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.

• PrefaceAuthor’s BiographyChapter 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 Equation2.1 Introduction2.2 Planck’s Equation and Wave Optics2.3 Planck’s Constant h 2.3.1 Back to E = h ProblemsReferencesChapter 3 The Uncertainty Principle3.1 Heisenberg’s Uncertainty Principle3.2 The Wave-Particle Duality3.3 The Feynman Approximation3.1.1 Example3.4 The Interferometric Approximation3.5 The Minimum Uncertainty Principle3.6 The Generalized Uncertainty Principle3.7 Equivalent Versions of Heisenberg’s Uncertainty Principle3.7.1 Example3.8 Applications of the Uncertainty Principle in Optics3.8.1 Beam Divergence3.8.2 Beam Divergence in Astronomy3.8.3 The Uncertainty Principle and the Cavity Linewidth Equation3.8.4 Tuning Laser Microcavities3.8.5 NanocavitiesProblemsReferencesChapter 4 The Dirac–Feynman Quantum Interferometric Principle4.1 Dirac’s Notation in Optics4.2 The Dirac–Feynman Interferometric Principle4.3 Interference and the Interferometric Probability Equation4.3.1 Examples: Double-, Triple-, Quadruple-, and Quintuple-Slit Interference 4.3.2 Geometry of the N-Slit Quantum Interferometer4.3.3 The Diffraction Grating Equation4.3.4 N-Slit Interferometer Experiment4.4 Coherent and Semi-Coherent Interferograms4.5 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 Notation5.1 Introduction5.2 Interference and Diffraction5.2.1 Generalized Diffraction5.2.2 Positive Diffraction5.3 Positive and Negative Refraction5.3.1 Focusing5.4 Reflection5.5 Succinct Description of Optics5.6 Quantum Interference and Classical InterferenceProblemsReferencesChapter 6 Dirac’s Notation Identities6.1 Useful Identities6.1.1 Example6.2 Linear Operations6.2.1 Example6.3 Extension to Indistinguishable Quanta EnsemblesProblemsReferencesChapter 7 Interferometry via Dirac’s Notation7.1 Interference à la Dirac7.2 The N-Slit Interferometer7.3 The Hanbury Brown–Twiss Interferometer7.4 Beam-Splitter Interferometers7.4.1 The Mach–Zehnder Interferometer7.4.2 The Michelson Interferometer7.4.3 The Sagnac Interferometer7.4.4 The HOM Interferometer7.5 Multiple-Beam Interferometers7.6 The Ramsey InterferometerProblemsReferencesChapter 8 Quantum Interferometric Communications in Free Space8.1 Introduction8.2 Theory8.3 N-Slit Interferometer for Secure Free-Space Quantum Communications 8.4 Interferometric Characters8.5 Propagation in Terrestrial Free Space8.5.1 Clear-Air Turbulence8.6 Additional Applications8.7 DiscussionProblemsReferencesChapter 9 Schrödinger’s Equation9.1 Introduction9.2 A Heuristic Explicit Approach to Schrödinger’s Equation9.3 Schrödinger’s Equation via Dirac’s Notation9.4 The Time-Independent Schrödinger Equation9.4.1 Quantized Energy Levels9.4.2 Semiconductor Emission9.4.3 Quantum Wells9.4.4 Quantum Cascade Lasers9.4.5 Quantum Dots9.5 Nonlinear Schrödinger Equation9.6 DiscussionProblemsReferencesChapter 10 Introduction to Feynman Path Integrals10.1 Introduction10.2 The Classical Action10.3 The Quantum Link10.4 Propagation through a Slit and the Uncertainty Principle10.4.1 Discussion10.5 Feynman Diagrams in OpticsProblemsReferencesChapter 11 Matrix Aspects of Quantum Mechanics and Quantum Operators11.1 Introduction11.2 Introduction to Vector and Matrix Algebra11.2.1 Vector Algebra11.2.2 Matrix Algebra11.2.3 Unitary Matrices11.3 Pauli Matrices11.3.1 Eigenvalues of Pauli Matrices11.3.2 Pauli Matrices for Spin One-Half Particles11.3.3 The Tensor Product11.4 Introduction to the Density Matrix11.4.1 Examples11.4.2 Transitions Via the Density Matrix11.5 Quantum Operators11.5.1 The Position Operator11.5.2 The Momentum Operator11.5.3 Example11.5.4 The Energy Operator11.5.5 The Heisenberg Equation of MotionProblemsReferencesChapter 12 Classical Polarization12.1 Introduction12.2 Maxwell Equations12.2.1 Symmetry in Maxwell Equations12.3 Polarization and Reflection12.3.1 The Plane of Incidence12.4 Jones Calculus12.4.1 Example12.5 Polarizing Prisms12.5.1 Transmission Efficiency in Multiple-Prism Arrays12.5.2 Induced Polarization in a Double-Prism Beam Expander12.5.3 Double-Refraction Polarizers12.5.4 Attenuation of the Intensity of Laser Beams Using Polarization12.6 Polarization Rotators12.6.1 Birefringent Polarization Rotators12.6.2 Example12.6.3 Broadband Prismatic Polarization Rotators12.6.4 ExampleProblemsReferencesChapter 13 Quantum Polarization13.1 Introduction13.2 Linear Polarization13.2.1 Example13.3 Polarization as a Two-State System13.3.1 Diagonal Polarization13.3.2 Circular Polarization13.4 Density Matrix Notation13.4.1 Stokes Parameters and Pauli Matrices13.4.2 The Density Matrix and Circular Polarization13.4.3 ExampleProblemsReferencesChapter 14 Bell’s Theorem14.1 Introduction14.2 Bell’s Theorem14.3 Quantum Entanglement Probabilities14.4 Example14.5 DiscussionProblemsReferencesChapter 15 Quantum Entanglement Probability Amplitude for n = N = 215.1 Introduction15.2 The Dirac–Feynman Probability Amplitude15.3 The Quantum Entanglement Probability Amplitude15.4 Identical States of Polarization15.5 Entanglement of Indistinguishable Ensembles15.6 DiscussionProblemsReferencesChapter 16 Quantum Entanglement Probability Amplitude for n = N = 21, 22, 23,…, 2r16.1 Introduction16.2 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 = 1616.5 Quantum Entanglement Probability Amplitude for n = N = 21, 22, 23, … 2r 16.5.1 Example16.6 SummaryProblemsReferencesChapter 17 Quantum Entanglement Probability Amplitudes for n = N = 3, 617.1 Introduction17.2 Quantum Entanglement Probability Amplitude for n = N = 3 17.3 Quantum Entanglement Probability Amplitude for n = N = 6 17.4 DiscussionProblemsReferencesChapter 18 Quantum Entanglement in Matrix Form18.1 Introduction18.2 Quantum Entanglement Probability Amplitudes18.3 Quantum Entanglement via Pauli Matrices18.3.1 Example18.3.2 Pauli Matrices Identities18.4 Quantum Entanglement via the Hadamard Gate18.5 Quantum Entanglement Probability Amplitude Matrices18.6 Quantum Entanglement Polarization Rotator Mathematics18.7 Quantum Mathematics via Hadamard’s Gate18.8 Reversibility in Quantum MechanicsProblemsReferencesChapter 19 Quantum Computing in Matrix Notation19.1 Introduction19.2 Interferometric Computer19.3 Classical Logic Gates19.4 von Neumann Entropy19.5 Qbits19.6 Quantum Entanglement via Pauli Matrices19.7 Rotation of Quantum Entanglement States19.8 Quantum Gates19.8.1 Pauli Gates19.8.2 The Hadamard Gate19.8.3 The CNOT Gate19.9 Quantum Entanglement Mathematics via the Hadamard Gate 19.9.1 Example19.10 Multiple Entangled States19.11 DiscussionProblemsReferencesChapter 20 Quantum Cryptography and Quantum Teleportation20.1 Introduction20.2 Quantum Cryptography20.2.1 Bennett and Brassard Cryptography20.2.2 Quantum Entanglement Cryptography Using Bell’s Theorem20.2.3 All-Quantum Quantum Entanglement Cryptography20.3 Quantum TeleportationProblemsReferencesChapter 21 Quantum Measurements21.1 Introduction21.1.1 The Two Realms of Quantum Mechanics21.2 The Interferometric Irreversible Measurements21.2.1 The Quantum Measurement Mechanics21.2.2 Additional Irreversible Quantum Measurements21.3 Quantum Non-demolition Measurements21.3.1 Soft Probing of Quantum States21.4 Soft Intersection of Interferometric Characters21.4.1 Comparison between Theoretical andbMeasured N-Slit Interferograms 21.4.2 Soft Interferometric Probing21.4.3 The Mechanics of Soft Interferometric Probing21.5 On the Quantum Measurer21.5.1 External Intrusions21.6 Quantum Entropy21.7 DiscussionProblemsReferencesChapter 22 Quantum Principles and the Probability Amplitude22.1 Introduction22.2 Fundamental Principles of Quantum Mechanics22.3 Probability Amplitudes22.3.1 Probability Amplitude Refinement22.4 From Probability Amplitudes to Probabilities22.4.1 Interferometric Cascade22.5 Nonlocality of the Photon22.6 Indistinguishability and Dirac’s Identities22.7 Quantum Entanglement and the Foundations of Quantum Mechanics 22.8 The Dirac–Feynman Interferometric PrincipleProblemsReferencesChapter 23 On the Interpretation of Quantum Mechanics23.1 Introduction23.2 Einstein Podolsky and Rosen (EPR)23.3 Heisenberg’s Uncertainty Principle and EPR23.4 Quantum Physicists on the Interpretation of Quantum Mechanics 23.4.1 The Pragmatic Practitioners23.4.2 Bell’s Criticisms23.5 On Hidden Variable Theories23.6 On the Absence of ‘The Measurement Problem’23.7 The Physical Bases of Quantum Entanglement23.8 The Mechanisms of Quantum Mechanics23.8.1 The Quantum Interference Mechanics23.8.2 The Quantum Entanglement Mechanics23.9 Philosophy23.10 DiscussionProblemsReferencesAppendix A: Laser ExcitationAppendix B: Laser Oscillators and Laser Cavities via Dirac’s NotationAppendix C: Generalized Multiple-Prism DispersionAppendix D: Multiple-Prism Dispersion Power SeriesAppendix E: N-Slit Interferometric CalculationsAppendix F: Ray Transfer MatricesAppendix G: Complex Numbers and QuaternionsAppendix H: Trigonometric IdentitiesAppendix I: Calculus BasicsAppendix J: Poincare’s SpaceAppendix K: Physical Constants and Optical QuantitiesIndex