Super-radiance

Multiatomic Coherent Emission

M.G Benedict, M.G Benedict

• Publisher: CRC Press
• Year: 2018
• ISBN:
  9781351412759
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Optics & Light

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.

Chapter 1

The elementary theory of super-radiance

In this Chapter we shall consider 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 Dicke [D54]. The attention of the reader will be directed mainly to the physical aspects of the problem. In doing so the treatment will be restricted to simple models where results of some general significance can be obtained without using complicated mathematical tools. By making the exposition more accessible we have intended to lay down the groundwork for subsequent chapters of the book where some results obtained here will be refined and generalized.

1.1. Cooperative spontaneous emission of two two-level atoms separated by a distance less than the wavelength

We shall start with a system of two identical atoms separated by a distance less than the emission wavelength, but at the same time where the direct interaction between the atoms is neglected. This is the simplest model of an atomic system for which the spontaneous decay, as we shall see, is no longer that of a single atom.

We shall assume that each of the atoms may be either in the ground state |g〉 or in the excited stationary quantum state |e〉, 〈g|g〉 = 〈e|e〉 = 1, 〈g|e〉 = 0 with respective non-degenerate energy levels E_g and E_e. The existence of other (excited) states of the atom will be neglected. The two-level model of the atom [AE75] is an idealization that is useful in the situations where coherent resonant interactions involve only two states of the atom. Radiative transitions in the atom will be considered in the dipole approxi...