Preface
Authorâs Biography
Chapter 1 Introduction
- 1.1 Introduction
- 1.2 Brief Historical Perspective
- 1.3 The Principles of Quantum Mechanics
- 1.4 The Feynman Lectures on Physics
- 1.5 The Photon
- 1.6 Quantum Optics
- 1.7 Quantum Optics for Engineers
- 1.7.1 Quantum Optics for Engineers: Quantum Entanglement, Second Edition
- References
Chapter 2 Planckâs Quantum Energy Equation
- 2.1 Introduction
- 2.2 Planckâs Equation and Wave Optics
- 2.3 Planckâs Constant h
- 2.3.1 Back to E = h
- Problems
- References
Chapter 3 The Uncertainty Principle
- 3.1 Heisenbergâs Uncertainty Principle
- 3.2 The Wave-Particle Duality
- 3.3 The Feynman Approximation
- 3.1.1 Example
- 3.4 The Interferometric Approximation
- 3.5 The Minimum Uncertainty Principle
- 3.6 The Generalized Uncertainty Principle
- 3.7 Equivalent Versions of Heisenbergâs Uncertainty Principle
- 3.7.1 Example
- 3.8 Applications of the Uncertainty Principle in Optics
- 3.8.1 Beam Divergence
- 3.8.2 Beam Divergence in Astronomy
- 3.8.3 The Uncertainty Principle and the Cavity Linewidth Equation
- 3.8.4 Tuning Laser Microcavities
- 3.8.5 Nanocavities
- Problems
- References
Chapter 4 The Diracâ"Feynman Quantum Interferometric Principle
- 4.1 Diracâs Notation in Optics
- 4.2 The Diracâ"Feynman Interferometric Principle
- 4.3 Interference and the Interferometric Probability Equation
- 4.3.1 Examples: Double-, Triple-, Quadruple-, and Quintuple-Slit Interference
- 4.3.2 Geometry of the N-Slit Quantum Interferometer
- 4.3.3 The Diffraction Grating Equation
- 4.3.4 N-Slit Interferometer Experiment
- 4.4 Coherent and Semi-Coherent Interferograms
- 4.5 The Interferometric Probability Equation in Two and Three Dimensions
- 4.6 Classical and Quantum Alternatives
- Problems
- References
Chapter 5 Interference, Diffraction, Refraction, and Reflection via Diracâs Notation
- 5.1 Introduction
- 5.2 Interference and Diffraction
- 5.2.1 Generalized Diffraction
- 5.2.2 Positive Diffraction
- 5.3 Positive and Negative Refraction
- 5.3.1 Focusing
- 5.4 Reflection
- 5.5 Succinct Description of Optics
- 5.6 Quantum Interference and Classical Interference
- Problems
- References
Chapter 6 Diracâs Notation Identities
- 6.1 Useful Identities
- 6.1.1 Example
- 6.2 Linear Operations
- 6.2.1 Example
- 6.3 Extension to Indistinguishable Quanta Ensembles
- Problems
- References
Chapter 7 Interferometry via Diracâs Notation
- 7.1 Interference la Dirac
- 7.2 The N-Slit Interferometer
- 7.3 The Hanbury Brownâ"Twiss Interferometer
- 7.4 Beam-Splitter Interferometers
- 7.4.1 The Machâ"Zehnder Interferometer
- 7.4.2 The Michelson Interferometer
- 7.4.3 The Sagnac Interferometer
- 7.4.4 The HOM Interferometer
- 7.5 Multiple-Beam Interferometers
- 7.6 The Ramsey Interferometer
- Problems
- References
Chapter 8 Quantum Interferometric Communications in Free Space
- 8.1 Introduction
- 8.2 Theory
- 8.3 N-Slit Interferometer for Secure Free-Space Quantum Communications
- 8.4 Interferometric Characters
- 8.5 Propagation in Terrestrial Free Space
- 8.5.1 Clear-Air Turbulence
- 8.6 Additional Applications
- 8.7 Discussion
- Problems
- References
Chapter 9 Schr¶dingerâs Equation
- 9.1 Introduction
- 9.2 A Heuristic Explicit Approach to Schr¶dingerâs Equation
- 9.3 Schr¶dingerâs Equation via Diracâs Notation
- 9.4 The Time-Independent Schr¶dinger Equation
- 9.4.1 Quantized Energy Levels
- 9.4.2 Semiconductor Emission
- 9.4.3 Quantum Wells
- 9.4.4 Quantum Cascade Lasers
- 9.4.5 Quantum Dots
- 9.5 Nonlinear Schr¶dinger Equation
- 9.6 Discussion
- Problems
- References
Chapter 10 Introduction to Feynman Path Integrals
- 10.1 Introduction
- 10.2 The Classical Action
- 10.3 The Quantum Link
- 10.4 Propagation through a Slit and the Uncertainty Principle
- 10.4.1 Discussion
- 10.5 Feynman Diagrams in Optics
- Problems
- References
Chapter 11 Matrix Aspects of Quantum Mechanics and Quantum Operators
- 11.1 Introduction
- 11.2 Introduction to Vector and Matrix Algebra
- 11.2.1 Vector Algebra
- 11.2.2 Matrix Algebra
- 11.2.3 Unitary Matrices
- 11.3 Pauli Matrices
- 11.3.1 Eigenvalues of Pauli Matrices
- 11.3.2 Pauli Matrices for Spin One-Half Particles
- 11.3.3 The Tensor Product
- 11.4 Introduction to the Density Matrix
- 11.4.1 Examples
- 11.4.2 Transitions Via the Density Matrix
- 11.5 Quantum Operators
- 11.5.1 The Position Operator
- 11.5.2 The Momentum Operator
- 11.5.3 Example
- 11.5.4 The Energy Operator
- 11.5.5 The Heisenberg Equation of Motion
- Problems
- References
Chapter 12 Classical Polarization
- 12.1 Introduction
- 12.2 Maxwell Equations
- 12.2.1 Symmetry in Maxwell Equations
- 12.3 Polarization and Reflection
- 12.3.1 The Plane of Incidence
- 12.4 Jones Calculus
- 12.4.1 Example
- 12.5 Polarizing Prisms
- 12.5.1 Transmission Efficiency in Multiple-Prism Arrays
- 12.5.2 Induced Polarization in a Double-Prism Beam Expander
- 12.5.3 Double-Refraction Polarizers
- 12.5.4 Attenuation of the Intensity of Laser Beams Using Polarization
- 12.6 Polarization Rotators
- 12.6.1 Birefringent Polarization Rotators
- 12.6.2 Example
- 12.6.3 Broadband Prismatic Polarization Rotators
- 12.6.4 Example
- Problems
- References
Chapter 13 Quantum Polarization
- 13.1 Introduction
- 13.2 Linear Polarization
- 13.2.1 Example
- 13.3 Polarization as a Two-State System
- 13.3.1 Diagonal Polarization
- 13.3.2 Circular Polarization
- 13.4 Density Matrix Notation
- 13.4.1 Stokes Parameters and Pauli Matrices
- 13.4.2 The Density Matrix and Circular Polarization
- 13.4.3 Example
- Problems
- References
Chapter 14 Bellâs Theorem
14.1 Introduction
14.2 Bellâs Theorem
14.3 Quantum Entanglement Probabilities
14.4 Example
14.5 Discussion
Problems
References
Chapter 15 Quantum Entanglement Probability Amplitude for n = N = 2
- 15.1 Introduction
- 15.2 The Diracâ"Feynman Probability Amplitude
- 15.3 The Quantum Entanglement Probability Amplitude
- 15.4 Identical States of Polarization
- 15.5 Entanglement of Indistinguishable Ensembles
- 15.6 Discussion
- Problems
- References
Chapter 16 Quantum Entanglement Probability Amplitude for n = N = 21, 22, 23,â¦, 2r
- 16.1 Introduction
- 16.2 Quantum Entanglement Probability Amplitude for n = N = 4
- 16.3 Quantum Entanglement Probability Amplitude for n = N = 8
- 16.4 Quantum Entanglement Probability Amplitude for n = N = 16
- 16.5 Quantum Entanglement Probability Amplitude for n = N = 21, 22, 23, ⦠2r
- 16.5.1 Example
- 16.6 Summary
- Problems
- References
Chapter 17 Quantum Entanglement Probability Amplitudes for n = N = 3, 6
- 17.1 Introduction
- 17.2 Quantum Entanglement Probability Amplitude for n = N = 3
- 17.3 Quantum Entanglement Probability Amplitude for n = N = 6
- 17.4 Discussion
- Problems
- References
Chapter 18 Quantum Entanglement in Matrix Form
- 18.1 Introduction
- 18.2 Quantum Entanglement Probability Amplitudes
- 18.3 Quantum Entanglement via Pauli Matrices
- 18.3.1 Example
- 18.3.2 Pauli Matrices Identities
- 18.4 Quantum Entanglement via the Hadamard Gate
- 18.5 Quantum Entanglement Probability Amplitude Matrices
- 18.6 Quantum Entanglement Polarization Rotator Mathematics
- 18.7 Quantum Mathematics via Hadamardâs Gate
- 18.8 Reversibility in Quantum Mechanics
- Problems
- References
Chapter 19 Quantum Computing in Matrix Notation
- 19.1 Introduction
- 19.2 Interferometric Computer
- 19.3 Classical Logic Gates
- 19.4 von Neumann Entropy
- 19.5 Qbits
- 19.6 Quantum Entanglement via Pauli Matrices
- 19.7 Rotation of Quantum Entanglement States
- 19.8 Quantum Gates
- 19.8.1 Pauli Gates
- 19.8.2 The Hadamard Gate
- 19.8.3 The CNOT Gate
- 19.9 Quantum Entanglement Mathematics via the Hadamard Gate
- 19.9.1 Example
- 19.10 Multiple Entangled States
- 19.11 Discussion
- Problems
- References
Chapter 20 Quantum Cryptography and Quantum Teleportation
- 20.1 Introduction
- 20.2 Quantum Cryptography
- 20.2.1 Bennett and Brassard Cryptography
- 20.2.2 Quantum Entanglement Cryptography Using Bellâs Theorem
- 20.2.3 All-Quantum Quantum Entanglement Cryptography
- 20.3 Quantum Teleportation
- Problems
- References
Chapter 21 Quantum Measurements
- 21.1 Introduction
- 21.1.1 The Two Realms of Quantum Mechanics
- 21.2 The Interferometric Irreversible Measurements
- 21.2.1 The Quantum Measurement Mechanics
- 21.2.2 Additional Irreversible Quantum Measurements
- 21.3 Quantum Non-demolition Measurements
- 21.3.1 Soft Probing of Quantum States
- 21.4 Soft Intersection of Interferometric Characters
- 21.4.1 Comparison between Theoretical andbMeasured N-Slit Interferograms
- 21.4.2 Soft Interferometric Probing
- 21.4.3 The Mechanics of Soft Interferometric Probing
- 21.5 On the Quantum Measurer
- 21.5.1 External Intrusions
- 21.6 Quantum Entropy
- 21.7 Discussion
- Problems
- References
Chapter 22 Quantum Principles and the Probability Amplitude
- 22.1 Introduction
- 22.2 Fundamental Principles of Quantum Mechanics
- 22.3 Probability Amplitudes
- 22.3.1 Probability Amplitude Refinement
- 22.4 From Probability Amplitudes to Probabilities
- 22.4.1 Interferometric Cascade
- 22.5 Nonlocality of the Photon
- 22.6 Indistinguishability and Diracâs Identities
- 22.7 Quantum Entanglement and the Foundations of Quantum Mechanics
- 22.8 The Diracâ"Feynman Interferometric Principle
- Problems
- References
Chapter 23 On the Interpretation of Quantum Mechanics
- 23.1 Introduction
- 23.2 Einstein Podolsky and Rosen (EPR)
- 23.3 Heisenbergâs Uncertainty Principle and EPR
- 23.4 Quantum Physicists on the Interpretation of Quantum Mechanics
- 23.4.1 The Pragmatic Practitioners
- 23.4.2 Bellâs Criticisms
- 23.5 On Hidden Variable Theories
- 23.6 On the Absence of âThe Measurement Problemâ
- 23.7 The Physical Bases of Quantum Entanglement
- 23.8 The Mechanisms of Quantum Mechanics
- 23.8.1 The Quantum Interference Mechanics
- 23.8.2 The Quantum Entanglement Mechanics
- 23.9 Philosophy
- 23.10 Discussion
- Problems
- References
Appendix A: Laser Excitation
Appendix B: Laser Oscillators and Laser Cavities via Diracâs Notation
Appendix C: Generalized Multiple-Prism Dispersion
Appendix D: Multiple-Prism Dispersion Power Series
Appendix E: N-Slit Interferometric Calculations
Appendix F: Ray Transfer Matrices
Appendix G: Complex Numbers and Quaternions
Appendix H: Trigonometric Identities
Appendix I: Calculus Basics
Appendix J: Poincareâs Space
Appendix K: Physical Constants and Optical Quantities
Index
