Bose–Einstein Condensation , Lev Pitaevskii and Sandro Stringari Oxford U. Press, New York, 2003. $119.50 (382 pp.). ISBN 0-19-850719-4
In 1938, Pyotr Kapitza and, independently, John Allen and Donald Misener discovered superfluidity in liquid helium below the lambda point. Soon thereafter, Fritz London suggested that this extraordinary phenomenon was due to the onset, at the lambda point, of the peculiar “condensation” effect that Albert Einstein predicted following Satyendra N. Bose’s work on photons. The effect, now known as Bose–Einstein condensation (BEC), occurs in a system of bosons whose total number is conserved.
With the exception of the early work of Lev Landau, almost all subsequent attempts to understand the behavior of superfluid helium have been based on London’s hypothesis. Helium is a dense and strongly interacting system; thus, despite heroic efforts, it has been very difficult to observe the onset of BEC directly. Moreover, theoretical attempts to explain the phenomena have been hampered by the lack of any obvious small parameter. Thus researchers have developed various, more or less phenomenological approaches to help understand the behavior of superfluid helium. In 1961, Lev Pitaevskii and, independently, Eugene Gross introduced the concept of an “order parameter” describing the BEC phase; they proposed to describe the evolution of that parameter by the equation that now bears their names: the Gross–Pitaevskii equation. They recognized, however, that the equation’s applicability to real liquid helium was only qualitative.
In 1995, with the help of spectacular advances in laser cooling and other techniques, researchers achieved BEC in systems—namely, dilute monatomic alkali gases—that are almost the opposite of liquid helium in many relevant respects. Because the gas is dilute and its interactions are short range, these systems are characterized under most conditions by a small dimensionless parameter—the product of the number density and the cube of the S-wave scattering length. Researchers immediately recognized and rapidly confirmed by experiment that the Gross–Pitaevskii equation excellently describes much, though not all, of the behavior of the dilute alkali gases. In the past nine years, the number of published papers, experimental and theoretical, on these systems must run to several thousand.
Bose–Einstein Condensation by Pitaevskii and coauthor Sandro Stringari, who is another major contributor to the recent theoretical literature, reflects the brief history just sketched. The first part of the book, about a third of it, reviews some of the fundamental concepts that evolved to explain the behavior of helium. The remainder is devoted specifically to the dilute alkali gases. In this second part, and also in the chapter devoted explicitly to helium at the end of the first part, considerable emphasis is placed on the quantitative comparison of theory with existing experimental data.
The most obvious comparison of the book is with the earlier Bose–Einstein Condensation in Dilute Gases (Cambridge U. Press, 2001) by Christopher Pethick and Henrik Smith, whose content overlaps Pitaevskii and Stringari’s book substantially. Pethick and Smith’s book is written more or less explicitly as an introductory text for graduate students; Pitaevskii and Stringari’s book, on the other hand, is more a comprehensive review of some important areas in which theory, either long-standing or more recently developed, can be compared in detail with recent experiments. In fact, as Pitaevskii and Stringari comment in the introduction, their book is, to a large extent, an expansion of the 1999 article they published with Franco Dalfovo and Stefano Giorgini in Reviews of Modern Physics.
Bose–Einstein Condensation and Bose–Einstein Condensation in Dilute Gases both cover the basic theory at the level of the Gross–Pitaevskii and Bogoliubov–de Gennes equations. But Pitaevskii and Stringari’s book places less emphasis on what one might call the “atomic physics” aspects of dilute alkali gases. On the other hand, some facets of the many-body behavior, such as collective oscillations, are treated in considerable detail. For example, chapter 17 includes a substantial discussion of the behavior of collective oscillations in quasi one-dimensional traps. Other major topics covered include thermodynamic behavior, rotational properties, superfluidity, interference, Joseph-son-type effects, and the basics of the behavior in optical lattices.
Obvious omissions include experiments involving multiple hyperfine species (except for a brief discussion at the end of chapter 12) and the kinetics of BEC. A brief final chapter introduces dilute degenerate Fermi gases and the possibility of Cooper pairing, a subject that has mushroomed since the book was published.
Overall, Bose–Einstein Condensation is clearly written and well focused. It should be accessible to anyone who has had a beginning graduate-level course in quantum mechanics. I would have done things differently in a few places. In particular, I think the discussions of superfluidity in chapters 6 and 14 are less clear than they might be because, among other things, the authors never explicitly distinguish between two different manifestations of superfluidity. Those manifestations are the equilibrium phenomenon sometimes known as nonclassical rotational inertia (or the Hess–Fairbank effect), which is what is mostly discussed in chapter 14, and the nonequilibrium phenomenon of metastable supercurrents. I thus fear some readers may get the impression that the well-known Landau criterion applies to both phenomena rather than only to the latter. Also, in chapters 12 and 17, Pitaevskii and Stringari mention so many different cases in the very detailed discussions of collective excitations that I sometimes found it difficult to see the forest for the trees.
Despite these minor reservations, I believe Bose–Einstein Condensation is a most welcome and timely addition to the literature and will nicely complement Pethick and Smith’s text.
