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Journal of the Physical Society of Japan

Optical Response of a Randomly Modulated Two-Level Atom

Terumi Chikama, Kazuhiko Saikawa, Ryogo Kubo

Published Mar 1, 1984• 4 citations
Publisher

Abstract

In order to investigate the effect of perturbation caused by the interaction of a two-level atom with its environment on the coherency of light scattered by the atom when it is irradiated by an intense radiation, Mollow's theory is generalized to include a random modulation of the resonance frequency as well as fluctuations of the incident field. Expressions for the power spectrum, the total intensity, the coherent scattering intensity and the broad Rayleigh scattering intensity are derived. Some general aspects of the problem are discussed.

DOI
10.1143/jpsj.53.991

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In order to investigate the effect of perturbation caused by the interaction of a two-level atom with its environment on the coherency of light scattered by the atom when it is irradiated by an intense radiation, Mollow's theory is generalized to include a random modulation of the resonance frequency as well as fluctuations of the incident field. Expressions for the power spectrum, the total intensity, the coherent scattering intensity and the broad Rayleigh scattering intensity are derived. Some general aspects of the problem are discussed.
On the basis of a stochastic model of Burshtein et al. (1967) which assumes the phases, frequencies and/or amplitudes of the radiation field to constitute a randomly time-varying jump-like Markoff process, a generalisation of Mollow's theory (1975) of the dynamic Stark effect is formulated leading to predictions for the resonant scattering spectrum for a two-level atom quite similar to those published in the work of Agarwal (1976), of Eberly (1976) and of Kimble et al. (1977) who use a different approach. Apparently, the general form of the resonant scattering spectrum in a modulated radiation field depends less strongly on the particular stochastic model of the laser light than might be expected.
The nature of light scattered from a two-level atom, where the transition frequency between the two levels is a stochastic quantity, pumped by a strong monochromatic field is investigated. The optical Bloch equations, modified to include the stochastic nature of the atomic frequency, are solved using Monte Carlo techniques to include arbitrary strengths and bandwidths of the frequency noise. We find in the spectrum of scattered light a shift of the Rabi sidebands due to the stochastic nature of the transition frequency. We also find the height of the Rabi sideband first decreases and then increases with increasing strength of the noise. The intensity-intensity correlation function for the emitted fluorescence is observed to be sensitive to the time scale of the noise. The calculated line shapes for weak driving fields can be fitted to a superposition of Gaussian and Lorentzian lines.
Semi-classical calculation of an oscillating dipole induced in a two-level atom indicates that spherical radiation from the dipole under coherent interaction, i.e., Rayleigh scattering, has a power level comparable to that of spontaneous emission resulting from an incoherent process. Whereas spontaneous emission is nearly isotropic and has random polarization generally, Rayleigh scattering is strongly anisotropic and polarized in association with incident light. In the case where Rabi frequency is much larger than frequency detuning and spontaneous emission rate, while the power of spontaneous emission varies with time at the Rabi frequency, the power of Rayleigh scattering oscillates at twice the Rabi frequency. Moreover, the radiation pressure force acting on an atom due to Rayleigh scattering exceeds that caused by spontaneous emission when frequency detuning is large.
A general expression is found for the Green's function of a two-level system interacting with a classical monochromatic field of arbitrary frequency and intensity. The Green's function is first used to calculate the transition probability from the lower to the upper state as a function of the frequency and intensity of the field and a comparison of the results is made with experiment. It is then used to study the problem of scattering. It is found that the spectrum of the scattered radiation consists of a line at the frequency of the field (Rayleigh line) and two satellites symmetrically displaced from the Rayleigh line by an amount depending both on the intensity and frequency of the field. In addition there are emissions at three, five, etc., times the frequency of the field, and accompanying satellites. The cross sections for the production of the Rayleigh line and its satellites, and for the third-harmonic line and its satellites have been calculated for a range of values of the frequency and intensity of the incident field.
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.