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Journal of Physics B Atomic and Molecular Physics

Atomic response to the Lorentz wave

Henk F. Arnoldus, Gerard Nienhuis

Published Mar 28, 1986• 10 citations
Publisher

Abstract

The fluorescence radiation, emitted by a two-level atom in a perturber bath, is considered. The atom is driven by a single-mode laser with a Lorentzian profile, which is brought about by a fluctuating phase. The stochastics of this phase is taken to be the Markovian random-jump process. The authors derive explicit expressions for the atomic density matrix, the temporal photon correlations and the fluorescence spectrum. The results greatly resemble the results for a non-Gaussian diffusive phase, but deviate slightly from the corresponding expressions in the Wiener-Levy limit of the diffusion process.

DOI
10.1088/0022-3700/19/6/010

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The fluorescence radiation, emitted by a two-level atom in a perturber bath, is considered. The atom is driven by a single-mode laser with a Lorentzian profile, which is brought about by a fluctuating phase. The stochastics of this phase is taken to be the Markovian random-jump process. The authors derive explicit expressions for the atomic density matrix, the temporal photon correlations and the fluorescence spectrum. The results greatly resemble the results for a non-Gaussian diffusive phase, but deviate slightly from the corresponding expressions in the Wiener-Levy limit of the diffusion process.
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The relaxation process and resonance fluorescence of a two-level atom strongly driven by stochastically fluctuating laser light is studied. A laser with small intensity fluctuations about a constant mean value and a diffusing phase is assumed. Depending on the relative time scales of the intensity fluctuations and the atomic response to these fluctuations, the time decay of the atomic population is found to be non-exponential. The broadening of the sidebands in the triplet spectrum of resonance fluorescence is shown to be non-Lorentzian.
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 effect of environmental perturbations on a system of two-level atoms is to alter the coupling between the atoms and their surroundings, which manifests itself as a change in the relaxation rates of the atoms. One of the ways in which environmental fluctuations can affect an atom is to modulate its transition frequency in a stochastic manner. We study the response of such two-level atoms to irradiation by a monochromatic laser, and report the results of numerical experiments on the spectrum of scattered light. It is observed that this spectrum is a sensitive indicator of the parameters that describe the stochastic modulation. In addition, the spectra exhibit substantially different features depending on whether the stochastic process follows a diffusion or a jump mechanism. The numerical results are based on a Monte Carlo procedure, which can be applied to stochastic processes in a wide variety of biological, chemical, and physical processes.
The Jaynes-Cummings model of a two-level atom interacting with a single quantized mode of radiation field is generalized to include the effects of stochastic fluctuations in atom-field coupling. The coupling coefficient is assumed to fluctuate in phase and/or in amplitude. The phase fluctuations are described by a Wiener-Levy process and the amplitude fluctuations by a colored Gaussian noise. A secular approximation and the theory of the multiplicative stochastic processes are invoked to derive the master equation for the density operator averaged over both phase and amplitude ensembles. The solution of this equation is used to study the resulting decoherence effects in the dynamical behavior of the atom and the statistical properties of the field.
We present a continuation of a general theoretical approach to noisy laser-atom interactions based on a special Markov-chain description of external fluctuations. This chain, composed of n independent two-state jump processes, forms a non-Gaussian stochastic process from which a detailed discussion of the atomic response can be given. We show that the n-component Markov chain also has the property of pre-Gaussian noise, because in the limit of n → ∞ it converges to a Gaussian stochastic process. We exhibit solutions for the field spectrum and the atomic-fluorescence spectrum for phase, frequency, and amplitude pre-Gaussian fluctuations of the driving-laser light.