Book contents
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Classical nonlinear optics
- 2 Field quantization
- 3 Quantized fields in dielectric media
- 4 Microscopic description of media
- 5 Coherence and quantum dynamics in simple systems
- 6 Decoherence and reservoirs
- 7 Phase-space distributions
- 8 Single-mode devices
- 9 Degenerate parametric oscillator
- 10 Quantum field dynamics
- 11 Quantum propagation in fibers and waveguides
- 12 Quantum information
- List of symbols
- Index
- References
2 - Field quantization
Published online by Cambridge University Press: 05 May 2014
- Frontmatter
- Contents
- Preface
- Introduction
- 1 Classical nonlinear optics
- 2 Field quantization
- 3 Quantized fields in dielectric media
- 4 Microscopic description of media
- 5 Coherence and quantum dynamics in simple systems
- 6 Decoherence and reservoirs
- 7 Phase-space distributions
- 8 Single-mode devices
- 9 Degenerate parametric oscillator
- 10 Quantum field dynamics
- 11 Quantum propagation in fibers and waveguides
- 12 Quantum information
- List of symbols
- Index
- References
Summary
In Chapter 1, we treated the electromagnetic field as classical. Henceforth, we will want to treat it as a quantum field. In order to do so, we will first present some of the formalism of quantum field theory. This formalism is very useful in describing many-particle systems and processes in which the number of particles changes. Why this is important to a quantum description of nonlinear optics can be seen by considering a parametric amplifier of the type discussed in the last chapter. A pump field, consisting of many photons, amplifies idler and signal fields by means of a process in which a pump photon splits into two lower-energy photons, one at the idler frequency and one at the signal frequency. Therefore, what we would like to do in this chapter is to provide a discussion of some of the basics of quantum field theory that will be useful in the treatment of the quantization of the electromagnetic field.
In particular, we will begin with a summary of quantum theory notation, and a discussion of many-particle Hilbert spaces. These provide the arena in which all of the action takes place. We will then move on to a treatment of the canonical quantization procedure for fields. This will allow us to develop a scattering theory for fields, which is ideally what we need. This relates the properties of a field entering a medium to those of the field leaving it, and this corresponds to what is done in an experiment.
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- Information
- The Quantum Theory of Nonlinear Optics , pp. 37 - 82Publisher: Cambridge University PressPrint publication year: 2014