A group-theoretical approach to quantum optics : models of atom-field interactions /
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| Author / Creator: | Klimov, Andrei B. |
|---|---|
| Imprint: | Weinheim : Wiley-VCH, c2009. |
| Description: | ix, 322 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7730082 |
Table of Contents:
- Preface
- 1. Atomic Kinematics
- 1.1. Kinematics of an Atom with Two Energy Levels
- 1.2. Dicke States
- 1.3. Atomic Coherent States
- 1.4. Squeezed Atomic States
- 1.5. Atoms with n > 2 Energy Levels
- 1.5.1. Systems with n Energy Levels
- 1.5.2. Systems with Three Energy Levels
- 1.6. Problems
- 2. Atomic Dynamics
- 2.1. Spin in a Constant Magnetic Field
- 2.2. A Two-level Atom in a Linearly Polarized Field
- 2.2.1. The Rotating Wave Approximation
- 2.3. A Two-level Atom in a Circularly Polarized Field
- 2.4. Evolution of the Bloch Vector
- 2.5. Dynamics of the Two-level Atom without the RWA
- 2.6. Collective Atomic Systems
- 2.7. Atomic System in a Field of a Single Pulse
- 2.8. Problems
- 3. Quantized Electromagnetic Field
- 3.1. Quantization of the Electromagnetic Field
- 3.2. Coherent States
- 3.3. Properties of the Coherent States
- 3.4. Displacement Operator
- 3.5. Squeezed States
- 3.6. Thermal States
- 3.7. Phase Operator
- 3.8. Regularized Phase Operator
- 3.9. Phase Distribution
- 3.10. Problems
- 4. Field Dynamics
- 4.1. Evolution of a Field with Classical Pumping
- 4.2. Linear Parametric Amplifier
- 4.3. Evolution in the Kerr Medium
- 4.4. Second Harmonic Generation in the Dispersive Limit
- 4.5. Raman Dispersion
- 4.6. Problems
- 5. The Jaynes-Cummings Model
- 5.1. The Interaction Hamiltonian
- 5.2. The Spectrum and Wave Functions
- 5.3. Evolution Operator
- 5.4. The Classical Field Limit
- 5.5. Collapses and Revivals
- 5.5.1. The Dispersive Limit
- 5.5.2. Exact Resonance
- 5.6. The JCM with an Initial Thermal Field
- 5.7. Trapping States
- 5.8. Factorization of the Wave Function
- 5.9. Evolution I n Field Phase Space
- 5.10. The JCM without RWA
- 5.10.1. Diagonalization of the Hamiltonian
- 5.10.2. Atomic Inversion
- 5.10.3. Classical Field Limit
- 5.11. Problems
- 6. Collective Interactions
- 6.1. The Dicke Model (Exactly Solvable Examples)
- 6.2. The Dicke Model (Symmetry Properties)
- 6.3. The Dicke Model (Symmetric Case)
- 6.4. The Zeroth-Order Approximation
- 6.4.1. The Weak Field Case
- 6.4.2. The Strong Field Case
- 6.5. Perturbation Theory
- 6.6. Revivals of the First and Second Orders
- 6.6.1. Revivals of the Second Order
- 6.7. Atom-Field Dynamics for Different Initial Conditions
- 6.7.1. Initial Number States
- 6.7.2. Coherent and Thermal Fields
- 6.8. Three-Level Atoms Interacting with Two Quantum Field Modes
- 6.9. Problems
- 7. Atomic Systems in a Strong Quantum Field
- 7.1. Dicke Model in a Strong Field
- 7.2. Factorization of the Wave Function
- 7.3. Evolution in Phase Space
- 7.4. Dicke Model in the Presence of the Kerr Medium
- 7.5. Generation of the Field Squeezed States
- 7.6. Coherence Transfer Between Atoms and Field
- 7.7. Resonant Fluorescence Spectrum
- 7.8. Atomic Systems with n Energy Levels
- 7.8.1. Cascade Configuration ¿
- 7.8.2. A-Type Configuration
- 7.8.3. V-Type Configuration
- 7.9. Dicke Model in the Dispersive Limit
- 7.10. Two-Photon Dicke Model
- 7.11. Effective Transitions in Three-Level Atoms with A Configuration
- 7.12. N-Level Atoms of Cascade Configuration
- 7.13. Problems
- 8. Quantum Systems Beyond the Rotating Wave Approximation
- 8.1. Kinematic and Dynamic Resonances in Quantum Systems
- 8.2. Kinematic Resonances: Generic-Atom Field Interactions
- 8.3. Dynamic Resonances
- 8.3.1. Atom-Quantized Field Interaction
- 8.3.2. Atom-Classical Field Interaction
- 8.3.3. Interaction of Atoms with the Quantum Field in the Presence of Classical Fields
- 8.4. Dynamics of Slow and Fast Interacting Subsystems
- 8.4.1. Effective Field Dynamics
- 8.4.2. Effective Atomic Dynamics
- 8.5. Problems
- 9. Models with Dissipation
- 9.1. Dissipation and Pumping of the Quantum Field
- 9.2. Dicke Model with Dissipation and Pumping (Dispersive Limit)
- 9.3. Dicke Model with Dissipation (Resonant Case)
- 9.3.1. Initial Field Number State
- 9.3.2. Initial Field Coherent State
- 9.3.3. Factorized Dynamics
- 9.4. Strong Dissipation
- 9.4.1. Field-Field Interaction
- 9.4.2. Atom-Field Interaction
- 9.5. Problems
- 10. Quasi-distributions in Quantum Optics
- 10.1. Quantization and Quasi-distributions
- 10.1.1. Weyl Quantization Method
- 10.1.2. Moyal-Stratonovich-Weyl Quantization
- 10.1.3. Ordering Problem in L(H)
- 10.1.4. Star Product
- 10.1.5. Phase-Space Representation and Quantum-Classical Correspondence
- 10.2. Atomic Quasi-distributions
- 10.2.1. P Function
- 10.2.2. Q Function
- 10.2.3. Stratonovich-Weyl Distribution
- 10.2.4. s-Ordered Distributions
- 10.2.5. Star Product
- 10.2.6. Evolution Equations
- 10.2.7. Large Representation Dimensions (Semiclassical Limit)
- 10.3. Field Quasi-distributions
- 10.3.1. P Function
- 10.3.2. Q Function
- 10.3.3. Wigner Function
- 10.3.4. s-Ordered Distributions
- 10.4. Miscellaneous Applications
- 10.4.1. Kerr Hamiltonian
- 10.4.2. The Dicke Hamiltonian
- 10.5. Problems
- 11. Appendices
- 11.1. Lie Groups and Lie Algebras
- 11.1.1. Groups: Basic Concepts
- 11.1.2. Group Representations
- 11.1.3. Lie Algebras
- 11.1.4. Examples
- 11.2. Coherent States
- 11.2.1. Examples
- 11.3. Linear Systems
- 11.3.1. Diagonalization of the Time-independent Hamiltonian
- 11.3.2. Evolution Operator
- 11.3.3. Reference Formulas
- 11.4. Lie Transformation Method
- 11.5. Wigner d Function
- 11.6. Irreducible Tensor Operators
- References
- Index
