Chapter 4 Field quantization in optics

Kikuo Ujihara

In this chapter, a one-dimensional optical cavity with output coupling is con-sidered. The optical cavity has transmission loss at one or both of the end surfaces. The classical, natural cavity mode is defined, and decaying or growing mode functions are derived using the cavity boundary conditions. A series of resonant modes appears. But these modes are not orthogonal to each other and are not suitable for quantum-mechanical analysis of the optical field inside or outside of the cavity. Hypothetical boundaries are added at infinity in order to obtain orthogonal wave mode functions that satisfy the cavity and infinity boundary conditions. These new mode functions are suitable for field quantization, where each mode is quantized separately and the electric field of an optical wave is made up of contributions from each mode. Some results of quantization are described in the next chapter. Chapter 3 deals with the usual quasimode model: a perfect cavity with distributed internal loss or with a fictitious loss reservoir.

Steven Robbins

Ana Marı́a Cetto, Luis de la Peña

Chapter 17 begins by approaching the general problem of a quantum system subject to a time-dependent perturbation. We then apply perturbation theory to the interaction of atomic matter with the radiation field and derive the most important radiative corrections. Atomic transitions – both induced and spontaneous – are discussed in detail, with some important applications. The formal introduction of field quantization allows us to make contact with quantum electrodynamics and quantum optics and discuss the Jaynes–Cummings model. Stochastic electrodynamics, in which the matter–field interaction is not a perturbation but is present ab initio, is used to explain atomic stability and its breakdown leading to radiative transitions. In the same spirit, the quantization of the field is physically justified by deriving the conventionally postulated field operators and their basic commutators. The chapter ends with a brief introduction to second quantization, an elegant and powerful formalism for describing and analyzing quantum many-body systems.

R. Loudon

Abstract The theory of the electromagnetic field quantization developed in Chapter 4 simplifies considerably for applications Lo many of the key experiments in quantum optics. Thus many experiments use plane parallel light beams whose transverse intensity profiles are not important for the measured quantities. Again, it is often sufficient in interpreting the data to consider the light beams as exciting a single mode of the field. The present chapter begins with the specialization of the quantization to single-mode excitations. The quantum theory is illustrated by its application to several varieties of single-mode state and the main features of number Cates, coherent states, chaotic statistical mixtures and squeezed states are derived.

Прохоров Лев Васильевич