Introduction to Quantum Optics 2nd Edition: 2012 Edition Introduction "Modern Fundamentals of Physics 41: Introduction to Quantum Optics (2nd Edition)" starts from the classic and quantum properties of the interaction between light and matter and the latest experimental and theoretical research results The system introduces the establishment and development of this new discipline (as opposed to classical optics), that is, quantum optics. The content consists of 8 chapters. The first three chapters are semi-classical and optical quantum theory of the interaction between light and medium. They are the preliminaries of the book. Chapters 4-7 are the main body of quantum optics, including laser oscillation, coherence of light, field correlation function representation, coherent state of light, P appearance, second-order correlation function of light field, grouping and anti-grouping, EPR paradox , Bell inequality, entangled state of light, squeezed state, resonance fluorescence, laser deflected atomic beam, etc. Chapter 8 is the dynamics of optical parameter down-conversion and its applications. Modern Foundations of Physics Series 41: Introduction to Quantum Optics (2nd edition) "can be read by undergraduates of physics and laser majors and postgraduates of related majors in colleges and universities, and can also be used as a reference for scientific researchers engaged in basic theoretical research and application.
Chapter 1 Classical and Quantum Theory of Interaction between Light and Nonlinear Media 1.1 Classical Theory of Nonlinear Interaction 1.1.1 Propagation of Electromagnetic Waves in Nonlinear Media 1.1.2 Symmetry of Polarization Tensor 1.2 Waves in Optics Wave interaction 1.2.1 Three-wave coupling 1.2.2 Four-wave coupling 1.3 Quantum theory of interaction between light and nonlinear media 1.4 Weak field perturbation method for solving SchrSdinger equation 1.5 Density matrix equation and its perturbation solution 1.5.1 Density matrix equation 1.5 .2 Solving the Density Matrix Equation by Perturbation 1.6 Quantization of Wave Field ψ (r, t) 1.7 Quantization of Electromagnetic Field 1.7.1 Mode Expansion of Electromagnetic Field 1.7.2 Quantization of Electromagnetic Field 1.7.3 Photon Number State (Fock State 1
1.8 Line Width and Energy Level Shift of Atomic Radiation 1.8.1. Single Atomic Radiation 1.8.2 N-Atom Radiation Appendix 1A (1.2.27) Analytical Solution Reference Chapter 2 Density Matrix Solution and Light of Two-Level System Pulse Propagation in Nonlinear Media 2.1 Vector Model of Two-Level Atomic Density Matrix 2.2 Bloch Equation and Its Solutions 2.3 Linear and Saturated Absorption 2.4 Optical Nutation and Free Induced Decay 2.5 Immersion Asymptotic 2.6 Area of Propagation of Light Pulse Theorem 2.7 Multifocal phenomenon of light pulse self-convergence 2.7.1 Quasi-steady state theory of light pulse self-convergence 2.7.2 Analysis of instability of light pulse self-convergence 2.7.3 Numerical calculation of light pulse self-convergence 2.8 ABCD theorem of beam propagation 2.8.1 A called GD theorem for paraxial beam transmission 2.8.2 Proof of the universal beam transmission ABCD theorem 2.8.3 Diffraction integral calculation of beam transmission 2.9 "Super light speed transmission" of light pulses
2.9.1 Propagation of terminal waves in gain-type anomalous dispersion media 2.9.2 Propagation of rectangular pulses in gain-type anomalous dispersion media 2.9.3 Propagation of Gauss optical pulses in gain-type anomalous dispersion media Appendix 2A (2.6.24) Derivation of the equation Appendix 2B (2.7.26) Analytical solution of the equation References Chapter 3 Atomic Conjugation States 3.1 Solutions to the Schrodinger Equation for Two-Level Atoms 3.2 Atomic Conjugation States 3.3 Cohen-Tannoudji's Conjugated Atoms 3.4 Atomic Parts Embellished states and their expansions References Chapter 4 Laser oscillation theory 4.1 Semi-classical theory of laser oscillation 4.1.1 No activated ion f or atom) Case 4.1.2 Linear polarization PαE
4.1.3 First-order approximation 4.1.4 Hole burning effect of gas laser and Lamb depression 4.1.5 Multi-mode oscillation 4.2 Full quantum theory of laser oscillation 4.3 Thermal library model and statistical distribution of laser output 4.3.1 Thermal library model 4.3.2 Langevin's equation for the interaction of the laser field with the thermal reservoir 4.3.3 Langevin's equation for the interaction of the atomic system with the thermal reservoir 4.3.4 Equation of the density matrix of the radiation field 4.3.5 Statistical distribution of the laser output 4.4 Reduction of the laser-pumped quantum noise 4.4. 1 Regular pumping 4.4.2 General pumping 4.5 Quantum mode theory of micro-laser 4.5.1 Steady-state solution of the main equation of the density matrix in the case of laser 4.5.2 Quantum mode theory of microcavity 4.5.3 Deviations between the cavity quantum mode main equation solution and the stepwise mode solution 4.6 Monoatomic and diatomic microlaser 4.6.1 Equations of interaction between diatomic and laser fields 4.6.2 Comparison of steady-state output of monoatomic and diatomic microlasers References Chapter 5 Coherent Statistical Properties of Radiation 5.1 x, Statistical Thermodynamics of Fi Balanced Radiation 5.2 Coherence of Light 5.2.1 Coherence Conditions 5.2.2 "Photon Self-Interference" and "Homomorphic Photon Interference"
5.3 Light detection 5.3.1 Ideal detector 5.3.2 Quantum transition 5.4 Field correlation function and field coherence 5.5 Coherent state 5.6 Expansion with coherent state 5.6.1 P representation of coherent state 5.6.2 Parameter down conversion in P representation Satisfied Fokker-Planck equation 5.7 Second-order correlation function of photons, grouping and anti-grouping effects, ghost interference and entangled states of particles 5.7.1 Second-order correlation measurement of light field distribution 5.7.2 Classical light field and non-linearity Classical light field 5.7.3 Analysis of second-order correlation function of atomic resonance fluorescence field 5.7.4 Two-photon "ghost state interference" and EPR paradox 5.7.5 Bell inequality and entangled states of particles 5.7.6 Geometric derivation that violates Bell inequality 5.8 Squeezed state light field 5.8.1 Restrictions imposed by optical quantum fluctuations on optical precision measurement 5.8.2 iE cross-compressed state 5.8.3 Amplitude squeezed state 5.9 Detection of non-classical light fields 5.9.1 Zero-beat detection technology of intensity difference 5.9.2 Zero-beat detection when detection efficiency η ≠ 1 5.10 Generation and amplification of compressed state light 5.10.1 Principles and experimental results of degenerate parametric amplification (or degenerate four-wave mixing) to generate compressed state light 5.10.2 Degenerate parameter amplification IJangevin Equation and Fokker-Planc Satisfied by Mixing with Degenerate Four Waves k equation 5.10.3 Solution of degenerate parametric amplified Fokker-Planck equation 5.10.4 Solution of degenerate four-wave mixed Fokker-Planck equation Appendix 5A Boson Operator Algebra Appendix 5B Minimum Uncertainty State Appendix 5C About (5.7 .59), (5.7.70) Proof References Chapter 6 Atom's Resonance Fluorescence and Absorption 6.1 Experimental Study on the Interaction of Two-level Atoms with Monochromatic Light Intensity 6.1.1 Two-level Atoms in Strong Light Resonance Fluorescence under Low Power 6.1.2 Atomic Absorption Lines under Strong Fields 6.1.3 Power Broadening and Saturation of Two-Level Atomic Absorption Spectrum 6.2 Theory of Resonance Fluorescence of Two-Level Atoms 6.2.1 Two-Level Atoms and Radiation Field interaction equation and its solution 6.2.2 Calculation of resonance fluorescence of two-level atom 6.3 Resonance fluorescence of atom in squeezed light field 6.3.1 Density matrix equation of atom in squeezed light field 6.3.2 Atom in squeezed state Resonance fluorescence spectrum in the light field 6.4 Resonance fluorescence spectrum of two-level atoms without taking the spin wave approximation 6.4.1 Mollow's resonance fluorescence theory and initial conditions for integration 6.4.2 Not used: RFS of RWA two-level atomic system Theory 6.4.3 Numerical calculation and discussion 6.5 QED with atomic cavity
6.5.1 Enhancement and suppression of spontaneous emission 6.5.2 JC model of single-mode field interaction with two-level atoms 6.5.3 Analytical solution of single-mode field interaction with two-level atoms with damping 6.5.4 About the new Experimental examination of classical theory 6.6 Transmission spectrum of a two-level atomic cavity 6.6.1 Calculation of the polarizability of atoms in a resonant cavity 6.6.2 Transmission spectrum of a two-level atomic cavity Reference Chapter 7 Laser Deflection Atomic beam 7.1 Laser deflected atomic beam 7.1.1 Early laser deflected atomic beam scheme 7.1.2 Laser force on atoms 7.1.3 Atomic diffusion in velocity space 7.2 Laser-cooled atoms and optical viscose 7.3 Laser polarization gradient cooled atoms 7.4 Optical Adhesive Temperature Measurement 7.5 Force of Electromagnetic Decay Wave Field on Atoms and Atomic Mirror 7.6 Selective Reflection Experiment of Atomic Mirror Facing Atomic Quantum State 7.7 Accurate Solution of Two-level Atom Reflection in Laser Decay Field 7.7.1 Two Energy Schrodinger's Equation and Solutions Satisfied by First-Order Atoms in the Laser Decay Field 7.7.2 Boundary Conditions and Reflectivity Calculations for Two-Level Atomic Wave Functions 7.7.3 Numerical Calculation and Discussion 7.8 BEC for Laser-Cooled Atoms and Atoms
7.8.1 From "Photon Obey Bose Statistics" to "Bose Statistics of Ideal Gases"
7.8.2 BEC of Neutral Atoms in a Harmonic Well
7.8.3 Repulsion interactions: the effect of BEC 7.8.4 Effects of attraction interactions on .BEC 7.8.5 BEC of neutral atoms
Appendix 7A Calculation of I1, I2, I3, I4 Appendix 7B When y is small References to Limit Solutions of ug (y) Chapter 8 Dynamics of Optical Parameter Downconversion and Applications 8.1 Compression Obtained by Non-Degenerate Optical Parameter Amplification State 8.1.1 Parametric oscillator that generates degenerate and non-degenerate parameter down-conversion 8.1.2 Fokker-Planek equation satisfied by non-degenerate parameter down-conversion system 8.1.3 Solution of Fokker Planck equation of degenerate parameter down-conversion system 8.1. 4 Quantum fluctuation calculation of non-degenerate parametric down conversion system 8.1.5 Positive P appearance 8.2 Phase mismatch Fokker-P1anck equation application in QPM 8.2.1 Solution of Fokker-Planck equation with phase mismatch 8.2.2 Parameters Relationship between the down-converted Langevin equation and the solution of the Fokker-Planck equation 8.2.3 The solution of the mismatched Fokker-Planck equation is applied to QPM technology 8.2.4 Numerical calculation results and analysis 8.3 Time-driven linear degenerate parametric amplification system Quantum Fluctuations 8.3.1 Time-Driven Linear Driven Degenerate Parameter Amplification Fokker-Planck Equation 8.3.2 Time-Dependent Linear Driven Degenerate Parameter Amplification Fokker-Planck Equation 8.3.3 Solution 8.3.4 Calculation of Quantum Fluctuations in Parallel Parametric Amplification Systems 8.3.5 Summary 8.4 Quantum Fluctuations in Nonlinear Degenerate Optical Parametric Amplification Systems 8.4.1 General Solutions for Nonlinear Degenerate Parametric Amplification Fokker-Planck Equations in P-Images 8.4.2 Linear Approximate Solutions 8.4. 3 Nonlinear term correction 8.4.4 Summary 8.5 Application of non-degenerate parameter amplification output to demonstrate EPR paradox 8.5.1 The indivisible V1V2 criterion of a composite system 8.5.2 Non-degenerate parameter amplification output to achieve theoretical analysis of EPR paradox 8.5.3 Taking into account the pumping empty time solution: Fokker-Planck equation calculation of Ⅵ (%) 8.5.4 Summary 8.6 Quantum fluctuations of DOPA driven by periodic pumping and quantum entanglement of NOPA 8.7 Application IV non-degenerate parameters amplification The output demonstrates the EPR paradox 8.7.1 The solution of the Fokker-Planck equation for a single degenerate parametric system 8.7.2 The V criterion for multi-particle entanglement 8.7.3 Three-particle entanglement (N = 3)
8.7.4 entanglement of Ⅳ particles (N> 3)
8.7.5 Numerical calculation and discussion of Ⅳ particle entanglement 8.8 Density matrix factorization of composite systems 8.8.12 × 2 composite systems 8.8.2 3 × 3 composite systems 8.8.3 Summary 8.9 Multiphoton entangled states generated by ultrashort optical pulses Appendix 8A About the proof of equation (8.4.4) Appendix 8B 3 × 3 density matrix function, separable density matrix and separable density matrix square Appendix 8C Diagonal square matrix D1r eigenvalue reference