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Mathematical Methods of Quantum Optics

  • Book
  • © 2001

Overview

Authors:
  1. Ravinder Rupchand Puri

    1. Theoretical Physics Division, Central Complex, Bhabha Atomic Research Centre, Mumbai, India

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  • The first book to present the mathematical structure of quantum optics in an organized manner.
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Optical Sciences (SSOS, volume 79)

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Table of contents (14 chapters)

  1. Front Matter

    Pages I-XIII
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  2. Basic Quantum Mechanics

    • Ravinder Rupchand Puri
    Pages 1-36

  3. Algebra of the Exponential Operator

    • Ravinder Rupchand Puri
    Pages 37-53

  4. Representations of Some Lie Algebras

    • Ravinder Rupchand Puri
    Pages 55-79

  5. Quasiprobabilities and Non-classical States

    • Ravinder Rupchand Puri
    Pages 81-97

  6. Theory of Stochastic Processes

    • Ravinder Rupchand Puri
    Pages 99-117

  7. The Electromagnetic Field

    • Ravinder Rupchand Puri
    Pages 119-136

  8. Atom-Field Interaction Hamiltonians

    • Ravinder Rupchand Puri
    Pages 137-153

  9. Quantum Theory of Damping

    • Ravinder Rupchand Puri
    Pages 155-175

  10. Linear and Nonlinear Response of a System in an External Field

    • Ravinder Rupchand Puri
    Pages 177-183

  11. Solution of Linear Equations: Method of Eigenvector Expansion

    • Ravinder Rupchand Puri
    Pages 185-197

  12. Two-Level and Three-Level Hamiltonian Systems

    • Ravinder Rupchand Puri
    Pages 199-214

  13. Dissipative Atomic Systems

    • Ravinder Rupchand Puri
    Pages 215-238

  14. Dissipative Field Dynamics

    • Ravinder Rupchand Puri
    Pages 239-250

  15. Dissipative Cavity QED

    • Ravinder Rupchand Puri
    Pages 251-266

  16. Back Matter

    Pages 267-289
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Keywords

About this book

This book is intended to provide a much needed systematic exposition of the mathematical methods of quantum optics, something that is not found in existing books. It is primarily addressed to researchers who are new to the field. The emphasis, therefore, is on a simple and self-contained, yet concise, presentation. It provides a unified view of the concepts and the methods of quantum optics and aims to prepare a reader to handle specific situations. A number of formulae scattered throughout the scientific literature are also brought together in a natural manner. The broad plan of the book is to introduce first the basic physics and mathematical concepts, then to apply them to construct the model hamilto­ nians of the atom-field interaction and the master equation for an atom-field system interacting with the environment, and to analyze the equations so obtained. A brief description of the contents of the chapters is as follows.

Reviews

From the reviews of the first edition:

"This book provides an excellent introduction to the mathematical methods of quantum optics. It starts from the postulate of quantum mechanics, their mathematical consequences and paradoxes of quantum mechanics. Then, various SU algebras and representations of some Lie algebras are discussed. Then, stochastic processes, electromagnetic field quantization and atom-field interaction are presented. … This textbook can be recommended to teachers, postgraduate students and researchers as a book covering all the relevant mathematical and theoretical techniques of quantum optics." (Lubomír Skála, Zentralblatt MATH, Vol. 1041 (16), 2004)

"There are several good textbooks on quantum optics and there are also good textbooks on the mathematical theory of coherent states, which is a related area. This book covers the material in the middle and presents the mathematical methods used in quantum optics. It covers the mathematical formalism of quantum mechanics, coherent states and related group theory, stochastic processes, atom-field interactions, two- and three-level systems, dissipation, etc. The material is clearly presented and it is suitable for postgraduate students and researchers in the field." (Apostolos Vourdas, Mathematical Reviews, Issue 2002 j)

"The initial overview of quantum mechanics is quite useful because of its conciseness and I feel that postgraduate students would benefit particularly from this. … the question is whether this book adds sufficiently to this store of knowledge to be worth buying. Overall I think it does and I can certainly recommend quantum opticians ordering one for their institutional libraries. Those involved more with the theory on a daily basis may find it handy to have a copy in their office." (D. T. Pegg, The Physicist, Vol. 38 (5), 2001)

Authors and Affiliations

  • Theoretical Physics Division, Central Complex, Bhabha Atomic Research Centre, Mumbai, India

    Ravinder Rupchand Puri

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