Mathematical Methods of Quantum Optics
By: by Ravinder Rupchand Puri
Series: Springer Series in Optical Sciences, 0342-4111 -- 79; Springer series in optical sciences -- 79.
Publisher: Springer Berlin Heidelberg; Imprint: Springer
Published: 2001
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 289
ISBN-13: 9783540449539
Description: This book provides an accessible introduction to the mathematical methods of quantum optics. Starting from first principles, it reveals how a given system of atoms and a field is mathematically modelled. The method of eigenfunction expansion and the Lie algebraic method for solving equations are outlined. Analytically exactly solvable classes of equations are identified. The text also discusses consequences of Lie algebraic properties of Hamiltonians, such as the classification of their states as coherent, classical or non-classical based on the generalized uncertainty relation and the concept of quasiprobability distributions. A unified approach is developed for determining the dynamics of a two-level and a three-level atom interacting with combinations of quantized fields under certain conditions. Simple methods for solving a variety of linear and nonlinear dissipative master equations are given. The book will be valuable to newcomers to the field and to experimentalists in quantum optics.
Table of contents: title: 1. Basic Quantum Mechanics; title: 2. Theory of Stochastic Processes; title: 3. The Electromagnetic Field; title: 4. Model Atom-Field Interaction Hamiltonians; title: 5. Quantum Theory of Dissipation; title: 6. Linear and Nonlinear Response of a System to External Field; title: 7. Solution of Linear First-Order Equations with Constant Coefficients; title: 8. Solution of Linear First-Order Equations: Lie Algebraic Method; title: 9. Continuous Representations of Some Lie Algebras; title: 10. Quasiprobabilities and Non-classical States; title: 11. A Class of Exactly Solvable Two-Level and Three-Level Hamiltonian Systems; title: 12. N Two-Level and Three-Level Hamiltonian Systems; title: 13. Dissipative N Two-Level and Three-Level Atomic Systems in Quantized Fields; title: 14. Nonlinear Optical Processes.