Chapter

Quantized Fields and Coherent States

Stephen C. Rand

in Lectures on Light

Published in print May 2010 | ISBN: 9780199574872
Published online September 2010 | e-ISBN: 9780191722219 | DOI: http://dx.doi.org/10.1093/acprof:oso/9780199574872.003.0006
Quantized Fields and Coherent States

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Chapter 6 begins by transforming the optical wave itself into a quantized form, and the full implications of the wave‐particle duality of Chapter 2 become clear. The electric field may be pictured as an infinite ladder of discrete states and this structure allows optical interactions to be described photon by photon. The origin of spontaneous emission emerges from this treatment as a transition process that is stimulated by electric field fluctuations of the vacuum, and Weisskopf–Wigner theory explains why it is irreversible. The subject of coherent states is introduced and intriguing possibilities outlined regarding the noise properties of components of these states that form different quadratures in terms of the optical phase. Next, statistical analysis of light fields is considered to serve as a basis for more quantitative comparisons of fields and their noise properties. Methods of calculating the first and second degrees of coherence are presented, and the ranges of values corresponding to “classical” versus “quantum” light sources are discussed. The reduced density matrix is developed to justify analysis that focuses on only certain aspects of optical dynamics while ignoring others, as an important tool for simplifying complex problems. Finally, in view of its historical importance, the problem of calculating the fluorescence spectrum of resonantly excited two‐level atoms is considered using both a method of moments and dressed atom theory.

Keywords: quantization; photon; spontaneous emission; coherent states; quantum statistics; field correlations; reduced density matrix; resonance fluorescence; dressed atoms

Chapter.  30348 words.  Illustrated.

Subjects: Atomic, Molecular, and Optical Physics

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