Puri Mathematical Methods of Quantum Optics

2001
ISBN: 978-3-540-44953-9
Verlag: Springer
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 79, 289 Seiten, eBook

Reihe: Springer Series in Optical Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Puri, Ravinder R.

Inhaltsverzeichnis

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.