Quantum Optics for Engineers

**Quantum Optics for Engineers** provides a transparent and methodical introduction to quantum optics via the Dirac's bra–ket notation with an emphasis on practical applications and basic aspects of quantum mechanics such as Heisenberg's uncertainty principle and Schrodinger's equation. Self-contained and using mainly first-year calculus and algebra tools, the book: * Illustrates the interferometric quantum origin of fundamental optical principles such as diffraction, refraction, and reflection * Provides a transparent introduction, via Dirac's notation, to the probability amplitude of quantum entanglement * Explains applications of the probability amplitude of quantum entanglement to optical communications, quantum cryptography, quantum teleportation, and quantum computing. **Quantum Optics for Engineers** is succinct, transparent, and practical, revealing the intriguing world of quantum entanglement via many practical examples. Ample illustrations are used throughout its presentation and the theory is presented in a methodical, detailed approach. 1 Introduction Introduction Brief Historical Perspective Principles of Quantum Mechanics The Feynman Lectures on Physics Photon Quantum Optics Quantum Optics for Engineers 2 Planck’s Quantum Energy Equation Introduction Planck’s Equation and Wave Optics 3 Uncertainty Principle Heisenberg Uncertainty Principle Wave–Particle Duality Feynman Approximation Interferometric Approximation Minimum Uncertainty Principle Generalized Uncertainty Principle Additional Versions of the Heisenberg Uncertainty Principle Applications of the Uncertainty Principle in Optics 4 Dirac Quantum Optics Dirac Notation in Optics Dirac Quantum Principles Interference and the Interferometric Equation Coherent and Semicoherent Interferograms Interferometric Equation in Two and Three Dimensions Classical and Quantum Alternatives 5 Interference, Diffraction, Refraction, and Reflection via the Dirac Notation Introduction Interference and Diffraction Positive and Negative Refraction Reflection Succinct Description of Optics 6 Generalized Multiple-Prism Dispersion Introduction Generalized Multiple-Prism Dispersion Double-Pass Generalized Multiple-Prism Dispersion Multiple-Return-Pass Generalized Multiple-Prism Dispersion Multiple-Prism Dispersion and Laser Pulse Compression 7 Dirac Notation Identities Useful Identities Linear Operations 8 Laser Excitation Introduction Brief Laser Overview Laser Excitation Excitation and Emission Dynamics Quantum Transition Probabilities and Cross Sections 9 Laser Oscillators Described via the Dirac Notation Introduction Transverse and Longitudinal Modes Laser Cavity Equation: An Intuitive Approach Laser Cavity Equation via the Interferometric Equation 10 Interferometry via the Dirac Notation Interference à la Dirac Hanbury Brown–Twiss Interferometer Two-Beam Interferometers Multiple-Beam Interferometers N-Slit Interferometer as a Wavelength Meter Ramsey Interferometer 11 Secure Interferometric Communications in Free Space Introduction Theory N-Slit Interferometer for Secure Free-Space Optical Communications Interferometric Characters Propagation in Terrestrial Free Space Discussion 12 Schrödinger’s Equation Introduction Schrödinger’s Mind Heuristic Explicit Approach to Schrödinger’s Equation Schrödinger’s Equation via the Dirac Notation Time-Independent Schrödinger’s Equation Introduction to the Hydrogen Equation 13 Introduction to Feynman Path Integrals Introduction Classical Action Quantum Link Propagation through a Slit and the Uncertainty Principle Feynman Diagrams in Optics 14 Matrix Aspects of Quantum Mechanics Introduction Introduction to Vector and Matrix Algebra Quantum Operators Pauli Matrices Introduction to the Density Matrix 15 Classical Polarization Introduction Maxwell Equations Polarization and Reflection Jones Calculus Polarizing Prisms Polarization Rotators 16 Quantum Polarization Introduction Linear Polarization Polarization as a Two-State System Density Matrix Notation 17 Entangled Polarizations: Probability Amplitudes and Experimental Configurations Introduction Hamiltonian Approach Interferometric Approach Pryce–Ward–Snyder Probability Amplitude of Entanglement Pryce–Ward–Snyder Probability Pryce–Ward Experimental Arrangement Wu–Shaknov Experiment Conclusion 18 Quantum Computing Introduction Interferometric Computer Classical Logic Gates Qubits Quantum Logic 19 Quantum Cryptography and Teleportation Introduction Quantum Cryptography Quantum Teleportation 20 Quantum Measurements Introduction Interferometric Irreversible Measurements Quantum Nondemolition Measurements Soft Polarization Measurements Soft Intersection of Interferometric Characters 21 Interpretational Issues in Quantum Mechanics Introduction EPR Bohm Polarization Projection of the EPR Argument Bell’s Inequalities Some Prominent Quantum Physicists on Issues of Interpretation Eisenberg’s Uncertainty Principle and EPR van Kampen’s Quantum Theorems On Probabilities and Probability Amplitudes Comment on the Interpretational Issue Appendix A: Survey of Laser Emission Characteristics Appendix B: Brief Survey of Laser Resonators and Laser Cavities Appendix C: Ray Transfer Matrices Appendix D: Multiple-Prism Dispersion Series Appendix E: Complex Numbers Appendix F: Trigonometric Identities Appendix G: Calculus Basics Appendix H: Poincaré’s Space Appendix I: N-Slit Interferometric Calculations Appendix J: N-Slit Interferometric Calculations—Numerical Approach Appendix K: Physical Constants and Optical Quantities