerard Nienhuis

Published Jul 14, 1983• 30 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/16/13/007

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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 authors investigate collisional redistribution in a laser field with arbitrary lineshape. The phase diffusion model cannot be correct in general due to its inherent assumption of zero correlation times. The authors give general expressions for the state of the atom, the dipole correlation function and the steady-state fluorescence spectrum in the presence of collisions and phase fluctuations with finite correlation times. It turns out that collisional effects decouple from the free-atom stochastic problem to a good approximation and that modifications due to the laser bandwidth can be quite different from collisional effects, although they are additive on a microscopic level. They evaluate the fluorescence spectrum explicitly in the limit where the three lines are well separated and show that the spectrum is determined by simple field correlation functions. The arbitrary phase fluctuations do not affect the line strengths but only the lineshapes. Collisions, on the other hand, can transfer intensity between the lines, due to the very small collision time. For free atoms and strong driving fields, the fluorescence spectrum becomes a convolution of the normalised laser spectrum with the fluorescence spectrum at monochromatic irradiation, but this does not hold any more when collisions are present.
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.
As a first step in deriving accurate, calculable expressions for collisional redistribution of radiation, valid outside the impact regime, we present a method for calculating an accurate binary-collision density operator for an atom in the presence of a driving field and perturbers. We use projection-operator techniques to establish first the precise validity of the Markoff approximation for radiative relaxation. Using the same techniques, we show how the collisional-relaxation problem may be analyzed in a practical manner outside the Markoff approximation. The effect of correlations between radiative and collisional events is included in a consistent way, and the physical implications of these correlation effects are demonstrated for a simple example, the two-level atom with nondegenerate levels.
The author expresses the time-dependent physical spectrum of any signal as a twofold convolution over frequency and time of the Page-Lampard quasi-spectrum and a smoothing function that is determined by the properties of the spectrometer. This result is applied to the collisional redistribution of intense time-dependent radiation. Without resort to the adiabatic approximation the authors derive a differential equation that determines the time-dependent redistributed spectrum for any given time variation of the incident field. In the special case of adiabatic or sudden switch on the incident radiation he evaluates the approach to the steady state of the fluorescence spectrum of a two-state atom.
The author derives an expression for the spectrum of the radiation scattered by an atom that suffers binary collisions in the weak-field limit. The frequency of the incident radiation is in near-resonance with a multiplet transition. The authors accounts for strong atom-perturber correlations that are induced when the incident or the detected frequency is in the far wing of an absorption line. For an isolated transition between two degenerate atomic levels the model picture of quasistatic absorption followed by adiabatic reorientation of the excited state predicts a redistributed fluorescence line with a polarisation that is determined by geometrical factors.