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Journal of Physics A Mathematical Nuclear and General

Perturbation theory of super-radiance. I. Super-radiant emission

R Saunders, R. Bullough

Published Sep 1, 1973• 10 citations
Publisher

Abstract

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.

DOI
10.1088/0305-4470/6/9/010

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CRC Press eBooks•Mar 29, 2018•0 citations
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.
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.
For pt. I, see ibid., vol. 6, 1348 (1973). The authors extend the perturbation theory of super-radiant emission to derive a number of results on the level shifts of n atom systems. These also divide into 'coherent' and 'incoherent' parts. The incoherent part divides further into a generalized Lamb shift which is not cooperative, and an interatomic term which is. The former proves to be the only shift is not cooperative, and an interatomic term which is. The former proves to be the only shift which can depend on the presence of ambient free photons. These results for the generalized Lamb shift support the view that a dynamical neoclassical theory of the Lamb shift is unacceptable. The theory is compared with the pseudoboson theories of linear dielectrics. The pseudoboson theory of an inverted dielectric (the 'amplifier') should be intrinsically unstable unlike the pseudoboson theory of the refractive index which is concerned with the 'attenuator'.
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.
This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book discusses the main features of super-radiance using some simplified models. It presents a review of experimental work on super-radiance. The book also presents a generalization of the Wigner–Weisskopf approach to the N -atom system using a diagram method of non-stationary perturbation theory. It discusses several correlation functions for the field and the polarization, which characterize the coherence properties of super-radiation. The book uses the semiclassical approach to investigate the influence of de-phasing processes on radiation efficiency, or in other words, the influence of homogeneous and inhomogeneous broadening of the spectral line on the dynamics and spectrum of super-radiance. It considers the boundary value problem for the transmission and reflection of short pulses, taking into account the local field correction. Two effects are of special interest: the population-dependent frequency shift and the possibility of mirror-less bistability of ultra-short electromagnetic pulses.
This chapter investigates both diffraction and fluctuation effects on super-radiance within the framework of two models. Firstly, the two-dimensional theory of super-radiance of an extended system is developed. Secondly, the chapter considers the super-radiance of a 'sheet of paper' volume. However, quantum fluctuations of the initial polarization give rise to transverse inhomogeneity of atomic and field characteristics, which manifests itself in a change in the shape of the pulse and in the radiation polar diagram. The ringing of the envelope, which is typical of the one-dimensional model, becomes smoother. The super-radiance polar diagram has a ray structure, of which the angular size of individual components (rays) is of the order of the diffraction angle. The angular size of the ray is close to the diffraction angle, and its form changes relatively little from one realization of the initial polarization distribution to another.