This is an updated, and extended version of its first edition. New features include transparent interferometric derivation of the physics for quantum entanglement devoid of mysteries and paradoxes. It also provides utilitarian matrix version of quantum entanglement for engineering applications.

Francisco Javier "Frank" Duarte is a laser physicist and author/editor of several books on tunable lasers and quantum optics. His research on physical optics, quantum optics, and laser development has won several awards. He has made numerous original contributions to tunable lasers, multiple-prism optics, quantum interferometry, and quantum entanglement. Dr. Duarte was elected Fellow of the Australian Institute of Physics in 1987 and Fellow of the Optical Society (Optica) in 1993. He has received the Engineering Excellence Award (1995), for the invention of the N-slit laser interferometer, and the David Richardson Medal (2016) for his seminal contributions to the physics of narrow-linewidth tunable lasers and the theory of multiple-prism arrays for linewidth narrowing and laser pulse compression.

Preface

Author's 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 Planck's Quantum Energy Equation

• 2.1 Introduction
• 2.2 Planck's Equation and Wave Optics
• 2.3 Planck's Constant h
• 2.3.1 Back to E = h
• Problems
• References

Chapter 3 The Uncertainty Principle

• 3.1 Heisenberg's 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 Heisenberg's 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 Dirac-Feynman Quantum Interferometric Principle

• 4.1 Dirac's Notation in Optics
• 4.2 The Dirac-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 Dirac's 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 Dirac's 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 Dirac's Notation

• 7.1 Interference à la Dirac
• 7.2 The N-Slit Interferometer
• 7.3 The Hanbury Brown-Twiss Interferometer
• 7.4 Beam-Splitter Interferometers
• 7.4.1 The Mach-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 Schrödinger's Equation

• 9.1 Introduction
• 9.2 A Heuristic Explicit Approach to Schrödinger's Equation
• 9.3 Schrödinger's Equation via Dirac's Notation
• 9.4 The Time-Independent Schrödinger 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 Schrödinger 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 Bell's Theorem

14.1 Introduction

14.2 Bell's 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 Dirac-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,..., 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 Hadamard's 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 Bell's 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 Dirac's Identities
• 22.7 Quantum Entanglement and the Foundations of Quantum Mechanics
• 22.8 The Dirac-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 Heisenberg's Uncertainty Principle and EPR
• 23.4 Quantum Physicists on the Interpretation of Quantum Mechanics
• 23.4.1 The Pragmatic Practitioners
• 23.4.2 Bell's Criticisms
• 23.5 On Hidden Variable Theories
• 23.6 On the Absence of 'The Measurement Problem'
• 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 Dirac's 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: Poincare's Space

Appendix K: Physical Constants and Optical Quantities

Index