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**Introduction to quantum optics. From the semi-classical approach to quantized light.**
*(English)*
Zbl 1208.81001

Cambridge: Cambridge University Press (ISBN 978-0-521-55112-0/hbk; 978-0-511-78453-8/ebook). xxix, 665 p. (2010).

This is a fundamental textbook which aims to introduce quantum optics and (inter alia), nonlinear optics, at several different levels of the complexity.

In the first part, the standard semiclassical description is introduced, based on the use of classical Maxwell’s equations for the electromagnetic field, and nonrelativistic quantum mechanics for the description of material degrees of freedom (atoms) interacting with the electromagnetic field. This type of the description is based on what is called equations of the Maxwell-Bloch type (the Bloch equations for atomic density matrix being used for the description of the atomic subsystem of the coupled field-matter system).

The second part of the book provides the description of the underlying physics at a more sophisticated level, based on the full quantization of the electromagnetic field interacting with the quantum matter.

The third part of the book demonstrates how the particular type of the description should be chosen for sundry physical system. The physical problems considered in detail in the book, in the framework of the semi-classical and full quantum formalisms (whichever is most relevant for the given problem), comprise lasers, laser-assisted manipulations of atoms (including the important topics of laser cooling, control of atomic Bose-Einstein condensates by means of laser beams, and the design of atom lasers, i.e., settings capable to generate coherent beams of quantum matter, rather than beams of coherent light generated by the photonic lasers), entanglement of light (with applications to quantum information), nonlinear spectroscopy and other applications of nonlinear optics, cavity quantum electrodynamics, quantum squeezing of light, parametric amplification of light, and a number of other topics. The book consists of regular chapters, that present the basic material, and “complements”, that explain various more sophisticated problems. The book is intended to experienced undergraduate students and beginning graduate students, as well as to a broader readership of scientists working in various fields of fundamental and applied physics.

In the first part, the standard semiclassical description is introduced, based on the use of classical Maxwell’s equations for the electromagnetic field, and nonrelativistic quantum mechanics for the description of material degrees of freedom (atoms) interacting with the electromagnetic field. This type of the description is based on what is called equations of the Maxwell-Bloch type (the Bloch equations for atomic density matrix being used for the description of the atomic subsystem of the coupled field-matter system).

The second part of the book provides the description of the underlying physics at a more sophisticated level, based on the full quantization of the electromagnetic field interacting with the quantum matter.

The third part of the book demonstrates how the particular type of the description should be chosen for sundry physical system. The physical problems considered in detail in the book, in the framework of the semi-classical and full quantum formalisms (whichever is most relevant for the given problem), comprise lasers, laser-assisted manipulations of atoms (including the important topics of laser cooling, control of atomic Bose-Einstein condensates by means of laser beams, and the design of atom lasers, i.e., settings capable to generate coherent beams of quantum matter, rather than beams of coherent light generated by the photonic lasers), entanglement of light (with applications to quantum information), nonlinear spectroscopy and other applications of nonlinear optics, cavity quantum electrodynamics, quantum squeezing of light, parametric amplification of light, and a number of other topics. The book consists of regular chapters, that present the basic material, and “complements”, that explain various more sophisticated problems. The book is intended to experienced undergraduate students and beginning graduate students, as well as to a broader readership of scientists working in various fields of fundamental and applied physics.

Reviewer: Boris A. Malomed (Tel Aviv)

### MSC:

81-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to quantum theory |

78-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to optics and electromagnetic theory |

78A60 | Lasers, masers, optical bistability, nonlinear optics |

81V80 | Quantum optics |