Mathematical Methods of Quantum Optics
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 out...
| Κύριος συγγραφέας: | |
|---|---|
| Συγγραφή απο Οργανισμό/Αρχή: | |
| Μορφή: | Ηλεκτρονική πηγή Ηλ. βιβλίο |
| Γλώσσα: | English |
| Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg : Imprint: Springer,
2001.
|
| Έκδοση: | 1st ed. 2001. |
| Σειρά: | Springer Series in Optical Sciences,
79 |
| Θέματα: | |
| Διαθέσιμο Online: | Full Text via HEAL-Link |
Πίνακας περιεχομένων:
- 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 Dipole Interaction
- 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.
