The subtitle, Nonclassical Fields, is perhaps not as accurate as it might be as a summary of content; or to put it another way, if my aim from the start had been to write a book on this topic, parts of that book would differ significantly from what follows here. Possibly the most important thing missing, and something that should be said, is that there are two quite distinct paths to a definition of nonclassicality in quantum optics. The first is grounded in the existence, or otherwise, of a nonsingular and positrve Glauber-Sudarshan P function. The physical grounding is in the treatment of optical measurements, specifically the photoelectric effect: for a given optical field, can the photoelectron counting statistics, including all correlations, be reproduced by a Poisson process of photoelectron generation driven by a classicallight intensity, allowed most generally to be stochastic? Viewed at a more informallevel, the question asks whether or not the infamous proposal of Bohr, Kramers, and Slater for the interaction of classical light and quantized atoms can be upheld in the presence of the observable photoelectron counting statistics.
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