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Journal of Physics B Atomic and Molecular Physics

Time-dependent spectra of colliding atoms in an intense radiation field

Gerard Nienhuis

Published Aug 14, 1983• 21 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/16/15/011

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Journal of Physics B Atomic and Molecular Physics•Jun 14, 1980•12 citations
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 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 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.
The formal structure of the time dependence of the state of an atom in a perturber bath in an intense classical monochromatic radiation field is studied. The authors allow the cross sections of binary collisions to be affected by the radiation field. The result is used to derive an expression for the collision-broadened saturated fluorescence excitation spectrum and absorption rate in terms of a collisional relaxation operator. This operator can be related to the rate of collisionally aided radiative excitation.
A two-state atom in a perturber gas is irradiated by intense light with an arbitrary spectral profile. The authors derive a general expression for the fluorescence spectrum in terms of the conventional low-intensity absorption profile and the spectral density of the incident light. This result, which contains previous results as special limiting cases, describes the transition from the three-line fluorescence spectrum excited by intense monochromatic light and the power-broadened Lorentzian spectrum produced by broad-band excitation.
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.
The authors derive an expression for the spectrum of fluorescence by a two-state atom in a perturber gas irradiated by nearly resonant monochromatic light of arbitrary intensity. The result is fully expressed in terms of the absorption profile that would be measured in a conventional low-intensity absorption experiment and of the rate of radiative and collisional transitions. The present result generalises previous work and the authors demonstrate that expressions obtained before in special cases are recovered by taking the appropriate limits.