Atoms in Intense Laser Fields, C. J. Joachain, N. J. Kylstra, and R. M. Potvliege, Cambridge U. Press, New York, 2012. $135.00 (568 pp.). ISBN 978-0-521-79301-8

Research on intense laser interactions in atoms owes its growth primarily to three breakthroughs: the development of short-pulse, high-energy lasers; the discovery of extreme nonlinear ionization; and the discovery of the vacuum ultraviolet (VUV) light production that occurs when the magnitude of an optical field approaches that of the fields that bind electrons in atoms. The past quarter-century of research has led to new VUV light sources and to attosecond science, which explores the time scale of correlated electronic motion in atoms and molecules. Scientists now understand much of the underlying physics responsible for the two phenomena related to VUV light production—high-harmonic generation (HHG) and above-threshold ionization (ATI). As a result, interest has turned to light-source applications of HHG; attosecond pulses; and strong-field studies in atoms, molecules, solids, and plasmas.

*Atoms in Intense Laser Fields* explains the underlying physics and theoretical techniques needed to advance the work. Authors Charles Joachain, Niels Kylstra, and Robert Potvliege have made numerous contributions to the theory of atoms and strong fields and have collaborated in the past. Joachain, in particular, has written several other textbooks and monographs on quantum mechanics and electron–atom collisions.

Previous books on the topic have not covered the history and status of strong-field atomic theory so well and so completely. *Theoretical Femtosecond Physics: Atoms and Molecules in Strong Laser Fields* by Frank Grossmann (Springer, 2008; reviewed in *Physics Today*, November 2009, page 54) comes closest, but it is written at an advanced-undergraduate to beginning-graduate level, so it leaves out many of the more specialized methods used to carry out calculations. Other books on the subject are several years old, so this updated work is needed.

*Atoms in Intense Laser Fields* is a well-organized text. Part 1 summarizes the field in two chapters, introducing the history and importance of the subject with simple concepts and basic equations. The first chapter describes the experiments; the second chapter, on theory, lays out the elementary framework of HHG and ATI. The core of the book is part 2, chapters 3–7. Here the authors develop the concepts needed to perform calculations and interpret observations of strong-field phenomena. The chapters cover methods for solving Schrödinger’s equation for an atom in a strong laser field. Examples of standard tools for that task include Crank–Nicolson and split-operator methods, quantum defect theory, and Floquet theory. The authors describe and develop the major theoretical approaches for strong-field physics, laser–atom physics, and electron–atom collisions, covering theories introduced by Farhad Faisal, Maciej Lewenstein, Howard Reiss, and others. This book does not assume that the reader is a student of advanced theory, but it goes well beyond the usual elementary discussions of the single-electron systems hydrogen and H_{2}^{+}.

Whereas part 1 developed a more intuitive and qualitative understanding of strong-field concepts in atomic physics, part 2 is more formal and mathematical. Chapter 4, on Floquet theory, describes many aspects of dressed states and helps to establish a basis for comparing different computational approaches. The dressed-state approach is quite useful for situations in which the laser wavelength and intensity are both slowly varying, but it is less useful for subcycle phenomena that have dominated recent work in attosecond science. In chapter 5 the authors describe methods to integrate the time-dependent Schrödinger equation and compare direct integration to Floquet results in several examples. They also cover the highly successful single-active-electron model and provide a good discussion of its strengths and weaknesses.

Part 2 concludes with a pair of chapters that discuss the low-frequency and high-frequency regimes in strong-field photoionization. Low-frequency phenomena include above-threshold ionization, in which the energy scale is not set by the photon energy but rather by the ponderomotive or quiver energy of electrons. Particularly noteworthy is the high-frequency, high-intensity regime, which has led to predictions of such exotic phenomena as high-frequency stabilization. Recent developments that use few-cycle pulses could have been discussed more in this section, particularly since the strong-field community has largely embraced few-cycle pulses and subcycle attosecond physics in the past decade.

Part 3, chapters 8–10, applies the results of parts 1 and 2 to three characteristic strong-field phenomena: multiphoton ionization, HHG, and laser-assisted electron scattering. Those chapters also include full discussions of attosecond pulses, multiphoton-induced multiple ionization, and the state of theoretical understanding in those areas.

Overall, *Atoms in Intense Laser Fields* is an excellent introduction to the phenomena and methods of strong-field, laser–atom physics. Despite its few shortcomings, the book is a solid exposition of the central discoveries and theoretical concepts that form the foundation of the field.