Quantum Optics for Engineers

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