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Journal of Physics A Mathematical and General

The Heitler and Ma approach to resonance fluorescence of N two-level atoms in a weak electromagnetic field

R. Pyzalski

Published Oct 1, 1979• 0 citations
Publisher

Abstract

The spectral intensity distribution of resonance fluorescence radiation emitted by N two-level atoms is calculated for the case of a weak electromagnetic field. Using these results the spectrum is discussed in terms of the number of atoms, their localisation and the orientation of the transition dipole moments. It is shown that the spectrum can be expressed as a sum of Lorentzian lines only in some specific cases. The general condition describing these cases is given.

DOI
10.1088/0305-4470/12/10/020

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The spectral intensity distribution of resonance fluorescence radiation emitted by N two-level atoms is calculated for the case of a weak electromagnetic field. Using these results the spectrum is discussed in terms of the number of atoms, their localisation and the orientation of the transition dipole moments. It is shown that the spectrum can be expressed as a sum of Lorentzian lines only in some specific cases. The general condition describing these cases is given.
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.>
We have studied the fluorescence spectra arising from the interaction of a three-level atom with two strong electromagnetic fields whose initially populated modes are equal to the two atomic transition frequencies, respectively. The Green's function formalism has been used to calculate the excitation spectrum of the system. An expression for the spectral function describing the excitation spectrum of the system has been derived in a closed form in the limit of high photon densities. Numerical computation of the expression for the spectral function indicates that at each transition frequency there may exist either one pair or two pairs or three pairs of sidebands, in addition to the central peak, depending upon the relative strength of the Rabi frequencies involved.
The resonance fluorescence of a crystalline solid consisting of two-level atoms is studied. The method of Heitler and Ma (1949) is used to solve the equations. From the calculated result, it is found that the probability of emission of photons is discrete in angular and in wavelength distributions. The emission line in the incident direction is identical in shape with the absorption line. While there is no actual trapping of radiation, the effect of photon-trapping manifests itself in both the emission and the absorption spectra.