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Journal of Physics C Solid State Physics

Resonance fluorescence of crystalline solids

Yung-Chang Lee

Published Apr 14, 1979• 0 citations
Publisher

Abstract

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.

DOI
10.1088/0022-3719/12/7/031

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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.
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The frequency distribution of resonant radiation emitted by a system of two identical interacting atoms is calculated. The separation between the atoms is assumed to be much larger than the size of their charge distributions. Initially one atom is excited while the second one is in the ground state. The two atoms are coupled through the radiation field and the electrostatic interaction. For not too large internuclear separations the line shape of the emitted radiation exhibits two distinct peaks, and the general features are identical with the result obtained from resonance fluorescence scattering. In the decay process, however, there is equal probability of scattering through the symmetric and antisymmetric states, and thus the peak heights of the emitted radiation are different from the ones in the resonance fluorescent case. For large internuclear separations the two peaks merge into the one characteristic of the line shape of a single isolated atom.
We theoretically calculate the resonance fluorescence spectrum from a two-level atom which is embedded in a photonic bandgap crystal and is resonantly driven by a classical pump light. Non-Markovian noises caused by the non-uniform distribution of photon density states near the photonic bandgap are taken into account by a new approach which linearizes the optical Bloch equations by using the Liouville operator expansion. These linearized equations can be solved directly in the Fourier domain to obtain the correlation functions of the atomic operators and then the fluorescence spectrum from the atom. We find that if the atomic energy level is far from the bandgap, fluorescence spectra with Mollow triplets are observed. When the atomic energy level is near the bandgap, the relative magnitude and the number of the fluorescence peaks are found to be varied according to the wavelength offset.
A simple theoretical model is formulated which describes dynamical features of the interaction of two-level atoms with a continuum of radiation oscillators. In particular, this paper is concerned with resonance scattering by single atoms in the presence of an external classical field, and spontaneous emission by a system of identical atoms. In the case of resonance scattering, the response of an atom to rapid changes of the amplitude of the external field is studied. The model for spontaneous emission by a system of atoms is based on the assumptions that all atoms have the same resonance frequency, and that the atoms are contained in a volume whose extension is small compared with the wavelength of the emitted radiation. The complete evolution of a system of mmm atoms is determined by a set of coupled first-order linear differential equations, and explicit solutions are presented for the values m=1,2,3,4,and8m=1,2,3,4, \mathrm{and} 8m=1,2,3,4,and8. Pair correlations of the atoms and photon-number fluctuations are discussed. An approximation for resonance fluorescence by a system of atoms with a broad distribution of resonance frequencies is included in an Appendix.