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CRC Press eBooks

The elementary theory of super-radiance

M. G. Benedict, A. M. Ermolaev, Viktor A. Malyshev, I. V. Sokolov, E. D. Trifonov

Published Mar 29, 2018• 0 citations
Publisher

Abstract

This chapter considers super-radiance on an elementary level in the sense that the main notions and concepts of the phenomenon will be treated as they evolved in the course of the early studies starting with the classical works by R. H. Dicke. It considers super-radiance from a system with dimensions small compared with the wavelength of the emission that is the Dicke model. The chapter discusses the results to be obtained are also applicable to the single-mode super-radiance of an extended system. It then considers mainly the cooperative spontaneous emission of a collection of N identical atoms confined within a small volume. If the audience wish to investigate the super-radiance of an extended system, the dimensions of which exceed the emission wavelength, the semiclassical method is more convenient. In essence, the semiclassical approach discussed in the chapter combines the quantum mechanical treatment of the atomic system that uses the density matrix formalism with the classical treatment of the radiation field.

DOI
10.1201/9780203737880-2

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General properties of super-radiance--cooperative spontaneous emission of multi-atomic systems are explained on the basis of some simple models. First we consider spontaneous emission of two atoms separated from each other by a distance less than the wavelength. Then the kinetics of super-radiance of N-atomic system in a small volume are described. The main attention we put into super-radiance photon statistics. We show the Poissonian statistics for the main part of super-radiance pulse and demonstrate the special conditions when it can be Sub-Poissonian one.

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The quantum electrodynamical (QED) theory of the spontaneous decay of a single excited two-level atom was generalized and applied to the super-radiance problem by several authors. This chapter considers the evolution of the system of atom plus field, applying an approach equivalent to the master equation method. It uses the diagram representation of the quantum perturbation theory for the density matrix of the system. The diagram method provides an effective tool for the derivation of the master equations. The chapter presents the quantum theory of super-radiance of an extended three-dimensional polyatomic system within the Markov and the rotating wave approximations and neglecting retardation. It discusses the spatial properties of super-radiance, including the angular correlation of photons, which have been mentioned in earlier works by R. H. Dicke and V. Ernst and P. Stehle.

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Perturbation theory is used to show that that super-radiance as envisaged by Dicke, in which the radiation rate goes as N 2 , the square of the number of atoms, can be interpreted in the same terms as classical diffraction theory. The rate goes as N 2 from samples small in three dimensions compared with a wavelength but goes essentially as N from larger samples. There is a natural distinction between coherent and incoherent contributions to the total radiation rate from larger samples prepared (supposedly by an incident pulse) in Dicke states phased with a vector k.

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Collective spontaneous emission (Dicke superradiance)

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The present state of theoretical and experimental research on collective spontaneous emission (superradiance) in a system of radiators (atoms, molecules, or nuclei) is reviewed. The distinction between superradiance and the amplification of spontaneous emission is discussed. There is also a discussion of conditions under which the effect can be observed and of various theoretical methods for describing superradiance: the quantum single-mode and multimode models and the semiclassical approach. Theoretical papers on superradiance in systems with dimensions smaller than the wavelength of the radiation and also in extended systems are reviewed. It is shown that superradiance may occur in weakly amplifying media. A situation in which the superradiance is oscillatory is described. The possible use of superradiance to generate coherent emission in the x-ray and ? ranges is discussed. The superradiance accompanying Raman scattering of light in atomic and molecular media is studied. The theoretical results are compared with experimental observations of superradiance in the optical range. In an appendix, the nature of the phase transition in a system of radiators interacting through an electromagnetic field is discussed.

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The influence of dipole–dipole inter-atomic coupling upon super-radiance

M. G. Benedict, A. M. Ermolaev, Viktor A. Malyshev +2 more

The influence of the dipole–dipole inter-atomic coupling on collective spontaneous emission has been considered by many authors using both semiclassical and quantum theories. Specific results have been obtained for simple cases of regular atomic systems with a finite number of atoms. For disordered systems it has been found that the dipole–dipole coupling causes relaxation of the polarization phase (the effect of de-phasing), thus suppressing super-radiance. The main object of this chapter will be a regular linear chain of identical two-level atoms fully excited in the initial moment of time. The chapter considers the super-radiance of a regular linear chain of atoms. Such a system is the limiting case of a multi-atomic system characterized by a small Fresnel number. The dipole–dipole inter-atomic coupling modifies the super-radiance dynamics only slightly, but has a strong effect on the shape and width of the spectrum.

CRC Press eBooks•Mar 29, 2018•0 citations

The semiclassical theory

M. G. Benedict, A. M. Ermolaev, В. А. Малышев +2 more

This chapter introduces a three-level atomic model and discusses two other coherent atomic phenomena; namely, coherent Raman scattering and lasing without inversion. Lasing without inversion may take place in three-level resonant atomic systems and, like super-radiance, results from atomic coherence. Super-radiation is initiated by spontaneous fluctuations of the polarization in the medium. The semiclassical method is a powerful tool that is useful for the treatment of propagation effects in super-radiance as well as in such coherent emission processes as self-induced transparency, photon echo and others. The use of the Maxwell—Bloch equations allows one to consider these phenomena in elongated systems. Fortunately, the semiclassical approach is readily applicable to low-density systems that are to gases. However, one has to exercise greater care when applying it to coherent emission in solids. In high-density systems there is a strong mixing of the field and atomic states in the vicinity of resonance.

CRC Press eBooks•Mar 29, 2018•0 citations
This chapter considers super-radiance on an elementary level in the sense that the main notions and concepts of the phenomenon will be treated as they evolved in the course of the early studies starting with the classical works by R. H. Dicke. It considers super-radiance from a system with dimensions small compared with the wavelength of the emission that is the Dicke model. The chapter discusses the results to be obtained are also applicable to the single-mode super-radiance of an extended system. It then considers mainly the cooperative spontaneous emission of a collection of N identical atoms confined within a small volume. If the audience wish to investigate the super-radiance of an extended system, the dimensions of which exceed the emission wavelength, the semiclassical method is more convenient. In essence, the semiclassical approach discussed in the chapter combines the quantum mechanical treatment of the atomic system that uses the density matrix formalism with the classical treatment of the radiation field.
General properties of super-radiance--cooperative spontaneous emission of multi-atomic systems are explained on the basis of some simple models. First we consider spontaneous emission of two atoms separated from each other by a distance less than the wavelength. Then the kinetics of super-radiance of N-atomic system in a small volume are described. The main attention we put into super-radiance photon statistics. We show the Poissonian statistics for the main part of super-radiance pulse and demonstrate the special conditions when it can be Sub-Poissonian one.
The quantum electrodynamical (QED) theory of the spontaneous decay of a single excited two-level atom was generalized and applied to the super-radiance problem by several authors. This chapter considers the evolution of the system of atom plus field, applying an approach equivalent to the master equation method. It uses the diagram representation of the quantum perturbation theory for the density matrix of the system. The diagram method provides an effective tool for the derivation of the master equations. The chapter presents the quantum theory of super-radiance of an extended three-dimensional polyatomic system within the Markov and the rotating wave approximations and neglecting retardation. It discusses the spatial properties of super-radiance, including the angular correlation of photons, which have been mentioned in earlier works by R. H. Dicke and V. Ernst and P. Stehle.
Perturbation theory is used to show that that super-radiance as envisaged by Dicke, in which the radiation rate goes as N 2 , the square of the number of atoms, can be interpreted in the same terms as classical diffraction theory. The rate goes as N 2 from samples small in three dimensions compared with a wavelength but goes essentially as N from larger samples. There is a natural distinction between coherent and incoherent contributions to the total radiation rate from larger samples prepared (supposedly by an incident pulse) in Dicke states phased with a vector k.
The present state of theoretical and experimental research on collective spontaneous emission (superradiance) in a system of radiators (atoms, molecules, or nuclei) is reviewed. The distinction between superradiance and the amplification of spontaneous emission is discussed. There is also a discussion of conditions under which the effect can be observed and of various theoretical methods for describing superradiance: the quantum single-mode and multimode models and the semiclassical approach. Theoretical papers on superradiance in systems with dimensions smaller than the wavelength of the radiation and also in extended systems are reviewed. It is shown that superradiance may occur in weakly amplifying media. A situation in which the superradiance is oscillatory is described. The possible use of superradiance to generate coherent emission in the x-ray and ? ranges is discussed. The superradiance accompanying Raman scattering of light in atomic and molecular media is studied. The theoretical results are compared with experimental observations of superradiance in the optical range. In an appendix, the nature of the phase transition in a system of radiators interacting through an electromagnetic field is discussed.
The influence of the dipole–dipole inter-atomic coupling on collective spontaneous emission has been considered by many authors using both semiclassical and quantum theories. Specific results have been obtained for simple cases of regular atomic systems with a finite number of atoms. For disordered systems it has been found that the dipole–dipole coupling causes relaxation of the polarization phase (the effect of de-phasing), thus suppressing super-radiance. The main object of this chapter will be a regular linear chain of identical two-level atoms fully excited in the initial moment of time. The chapter considers the super-radiance of a regular linear chain of atoms. Such a system is the limiting case of a multi-atomic system characterized by a small Fresnel number. The dipole–dipole inter-atomic coupling modifies the super-radiance dynamics only slightly, but has a strong effect on the shape and width of the spectrum.
This chapter introduces a three-level atomic model and discusses two other coherent atomic phenomena; namely, coherent Raman scattering and lasing without inversion. Lasing without inversion may take place in three-level resonant atomic systems and, like super-radiance, results from atomic coherence. Super-radiation is initiated by spontaneous fluctuations of the polarization in the medium. The semiclassical method is a powerful tool that is useful for the treatment of propagation effects in super-radiance as well as in such coherent emission processes as self-induced transparency, photon echo and others. The use of the Maxwell—Bloch equations allows one to consider these phenomena in elongated systems. Fortunately, the semiclassical approach is readily applicable to low-density systems that are to gases. However, one has to exercise greater care when applying it to coherent emission in solids. In high-density systems there is a strong mixing of the field and atomic states in the vicinity of resonance.