Quantum Optics in Phase Space , Wolfgang P. Schleich Wiley-VCH, New York, 2001. $90.00 (695 pp.). ISBN 3-527-29435-X
Travel literature has its own vague rules and guidelines, flexible enough to include books that are little more than checklists of recommended museums, sights, and restaurants, along with careful descriptions of foreign climates both cultural and meteorological. They might even include intensely personal diaries that reveal the thinking of the writer as much as they reveal the geographic locale. Physicists can recognize analogs of all these types on their bookshelves, but the regions under review are not foreign countries but some part of physics or another.
Wolfgang P. Schleich’s Quantum Optics in Phase Space is a new contribution to physics travel literature, and it deserves praise as a guidebook. The book, suitable for almost any physicist contemplating an expedition through the quantum jungle, is timely, published at the same time that many of the jungle’s mysterious elements are being charted by physicists using the techniques of quantum optics. In effect, the book shows how the classical insights associated with wavepackets and phase space can be exploited to tame many of the jungle’s nonclassical creatures.
Schleich’s guided expedition begins in chapter 1 with an overview of the territory to come—something like a slide show on the evening before leaving base camp: highlights and snapshots (in no particular order) of some of the foundational ingredients and keynote topics of modern quantum optics. Schleich’s overview covers two-level atoms, single modes of radiation, antibunching, squeezing, cavity quantum electrodynamics and one-atom masing, de Broglie optics, fluorescence line-splitting, and entanglement. Schleich has selected these snapshots well, so an accurate impression is quickly obtained of the several ways in which quantum optics bridges the quantum—classical border. One easily gets the impression, I think accurately, that quantum phenomena are both highly puzzling and best illuminated by quantum optical investigations in the vicinity of this not-so-well-defined border.
The tour continues with a chapter called simply Ante, basically another slide show and an important one for readers who want a quick refresher course on the apparatus of quantum theory, which they will encounter in later chapters. With admirable concision, Schleich defines and illustrates key elements of representation theory, the density matrix and quantum averages, the quantum harmonic oscillator, the concept of interaction Hamiltonian, and different approaches to time evolution. While doing so, he finds it easy to hand out an array of formulas that will be useful in what follows.
Schleich explains that the main journey will start with a visualization of quantum states using the Wigner function, which introduces easily the notions of state squeezing and state reconstruction. A review of the WKB (Wentzel-Kramers-Brillouin) method is then connected to the Berry phase, leading the reader to interference in phase space and the dynamical behavior of wavepackets. Here Schleich takes his time, profitably deconstructing the character of revivals and fractional revivals as an illustration of the always fruitful procedure of time-scale analysis.
Generalizations of the Wigner function, particularly the quantum phase space machinery of Roy Glauber and George Sudarshan, are important in quantum optics in connection with photon detection, so several chapters are devoted to aspects of field quantization and photon states (Fock, coherent, Schrödinger-cat, and so on). These are followed by discussions of fundamental photonic devices and techniques, including beam splitters, homodyne detection, interferometers, and photon-count statistics.
Field quantization is also needed for examination of the quantized atom–field interaction, and Schleich commendably includes such topics as the gauge principle and the validity of the dipole approximation, topics that are frequently dodged for convenience. Introduction of the two-level atom artifice is justified, and one is led naturally to one of the central themes of quantum optics, cavity QED, where one encounters the interaction between light and matter in the context of the famous Jaynes–Cummings model (the spin-boson model made exactly soluble in rotating wave approximation). Schleich uses the designation Jaynes-Cummings-Paul model to alert readers to the less well-known work of Harry Paul. Exact dynamical solutions and many examples are given, including instructive ones that include atom–field entanglement and its use in state preparation. Three chapters then exploit these developments to examine interactions that include the quantum effects of atomic motion. In this context, Schleich treats atoms and ions in traps, in free space, and in optical lattices.
The concluding chapter uses Wigner functions and phase space visualization to examine aspects of atom optics, returning the book to its opening theme and completing our guided tour of the quantum jungle. Except that it’s not the end of the book. There are fully 90 pages of side thoughts, derivations, and overflow discussions in 17 appendices that include, for example, one devoted to the square root of the Dirac delta function. These would make a small reference work by themselves, and they show in another way Schleich’s sensitive attention to detail, for which most students will be grateful. The same care is also displayed in the annotated citations, a score or more at the end of nearly every chapter. There are also homework-style problems, for the dedicated reader. Is there anything for the student that should be here that is not? I doubt it. My strong recommendation is to sign on and enjoy the tour.
