基本説明
Contents: Theory of Stochastic Processes; The Electromagnetic Field; Model Atom-Field Interaction Hamiltonians; Continuous Representations of Some Lie Algebras; Quasiprobabilities and Non-classical States; and more.
Full Description
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.
Contents
1. Basic Quantum Mechanics.- 1.1 Postulates of Quantum Mechanics.- 1.2 Geometric Phase.- 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 Wave—Particle Duality.- 1.8 Measurement Postulate and Paradoxes of Quantum Theory.- 1.9 Local Hidden Variables Theory.- 2. Algebra of the Exponential Operator.- 2.1 Parametric Differentiation of the Exponential.- 2.2 Exponential of a Finite-Dimensional Operator.- 2.3 Lie Algebraic Similarity Transformations.- 2.4 Disentangling an Exponential.- 2.5 Time-Ordered Exponential Integral.- 3. Representations of Some Lie Algebras.- 3.1 Representation by Eigenvectors and Group Parameters.- 3.2 Representations of Harmonic Oscillator Algebra.- 3.3 Representations of SU(2).- 3.4 Representations of SU(1, 1).- 4. Quasiprobabilities and Non-classical States.- 4.1 Phase Space Distribution Functions.- 4.2 Phase Space Representation of Spins.- 4.3 Quasiprobabilitiy Distributions for Eigenvalues of Spin Components.- 4.4 Classical and Non-classical States.- 5. Theory of Stochastic Processes.- 5.1 Probability Distributions.- 5.2 Markov Processes.- 5.3 Detailed Balance.- 5.4 Liouville and Fokker—Planck Equations.- 5.5 Stochastic Differential Equations.- 5.6 Linear Equations with Additive Noise.- 5.7 Linear Equations with Multiplicative Noise.- 5.8 The Poisson Process.- 5.9 Stochastic Differential Equation Driven by Random Telegraph Noise.- 6. The Electromagnetic Field.- 6.1 Free Classical Field.- 6.2 Field Quantization.- 6.3 Statistical Properties of Classical Field.- 6.4 Statistical Properties of Quantized Field.- 6.5 Homodvned Detection.- 6.6 Spectrum.- 7. Atom-Field Interaction Hamiltonians.- 7.1 DipoleInteraction.- 7.2 Rotating Wave and Resonance Approximations.- 7.3 Two-Level Atom.- 7.4 Three-Level Atom.- 7.5 Effective Two-Level Atom.- 7.6 Multi-channel Models.- 7.7 Parametric Processes.- 7.8 Cavity QED.- 7.9 Moving Atom.- 8. Quantum Theory of Damping.- 8.1 The Master Equation.- 8.2 Solving a Master Equation.- 8.3 Multi-Time Average of System Operators.- 8.4 Bath of Harmonic Oscillators.- 8.5 Master Equation for a Harmonic Oscillator.- 8.6 Master Equation for Two-Level Atoms.- 8.7 aster Equation for a Three-Level Atom.- 8.8 Master Equation for Field Interacting with a Reservoir of Atoms.- 9. Linear and Nonlinear Response of a System in an External Field.- 9.1 Steady State of a System in an External Field.- 9.2 Optical Susceptibility.- 9.3 Rate of Absorption of Energy.- 9.4 Response in a Fluctuating Field.- 10. Solution of Linear Equations: Method of Eigenvector Expansion.- 10.1 Eigenvalues and Eigenvectors.- 10.2 Generalized Eigenvalues and Eigenvectors.- 10.3 Solution of Two-Term Difference-Differential Equation.- 10.4 Exactly Solvable Two- and Three-Term Recursion Relations.- 11. Two-Level and Three-Level Hamiltonian Systems.- 11.1 Exactly Solvable Two-Level Systems.- 11.2 N Two-Level Atoms in a Quantized Field.- 11.3 Exactly Solvable Three-Level Systems.- 11.4 Effective Two-Level Approximation.- 12. Dissipative Atomic Systems.- 12.1 Two-Level Atom in a Quasimonochromatic Field.- 12.2 N Two-Level Atoms in a Monochromatic Field.- 12.3 Two-Level Atoms in a Fluctuating Field.- 12.4 Driven Three-Level Atom.- 13. Dissipative Field Dynamics.- 13.1 Down-Conversion in a Damped Cavity.- 13.2 Field Interacting with a Two-Photon Reservoir.- 13.3 Reservoir in the Lambda Configuration.- 14. Dissipative Cavity QED.- 14.1 Two-Level Atoms in a Single-Mode Cavity.- 14.2 Strong Atom—Field Coupling.- 14.3 Response to an External Field.- 14.4 The Micromaser.- Appendices.- A. Some Mathematical Formulae.- B. Hypergeometric Equation.- C. Solution of Twoand Three-Dimensional Linear Equations.- D. Roots of a Polynomial.- References.
