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信州大学理学部紀要

Power Spectrum of Light Scattered by Three-Level Systems

M. Fujii, Kazuhiko Saikawa

Published Mar 25, 1987• 1 citation
OpenAlex

Abstract

The power spectrum of the light scattered by a three-level atom driven near resonance between the ground state (|1>) and the second excited state (|3>) by a monochromatic classical electric field is evaluated following the method developed by B. R. Mollow. The incident field is assumed to interact with the dipole moment between the states |1> and |3>, while the emitted light is assumed to interact with that between the state |3> and the first excited state |2> of the atom. The atom is assumed to relax to equilibrium only via radiation damping for the sake of simplicity. The power spectrum of the scattered field is explicitly calculated from the two-time atomic dipole moment correlation function, which is evaluated on a Markoff-type assumption, and various limiting cases are discussed. In Appendix the case is considered in which radiative damping between the higher excited state and the ground state is also present.

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Journal of Physics B Atomic and Molecular Physics•Aug 1, 1972•2 citations
The power spectrum of the light scattered by a three-level atom driven near resonance between the ground state (|1>) and the second excited state (|3>) by a monochromatic classical electric field is evaluated following the method developed by B. R. Mollow. The incident field is assumed to interact with the dipole moment between the states |1> and |3>, while the emitted light is assumed to interact with that between the state |3> and the first excited state |2> of the atom. The atom is assumed to relax to equilibrium only via radiation damping for the sake of simplicity. The power spectrum of the scattered field is explicitly calculated from the two-time atomic dipole moment correlation function, which is evaluated on a Markoff-type assumption, and various limiting cases are discussed. In Appendix the case is considered in which radiative damping between the higher excited state and the ground state is also present.
The power spectrum of the light scattered by a two-level atom driven near resonance by a monochromatic classical electric field is evaluated. The atom is assumed to relax to equilibrium with the driving field via radiation damping, which is treated by explicitly coupling the atom to the quantized electromagnetic field modes. The power spectrum of the scattered field is directly obtainable from the two-time atomic dipole moment correlation function, which is evaluated by a method based on a Markoff-type assumption analogous to that used to evaluate the time evolution of single-time atomic expectation values.
The power spectrum of the radiation emitted by a driven collision-damped two-level system is evaluated. The driving field, which is treated classically, is assumed to oscillate harmonically near the atomic resonance frequency, and its intensity is allowed to assume arbitrary values. The collisions are assumed to be strong, i.e., to instantaneously thermalize the state of the atom. The limiting forms of the power spectrum of the radiated field are discussed for the cases of low and high excitation of the atomic system.
The calculation is given of the spectral distribution of resonance fluorescence from an atom that is driven near a j=12j=\frac{1}{2}j=21​ to j=12j=\frac{1}{2}j=21​ transition by a monochromatic, xxx-polarized electric field and that is subject to radiation damping only. In accordance with Mollow's results for a two-level system, the power spectrum of the scattered radiation corresponding to the xxx component of the dipole moment contains a coherent part for all driving-field intensities. The coherent part is absent in the fluorescence radiation corresponding to the yyy and zzz components of the dipole moment. For weak driving fields all power scattered by these latter components is present in a narrow Lorentzian. Consistent with energy conservation, the width of the Lorentzian corresponds to the probability of excitation of the atom out of its ground level due to the presence of the driving field. For strong driving fields the power spectra corresponding to the xxx component and to the yyy or zzz component mainly differ in the heights and widths of their central incoherent band and their Rabi-precession-frequency-shifted side bands.
A theoretical analysis is developed for the spectrum of the light scattered by two two-level atoms driven near resonance by an external coherent electromagnetic field. The atoms are assumed to relax to equilibrium with the driving field as a result of radiation damping. The explicit dependence of the coherent dipole-dipole interactions on the distance between the two atoms is taken into account. For the case of two two-level atoms with a fixed distance smaller than a wavelength, an analytical result for the resonance fluorescence line shape is obtained, and the result is compared to previous work.>
A complete and detailed treatment of a three-level atom interacting with two near-resonant monochromatic fields is presented. It is assumed that the only damping mechanism is radiative damping, and that the atoms all have the same resonance frequencies, as is the case in an atomic beam. Detailed analytic solutions as well as numerical examples are determined from quantum-electrodynamic equations of motion. In addition, approximation techniques are presented which allow one to get accurate quantitative predictions for strong applied fields from simple rate-equation-like arguments. Absorption and emission spectra are determined, as are the transient and steady-state response of the atom. Two of the more interesting predictions are an emission spectrum containing up to seven components and a prediction of steady-state populations larger than 0.5 in the second excited state.
The semi-classical method for calculating the observable properties of light scattered from an optically thin atomic vapour is placed in the context of the well known input-output relations for random signals transmitted through a linear system. The autocorrelation of the scattered field amplitude, the statistic from which the mean intensity spectral density and intensity fluctuations may be deduced, is expressed in terms of the autocorrelation of the incident optical field and the autocorrelation of the scattering system; these latter are quantities that can be readily measured or calculated. An appendix contains a classical and a semi-classical calculation of the scattering system autocorrelation function for a vapour of atoms optically excited from a J=0 level under the conditions of a level crossing experiment. In the course of this calculation the relationship between the matrix element of the electric dipole moment operator and the corresponding classical quantity is carefully examined.