Quantum Optics for Engineers

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