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Journal of Physics B Atomic and Molecular Physics

Effects of an arbitrary laser lineshape on fluorescence radiation, redistributed by collisions

Henk F. Arnoldus, Gerard Nienhuis

Published Mar 28, 1985• 3 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3700/18/6/012

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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 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 apply the recently developed theory of multiplicative stochastic correlation functions with Markovian random jumps to the problem of resonance fluorescence from a two-level atom in a strong laser field. The finite bandwidth of a single-mode laser or the appearance of distinct lines in a multimode laser is considered to be brought about by a random mode-switching process. The two-time dipole correlation functions, which determine the spectral distribution of the fluorescence and the temporal correlations between the emitted photons are averaged exactly over the stochastics of the driving field. The authors' explicit expressions only involve single-time averages, which can be easily evaluated for a given probability distribution. These results generalise and modify earlier results. The authors obtain closed expressions, rather than implicit differential equations, which can handle the continuous case as well, and take into account the initial correlations, which always arise when the laser coherence time is finite. They illustrate the dependence on the stochastics of the laser model by comparing the multimode description with the phase-diffusion process and the Lorentz wave, which all give rise to the same laser profile, but to a different fluorescence spectrum.
The effect of binary collisions on the fluorescence spectrum of an atom in a nearly resonant monochromatic radiation fievd is evaluated in terms of formal relaxation and correlation operators that refer to a single collision. The driving field can be included in the atomic Hamiltonian, and its time dependence is transformed away, giving rise to a modified atom. The authors relate the strengths and the widths of line occurring in the fluorescence spectrum to the rate of optical collisions, and to other elements of the scattering matrix of the modified atom.
A method of calculation of multiple-time correlation functions of the resonance fluorescence light from a two-level atom driven by a realistic laser field with phase and amplitude fluctuations is developed. Both kinds of fluctuations are assumed to be Gaussian. The phase fluctuations are treated in the phase-diffusion model. The averaging over the amplitude fluctuations can be performed in a closed way when the relative mean-square amplitude fluctuation is small compared with the ratio of the amplitude correlation decay rate to the characteristic atomic relaxation rate. There is no restriction to Markovian amplitude fluctuations. Arbitrary values for the mean Rabi frequency are allowed. Results are presented for the intensity, the intensity correlation function, and the spectrum of the fluorescent light. It is shown that even in the case when the relative strength of the amplitude fluctuations is small, significant effects can occur due to the finite correlation length of the fluctuations. The results for fast amplitude correlation decay correspond to the situation without amplitude fluctuations. When the correlation time of the amplitude fluctuations becomes comparable with the atomic relaxation times, the Rabi oscillations of the intensity and the intensity correlation function are nearly washed out, and non-Lorentzian line shapes for the side peaks in the spectrum are observed. It is found that the ratio of the heights of the central peak to the side peak increases with increasing correlation time.
The authors study cooperative effects on the fluorescence spectrum of several atoms in an intense radiation field. In the secular approximation the spectrum contains three lines, as in the single-atom case. The authors evaluate the strengths of these lines for an arbitrary number of atoms without collisions. In the case of two atoms, collisional interactions with a perturber bath are included. The interatomic coherence in the absence of collisions leads to an enhancement of the line strengths, which is most pronounced for the central Rayleigh line. When collisions are present, the strengths of the two sidebands can actually be diminished by the cooperative effects.