Mathematical Methods of Quantum Optics [Paperback]

Starting from first principles, this reference treats the theoretical aspects of quantum optics. It develops a unified approach for determining the dynamics of a two-level and three-level atom in combinations of quantized field under certain conditions.

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.1. Basic Quantum Mechanics.- 1.1 Postulates of Quantum Mechanics.- 1.1.1 Postulate 1.- 1.1.2 Postulate 2.- 1.1.3 Postulate 3.- 1.1.4 Postulate 4.- 1.1.5 Postulate 5.- 1.2 Geometric Phase.- 1.2.1 Geometric Phase of a Harmonic Oscillator.- 1.2.2 Geometric Phase of a Two-Level System.- 1.2.3 Geometric Phase in Adiabatic Evolution.- 1.3 Time-Dependent Approximation Method.- 1.4 Quantum Mechanics of a Composite System.- 1.5 Quantum Mechanics of a Subsystem and Density Operator.- 1.6 Systems of One and Two Spin-1/2s.- 1.7 WaveParticle Duality.- 1.8 Measurement Postulate and Paradoxes of Quantum Theory.- 1.8.1 The Measurement Problem.- 1.8.2 Schr?dingers Cat Paradox.- 1.8.3 EPR Paradox.- 1.9 Local Hidden Variables Theory.- 2. Algebra of the Exponential Operator.- 2.1 Parametric Dil%