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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE

Superradiance: multiatomic coherent emission

Evgeni D. Trifonov

Published Mar 4, 1999• 202 citations
Publisher

Abstract

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.

DOI
10.1117/12.341383

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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.
We consider the problem of two-photon cooperative emission in systems of two-level atoms. Two physically distinct regimes are analyzed. First, we investigate the case of a small number of atoms. We study the evolution of two-photon super- and sub-radiant states and associated two-photon spectra. Second, we investigate the problem of a constant density of atoms confined to a spherical volume. We analyze separately the cases in which the radius is small or large in comparison to the resonant wavelength.
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.
Super-radiance: Multiatomic Coherent Emission provides a comprehensive, self-contained account of the theory and experiments of the quantum optic phenomenon of superradiance. Contributed by highly regarded researchers in the field, the book first presents the theory of superradiance at a level suitable for graduate physicists approaching the subject for the first time. This introduction is followed by a more rigorous treatment that is supported by the analysis of experiments dealing with superradiance and by a discussion on the possible uses of the effect in other areas of optics and electronics. The theoretical and experimental results presented in this book will introduce a wide audience to this important area of quantum optics.
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.
We study cooperative single-photon spontaneous emission from three multilevel atoms with one of them being excited for different atomic configurations in optical vector theory. The dynamic evolution is solved by finding the eigenvalues of a 3 \ifmmode\times\else\texttimes\fi{} 3 matrix, and then the relevant decay rates and Lamb shifts are obtained analytically. It is shown that the symmetry of atomic configuration has a big influence on the super-radiance of the system. To obtain strong super-radiance requires not only the distances among the three atoms to be much shorter than the wavelength, but also to have symmetrical distribution. We also calculate the emission spectra and find that it normally has three peaks, but it has two peaks under the equilateral-triangle configuration.
The interaction between electromagnetic radiation and two three-level atoms is investigated. The atom-atom separation is assumed to be smaller than the corresponding mean resonance wavelength. The total radiance rate of the atomic system is calculated as a function of time. Explicit results are given for several different initial states of the atomic system. Some of them exhibit superradiance, and some act as photon-trapping states. Instead of exponential decay, the oscillations appear in the time evolution of the radiation rate due to the correlation between atoms. The decay constants and coupling decay constants show strong effects on the emission rates. Completely differing from two identical double-level atoms, the cooperative effects always exist in the three-level atomic system except for the case in which the coupling decay constants ${\ensuremath{\gamma}}_{12}$ and ${\ensuremath{\gamma}}_{21}$ are zero.