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The International Atlas of Mars Exploration: The First Five Decades, Vol. 1, 1953 to 2003

form the basis of many modern applications of quantum mechanics such as quantum computing, quantum metrology and photonics. The book under review, written by one of the leading figures in the field, presents the theoretical foundations of all these applications and bridges the gap between advanced textbooks on quantum mechanics and the current research frontier. The reader is presumed to have a good understanding of classical electrodynamics, quantum mechanics and statistical physics at the graduate level. The focus of the book is on the theory of quantum optics. Experiments are mentioned throughout the entire text but only discussed briefly. The style of writing is dense. Not much space is spent on motivation, and basic concepts such as Bell states are assumed to be known. Instead, the reader is immersed in the theoretical intricacies of quantum optical problems. The amount of material the author covers is breathtaking. After an introduction to the description of quantised electromagnetic fields and non-classical radiation fields, the author discusses squeezed states, quantum entanglement, optical interferometry with single photons and non-classical light, polarisation and orbital angular momentum of quantum fields. Then, light–matter interaction and open quantum systems are analysed. This paves the way for further topics such as the amplification and attenuation of quantum fields, quantum coherence, cavity quantum electrodynamics, coherent control of optical properties, slow light and quantum optical effects in nano-mechanical systems. There is hardly any subject in modern quantum optics that is not covered in this book (only semiconductor quantum optics comes to mind). Many references to original theoretical and experimental work are given, and it is amazing to see to how many different areas the author has contributed himself. The author tries hard to make the complex theoretical considerations and the accompanying (at times lengthy) mathematics transparent. His language is clear and precise, and the text is enriched with many figures and graphs of good quality. Each chapter ends with a set of exercises, and the book contains hundreds of references to research papers. Only the very incomplete index is disappointing. The target group of this book are clearly graduate students who want to start doing research in theoretical quantum optics. Working through this book will be the ideal preparation to start with a research project in the field. For experimental physicists who hope to get a better theoretical understanding of their laboratory work, this book will definitely be a challenge (though certainly not of the kind that cannot be mastered). I recommend it to anyone with a serious interest in one of the most fascinating branches of modern physics.