Quantum Optics: An Introduction , Mark Fox , Oxford U. Press, New York, 2006. $44.50 paper (400 pp.). ISBN 978-0-19-856673-1
Quantum optics, literally the study of quantized light, has morphed into a name for the investigations of the interactions between light and matter, with an emphasis on qualitative microscopic models, time dependence, and coherence, rather than on the atomic-structure calculations of transition-matrix elements. Much of the current activity in quantum information science, laser cooling and trapping, and quantum-degenerate atomic gases has grown out of quantum optics. Mark Fox’s Quantum Optics: An Introduction covers, or at least brings up, much of the core material in traditional quantum optics, quantum information, and cold gases. This could have been 1000 pages of stiff mathematics, but what is on hand is an undergraduate textbook with fewer than 400 pages.
Fox, a reader in the department of physics and astronomy at the University of Sheffield in the UK, has done a remarkable job at picking the key topics from a broad field—one that the more-expansive quantum opticians nowadays claim as their own. I do not know of a comparable quantum optics textbook aimed at undergraduates. Part 1 presents background on classical optics, quantum mechanics, and radiative transitions in atoms. Parts 2, 3, and 4 cover, respectively, photons, atom-photon interactions, and quantum information processing. A couple hundred exercises, mostly straightforward, and brief answers are included.
Fox’s strategy is to accommodate undergraduates by emphasizing intuition, experiments, and devices at the expense of mathematics. Sometimes his approach works very well. A hardcore theorist may cringe at seeing anti-bunched light represented as a regular stream of little balls, but those sorts of pictures have guided, and will guide, designs of successful experiments and devices. At times, though, avoiding mathematics may have become a goal of its own: The contorted presentation of the two-level system in terms of rate equations and Einstein’s A and B coefficients is a case in point. By not using something equivalent to optical Bloch equations, the author may have by-passed some mathematics, but a student’s understanding of one of the central themes in quantum optics is seriously compromised.
The style and depth of the presentation vary depending on the topic and, presumably, on the interests and expertise of the author. By the nature of the book, though, shortcuts are inevitable and lead to predictable quan-daries. In spite of helpful margin notes, on many occasions it would be impossible for a novice to figure out whether an argument is new or follows from something that has already been established. Similarly, Fox sometimes fails to successfully convey subtler points. For instance, I do not think he has managed to put his finger on what exactly is counterintuitive about David Bohm’s version of the Einstein-Podolsky-Rosen paradox. The book also contains oddities ranging from simple typos to inaccuracies such as a supposed description of the magneto-optical trap (MOT) that actually describes something halfway between a MOT and a magnetic trap. Yet such questionable items are by no means unusual for a textbook.
Given the book’s broad coverage, instructors need to be selective. Woe to the student who is supposed to absorb all of the material in a semester. Fortunately, there is ample material to choose from, and one cannot go too wrong picking from Fox’s book. Instructors do not have to be experts in quantum optics to put together a good course. However, they probably need some experience in modern optics or atomic, molecular, and optical physics, lest sorting out the more impressionistic arguments in the book prove to be a tough outing.
To run a class, you need a slot in the curriculum, students, and an instructor; a text would be good. Today’s quantum optics can make a much more interesting topical and engaging undergraduate course than most traditional areas of physics. Attracting students should not be a problem. The unique virtue and the main shortfall of Quantum Optics are one and the same—good coverage of quantum optics on a semi-quantitative level. You may want an instructor with prior exposure to the subject matter, to make sure a coherent message goes out. But that decision still leaves a broad choice of faculty specialties. The way I see it, a genuinely interesting experiment in undergraduate education could be put together on the basis of Fox’s textbook.
