This book deals with theoretical methods in quantum optics. It is the first treatment of its kind in the field. It will appeal to researchers and advanced students.

Klappentext

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.

Inhalt

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 Wave-Particle Duality.- 1.8 Measurement Postulate and Paradoxes of Quantum Theory.- 1.8.1 The Measurement Problem.- 1.8.2 Schrödinger's Cat Paradox.- 1.8.3 EPR Paradox.- 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.- 2.3.1 Harmonic Oscillator Algebra.- 2.3.2 The SU(2) Algebra.- 2.3.3 The SU(1,1) Algebra.- 2.3.4 The SU(m) Algebra.- 2.3.5 The SU(m, n) Algebra.- 2.4 Disentangling an Exponential.- 2.4.1 The Harmonic Oscillator Algebra.- 2.4.2 The SU(2) Algebra.- 2.4.3 SU(1,1) Algebra.- 2.5 Time-Ordered Exponential Integral.- 2.5.1 Harmonic Oscillator Algebra.- 2.5.2 SU (2) Algebra.- 2.5.3 The SU(1,1) Algebra.- 3. Representations of Some Lie Algebras.- 3.1 Representation by Eigenvectors and Group Parameters.- 3.1.1 Bases Constituted by Eigenvectors.- 3.1.2 Bases Labeled by Group Parameters.- 3.2 Representations of Harmonic Oscillator Algebra.- 3.2.1 Orthonormal Bases.- 3.2.2 Minimum Uncertainty Coherent States.- 3.3 Representations of SU(2).- 3.3.1 Orthonormal Representation.- 3.3.2 Minimum Uncertainty Coherent States.- 3.4 Representations of SU(1, 1).- 3.4.1 Orthonormal Bases.- 3.4.2 Minimum Uncertainty Coherent States.- 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.- 4.4.1 Non-classical States of Electromagnetic Field.- 4.4.2 Non-classical States of Spin-1/2s.- 5. Theory of Stochastic Processes.- 5.1 Probability Distributions.- 5.2 Markov Processes.- 5.3 Detailed Balance.- 5.4 Liouville and Fokker-Planck Equations.- 5.4.1 Liouville Equation.- 5.4.2 The Fokker-Planck Equation.- 5.5 Stochastic Differential Equations.- 5.6 Linear Equations with Additive Noise.- 5.7 Linear Equations with Multiplicative Noise.- 5.7.1 Univariate Linear Multiplicative Stochastic Differential Equations.- 5.7.2 Multivariate Linear Multiplicative Stochastic Differential Equations.- 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.- 6.3.1 First-Order Correlation Function.- 6.3.2 Second-Order Correlation Function.- 6.3.3 Higher-Order Correlations.- 6.3.4 Stable and Chaotic Fields.- 6.4 Statistical Properties of Quantized Field.- 6.4.1 First-Order Correlation.- 6.4.2 Second-Order Correlation.- 6.4.3 Quantized Coherent and Thermal Fields.- 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.- 8.4.1 Thermal Reservoir.- 8.4.2 Squeezed Reservoir.- 8.4.3 Reservoir of the Electromagnetic Field.- 8.5 Master Equation for a Harmonic Oscillator.- 8.6 Master Equation for Two-Level Atoms.- 8.6.1 Two-Level Atom in a Monochromatic Field.- 8.6.2 Collisional Damping.- 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.- 10.4.1 Two-Term Recursion Relations.- 10.4.2 Three-Term Recursion Relations.- 11. Two-Level and Three-Level Hamiltonian Systems.- 11.1 Exactly Solvable Two-Level Systems.- 11.1.1 Time-Independent Detuning and Coupling.- 11.1.2 On-Resonant Real Time-Dependent Coupling.- 11.1.3 Fluctuating Coupling.- 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.- 12.1.1 Time-Dependent Evolution Operator Reducible to SU(2).- 12.1.2 Time-Independent Evolution Operator.- 12.1.3 Nonlinear Response in a Bichromatic 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.- 13.1.1 Averages and Variances of the Cavity Field Operators.- 13.1.2 Density Matrix.- 13.2 Field Interacting with a Two-Photon Reservoir.- 13.2.1 Two-Photon Absorption.- 13.2.2 Two-Photon Generation and Absorption.- 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.- 14.2.1 Single Two-Level Atom.- 14.3 Response to an External Field.- 14.3.1 Linear Response to a Monochromatic Field.- 14.3.2 Nonlinear Response to a Bichromatic Field.- 14.4 The Micromaser.- 14.4.1 Density Operator of the Field.- 14.4.2 Two-Level Atomic Micromaser.- 14.4.3 Atomic Statistics.- Appendices.- A. Some Mathematical Formulae.- B. Hypergeometric Equation.- C. Solution of Twoand Three-Dimensional Linear Equations.- D. Roots of a Polynomial.- References.