Hans Bachor, PhD, is Professor at the Australian National University and the Director of the ARC Centre of Excellence for Quantum-Atom Optics. He is a Fellow of the AIP, IOP, and AOS, and has won several Humboldt prizes, an ARC Federation fellow, and the Australian Institute of Physics Award for Outstanding Services to Physics. Tim Ralph, PhD, is an Australian Research Council Professorial Fellow and Node Director and Program Manager of the Queensland Node of the ARC Centre of Excellence for Quantum Computation and Communication Technology.

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• Preface xvAcknowledgments xix1 Introduction 11.1 Optics in Modern Life 11.2 The Origin and Progress of Quantum Optics 31.3 Motivation Through Simple and Direct Teaching Experiments 71.4 Consequences of Photon Correlations 121.5 How to Use This Guide 14References 162 Classical Models of Light 192.1 Classical Waves 202.1.1 Mathematical Description of Waves 202.1.2 The Gaussian Beam 212.1.3 Quadrature Amplitudes 242.1.4 Field Energy, Intensity, and Power 252.1.5 A Classical Mode of Light 262.1.6 Light Carries Information 282.1.7 Modulations 302.2 Optical Modes and Degrees of Freedom 322.2.1 Lasers with Single and Multiple Modes 322.2.2 Polarization 332.2.2.1 Poincaré Sphere and Stokes Vectors 352.2.3 Multimode Systems 362.3 Statistical Properties of Classical Light 372.3.1 The Origin of Fluctuations 372.3.1.1 Gaussian Noise Approximation 382.3.2 Noise Spectra 392.3.3 Coherence 402.3.3.1 Correlation Functions 442.4 An Example: Light from a Chaotic Source as the Idealized Classical Case 462.5 Spatial Information and Imaging 502.5.1 State-of-the-Art Imaging 502.5.2 Classical Imaging 522.5.3 Image Detection 552.5.4 Scanning 562.5.5 Quantifying Noise and Contrast 582.5.6 Coincidence Imaging 592.5.7 Imaging with Coherent Light 602.5.8 Image Reconstruction with Structured Illumination 602.5.9 Image Analysis and Modes 612.5.10 Detection Modes and Displacement 612.6 Summary 62References 63Further Reading 643 Photons: The Motivation to Go Beyond Classical Optics 653.1 Detecting Light 653.2 The Concept of Photons 683.3 Light from a Thermal Source 703.4 Interference Experiments 733.5 Modelling Single-Photon Experiments 783.5.1 Polarization of a Single Photon 793.5.1.1 Some Mathematics 803.5.2 Polarization States 813.5.3 The Single-Photon Interferometer 833.6 Intensity Correlation, Bunching, and Anti-bunching 843.7 Observing Photons in Cavities 883.8 Summary 90References 90Further Reading 924 Quantum Models of Light 934.1 Quantization of Light 934.1.1 Some General Comments on Quantum Mechanics 934.1.2 Quantization of Cavity Modes 944.1.3 Quantized Energy 954.1.4 The Creation and Annihilation Operators 974.2 Quantum States of Light 974.2.1 Number or Fock States 974.2.2 Coherent States 994.2.3 Mixed States 1014.3 Quantum Optical Representations 1024.3.1 Quadrature Amplitude Operators 1024.3.2 Probability and Quasi-probability Distributions 1044.3.3 Photon Number Distributions 1084.3.4 Covariance Matrix 1114.3.4.1 Summary of Different Representations of Quantum States and Quantum Noise 1124.4 Propagation and Detection of Quantum Optical Fields 1134.4.1 Quantum Optical Modes in Free Space 1144.4.2 Propagation in Quantum Optics 1154.4.3 Detection in Quantum Optics 1174.4.4 An Example: The Beamsplitter 1184.5 Quantum Transfer Functions 1204.5.1 A Linearized Quantum Noise Description 1214.5.2 An Example: The Propagating Coherent State 1234.5.3 Real Laser Beams 1234.5.4 The Transfer of Operators, Signals, and Noise 1244.5.5 Sideband Modes as Quantum States 1264.5.6 Another Example: A Coherent State Pulse Through a Frequency Filter 1294.5.7 Transformation of the Covariance Matrix 1304.6 Quantum Correlations 1314.6.1 Photon Correlations 1314.6.2 Quadrature Correlations 1324.6.3 Two-Mode Covariance Matrix 1334.7 Summary 1344.7.1 The Photon Number Basis 1344.7.2 Quadrature Representations 1354.7.3 Quantum Operators 1354.7.4 The Quantum Noise Limit 136References 136Further Reading 1375 Basic Optical Components 1395.1 Beamsplitters 1405.1.1 Classical Description of a Beamsplitter 1405.1.1.1 Polarization Properties of Beamsplitters 1425.1.2 The Beamsplitter in the Quantum Operator Model 1435.1.3 The Beamsplitter with Single Photons 1445.1.4 The Beamsplitter and the Photon Statistics 1465.1.5 The Beamsplitter with Coherent States 1495.1.5.1 Transfer Function for a Beamsplitter 1495.1.6 Comparison Between a Beamsplitter and a Classical Current Junction 1515.1.7 The Beamsplitter as a Model of Loss 1525.2 Interferometers 1535.2.1 Classical Description of an Interferometer 1545.2.2 Quantum Model of the Interferometer 1555.2.3 The Single-Photon Interferometer 1565.2.4 Transfer of Intensity Noise Through the Interferometer 1565.2.5 Sensitivity Limit of an Interferometer 1575.2.6 Effect of Mode Mismatch on an Interferometer 1605.3 Optical Cavities 1625.3.1 Classical Description of a Linear Cavity 1645.3.2 The Special Case of High Reflectivities 1695.3.3 The Phase Response 1705.3.4 Spatial Properties of Cavities 1725.3.4.1 Mode Matching 1725.3.4.2 Polarization 1745.3.4.3 Tunable Mirrors 1755.3.5 Equations of Motion for the Cavity Mode 1755.3.6 The Quantum Equations of Motion for a Cavity 1765.3.7 The Propagation of Fluctuations Through the Cavity 1775.3.8 Single Photons Through a Cavity 1805.3.9 Multimode Cavities 1815.3.10 Engineering Beamsplitters, Interferometers, and Resonators 1825.4 Other Optical Components 1845.4.1 Lenses 1845.4.2 Holograms and Metasurfaces 1855.4.3 Crystals and Polarizers 1875.4.4 Optical Fibres and Waveguides 1885.4.5 Modulators 1895.4.5.1 Phase and Amplitude Modulators 1915.4.6 Spatial Light Modulators 1935.4.7 Optical Noise Sources 1955.4.8 Non-linear Processes 195References 1966 Lasers and Amplifiers 1996.1 The Laser Concept 1996.1.1 Technical Specifications of a Laser 2016.1.2 Rate Equations 2036.1.3 Quantum Model of a Laser 2076.1.4 Examples of Lasers 2096.1.4.1 Classes of Lasers 2096.1.4.2 Dye Lasers and Argon Ion Lasers 2096.1.4.3 The CW Nd: YAG Laser 2106.1.4.4 Diode Lasers 2136.1.4.5 Limits of the Single-Mode Approximation in Diode Lasers 2136.1.5 Laser Phase Noise 2146.1.6 Pulsed Lasers 2156.2 Amplification of Optical Signals 2156.3 Parametric Amplifiers and Oscillators 2186.3.1 The Second-Order Non-linearity 2196.3.2 Parametric Amplification 2206.3.3 Optical Parametric Oscillator 2216.3.3.1 Noise Spectrum of the Parametric Oscillator 2226.3.4 Pair Production 2236.4 Measurement-Based Amplifiers 2246.4.1 Deterministic Measurement-Based Amplifiers 2256.4.2 Heralded Measurement-Based Amplifiers 2286.5 Summary 230References 2317 Photon Generation and Detection 2337.1 Photon Sources 2367.1.1 Deterministic Photon Sources 2397.2 Photon Detection 2407.2.1 Detecting Individual Photons 2407.2.1.1 Photochemical Detectors 2417.2.1.2 Photoelectric Detectors 2417.2.1.3 Photo-thermal Detectors 2437.2.1.4 Multipixel and Imaging Devices 2437.2.2 Recording Electrical Signals from Individual Photons 2457.3 Generating, Detecting, and Analysing Photocurrents 2477.3.1 Properties of Photocurrents 2477.3.1.1 Beat Measurements 2477.3.1.2 Intensity Noise and the Shot Noise Level 2487.3.1.3 Quantum Efficiency 2497.3.1.4 Photodetector Materials 2507.3.2 Generating Photocurrents 2517.3.2.1 Photodiodes and Detector Circuit 2517.3.2.2 Amplifiers and Electronic Noise 2527.3.2.3 Detector Saturation 2547.3.3 Recording of Photocurrents 2557.3.4 Spectral Analysis of Photocurrents 2577.3.4.1 Digital Fourier Transform 2577.3.4.2 Analogue Fourier Transform 2587.3.4.3 From Optical Sidebands to the Current Spectrum 2587.3.4.4 The Operation of an Electronic Spectrum Analyser 2597.3.4.5 Detecting Signal and Noise Independently 2607.3.4.6 The Decibel Scale 2617.3.4.7 Adding Electronic AC Signals 2627.4 Imaging with Photons 263References 264Further Reading 2678 Quantum Noise: Basic Measurements and Techniques 2698.1 Detection and Calibration of Quantum Noise 2698.1.1 Direct Detection and Calibration 2698.1.1.1 White Light Calibration 2738.1.2 Balanced Detection 2738.1.3 Detection of Intensity Modulation and SNR 2758.1.4 Homodyne Detection 2758.1.4.1 The Homodyne Detector for Classical Waves 2758.1.5 Heterodyne Detection 2798.1.5.1 Measuring Other Properties 2808.2 Intensity Noise 2818.2.1 Laser Noise 2818.3 The Intensity Noise Eater 2828.3.1 Classical Intensity Control 2828.3.2 Quantum Noise Control 2858.3.2.1 Practical Consequences 2898.4 Frequency Stabilization and Locking of Cavities 2908.4.1 Pound–Drever–Hall Locking 2928.4.2 Tilt Locking 2938.4.3 The PID Controller 2948.4.4 How to Mount a Mirror 2958.4.5 The Extremes of Mirror Suspension: GW Detectors 2968.5 Injection Locking 296References 2999 Squeezed Light 3039.1 The Concept of Squeezing 3039.1.1 Tools for Squeezing: Two Simple Examples 3039.1.1.1 The Kerr Effect 3049.1.1.2 Four-Wave Mixing 3079.1.2 Properties of Squeezed States 3109.1.2.1 What Are the Uses of These Various Types of Squeezed Light? 3129.2 Quantum Model of Squeezed States 3149.2.1 The Formal Definition of a Squeezed State 3149.2.2 The Generation of Squeezed States 3179.2.3 Squeezing as Correlations Between Noise Sidebands 3199.3 Detecting Squeezed Light 3229.3.1 Detecting Amplitude Squeezed Light 3229.3.2 Detecting Quadrature Squeezed Light 3229.3.3 Using a Cavity to Measure Quadrature Squeezing 3249.3.4 Summary of Different Representations of Squeezed States 3259.3.5 Propagation of Squeezed Light 3259.4 Early Demonstrations of Squeezed Light 3309.4.1 Four Wave Mixing 3309.4.2 Optical Parametric Processes 3339.4.3 Second Harmonic Generation 3399.4.4 The Kerr Effect 3439.4.4.1 The Response of the Kerr Medium 3439.4.4.2 Optimizing the Kerr Effect 3459.4.4.3 Fibre Kerr Squeezing 3469.4.4.4 Atomic Kerr Squeezing 3489.4.4.5 Atomic Polarization Self-Rotation 3499.5 Pulsed Squeezing 3499.5.1 Quantum Noise of Optical Pulses 3499.5.2 Pulsed Squeezing Experiments with Kerr Media 3529.5.3 Pulsed SHG and OPO Experiments 3539.5.4 Soliton Squeezing 3549.5.5 Spectral Filtering 3559.5.6 Non-linear Interferometers 3569.6 Amplitude Squeezed Light from Diode Lasers 3589.7 Quantum State Tomography 3609.8 State of the Art of CW Squeezing 3639.9 Squeezing of Multiple Modes 3659.9.1 Twin-Photon Beams 3659.9.2 Polarization Squeezing 3679.9.3 Degenerate Multimode Squeezers 3689.10 Summary: Quantum Limits and Enhancement 370References 371Further Reading 37610 Applications of Quantum Light 37710.1 Quantum Enhanced Sensors 37710.1.1 Coherent Sensors and Sensitivity Scaling 37710.1.2 Practical Examples of Sensors 38010.1.3 Ultimate Sensing Limits 38210.1.4 Adaptive Phase Estimation 38410.2 Optical Communication 38410.3 Gravitational Wave Detection 38910.3.1 The Origin and Properties of GW 38910.3.1.1 Concept and Design of an Optical GW Detector 39210.3.2 Quantum Properties of the Ideal Interferometer 39310.3.2.1 Configurations of Interferometers 39610.3.2.2 Recycling 39710.3.2.3 Modulation Techniques 39810.3.3 The Sensitivity of GW Observatories 40010.3.3.1 Enhancement Below the SQL 40210.3.4 Interferometry with Squeezed Light 40510.3.4.1 Quantum Enhancement Beyond the SQL 41010.4 Quantum Enhanced Imaging 41110.4.1 Imaging with Photons on Demand 41110.4.2 Quantum Enhanced Coincidence Imaging 41210.5 Multimode Squeezing Enhancing Sensors 41410.5.1 Spatial Multimode Squeezing 41410.6 Summary and Outlook 419References 41911 QND 42511.1 QND Measurements of Quadrature Amplitudes 42511.2 Classification of QND Measurements 42711.3 Experimental Results 43011.4 Single-Photon QND 43211.4.1 Measurement-Based QND 434References 43712 Fundamental Tests of Quantum Mechanics 44112.1 Wave–Particle Duality 44112.2 Indistinguishability 44612.3 Non-locality 45312.3.1 Einstein–Podolsky–Rosen Paradox 45312.3.2 Characterization of Entangled Beams via Homodyne Detection 45812.3.2.1 Logarithmic Negativity and Two-Mode Squeezing 45912.3.2.2 Entanglement of Formation 46012.3.3 Bell Inequalities 46112.3.3.1 Long-Distance Bell Inequality Violations 46612.3.3.2 Loophole-Free Bell Inequality Violations 46612.4 Summary 468References 46813 Quantum Information 47313.1 Photons as Qubits 47313.1.1 Other Quantum Encodings 47513.2 Post-selection and Coincidence Counting 47513.3 True Single-Photon Sources 47713.3.1 Heralded Single Photons 47713.3.2 Single Photons on Demand 48013.4 Characterizing Photonic Qubits 48213.5 Quantum Key Distribution 48413.5.1 QKD Using Single Photons 48513.5.2 QKD Using Continuous Variables 48913.5.3 No Cloning 49213.6 Teleportation 49213.6.1 Teleportation of Photon Qubits 49313.6.2 Continuous Variable Teleportation 49513.6.3 Entanglement Swapping 50213.6.4 Entanglement Distillation 50213.7 Quantum Computation 50513.7.1 Dual-Rail Quantum Computing 50613.7.1.1 Quantum Circuits with Linear Optics 50713.7.1.2 Cluster States 51113.7.1.3 Quantum Gates with Non-linear Optics 51313.7.2 Single-Rail Quantum Computation 51413.7.2.1 Quantum Random Walks 51513.7.2.2 Boson Sampling 51613.7.3 Continuous Variable Quantum Computation 51813.7.3.1 Cat State Quantum Computing 51913.7.3.2 Continuous Variable Cluster States 52113.7.4 Large-Scale Quantum Computation 52213.8 Summary 525References 526Further Reading 53114 The Future: From Q-demonstrations to Q-technologies 53314.1 Demonstrating Quantum Effects 53314.2 Matter Waves and Atoms 53514.3 Q-Technology Based on Optics 53714.3.1 Applications of Squeezed Light 53714.3.2 Quantum Communication and Logic with Photons 53914.3.3 Cavity QED 54214.3.4 Extending to Other Wavelengths: Microwaves and Cryogenic Circuits 54214.3.5 Quantum Optomechanics 54214.3.6 Transfer of Quantum Information Between Different Physical Systems 54314.3.7 Transferring and Storing Quantum States 54414.4 Outlook 544References 545Further Reading 547Appendices 549Appendix A: List of Quantum Operators, States, and Functions 549Appendix B: Calculation of the Quantum Properties of a Feedback Loop 551Appendix C: Detection of Signal and Noise with an ESA 552Reference 554Appendix D: An Example of Analogue Processing of Photocurrents 554Appendix E: Symbols and Abbreviations 556Index 559

Hans Bachor, PhD, is Professor at the Australian National University and the Director of the ARC Centre of Excellence for Quantum-Atom Optics. He is a Fellow of the AIP, IOP, and AOS, and has won several Humboldt prizes, an ARC Federation fellow, and the Australian Institute of Physics Award for Outstanding Services to Physics. Tim Ralph, PhD, is an Australian Research Council Professorial Fellow and Node Director and Program Manager of the Queensland Node of the ARC Centre of Excellence for Quantum Computation and Communication Technology.

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• Preface xvAcknowledgments xix1 Introduction 11.1 Optics in Modern Life 11.2 The Origin and Progress of Quantum Optics 31.3 Motivation Through Simple and Direct Teaching Experiments 71.4 Consequences of Photon Correlations 121.5 How to Use This Guide 14References 162 Classical Models of Light 192.1 Classical Waves 202.1.1 Mathematical Description of Waves 202.1.2 The Gaussian Beam 212.1.3 Quadrature Amplitudes 242.1.4 Field Energy, Intensity, and Power 252.1.5 A Classical Mode of Light 262.1.6 Light Carries Information 282.1.7 Modulations 302.2 Optical Modes and Degrees of Freedom 322.2.1 Lasers with Single and Multiple Modes 322.2.2 Polarization 332.2.2.1 Poincaré Sphere and Stokes Vectors 352.2.3 Multimode Systems 362.3 Statistical Properties of Classical Light 372.3.1 The Origin of Fluctuations 372.3.1.1 Gaussian Noise Approximation 382.3.2 Noise Spectra 392.3.3 Coherence 402.3.3.1 Correlation Functions 442.4 An Example: Light from a Chaotic Source as the Idealized Classical Case 462.5 Spatial Information and Imaging 502.5.1 State-of-the-Art Imaging 502.5.2 Classical Imaging 522.5.3 Image Detection 552.5.4 Scanning 562.5.5 Quantifying Noise and Contrast 582.5.6 Coincidence Imaging 592.5.7 Imaging with Coherent Light 602.5.8 Image Reconstruction with Structured Illumination 602.5.9 Image Analysis and Modes 612.5.10 Detection Modes and Displacement 612.6 Summary 62References 63Further Reading 643 Photons: The Motivation to Go Beyond Classical Optics 653.1 Detecting Light 653.2 The Concept of Photons 683.3 Light from a Thermal Source 703.4 Interference Experiments 733.5 Modelling Single-Photon Experiments 783.5.1 Polarization of a Single Photon 793.5.1.1 Some Mathematics 803.5.2 Polarization States 813.5.3 The Single-Photon Interferometer 833.6 Intensity Correlation, Bunching, and Anti-bunching 843.7 Observing Photons in Cavities 883.8 Summary 90References 90Further Reading 924 Quantum Models of Light 934.1 Quantization of Light 934.1.1 Some General Comments on Quantum Mechanics 934.1.2 Quantization of Cavity Modes 944.1.3 Quantized Energy 954.1.4 The Creation and Annihilation Operators 974.2 Quantum States of Light 974.2.1 Number or Fock States 974.2.2 Coherent States 994.2.3 Mixed States 1014.3 Quantum Optical Representations 1024.3.1 Quadrature Amplitude Operators 1024.3.2 Probability and Quasi-probability Distributions 1044.3.3 Photon Number Distributions 1084.3.4 Covariance Matrix 1114.3.4.1 Summary of Different Representations of Quantum States and Quantum Noise 1124.4 Propagation and Detection of Quantum Optical Fields 1134.4.1 Quantum Optical Modes in Free Space 1144.4.2 Propagation in Quantum Optics 1154.4.3 Detection in Quantum Optics 1174.4.4 An Example: The Beamsplitter 1184.5 Quantum Transfer Functions 1204.5.1 A Linearized Quantum Noise Description 1214.5.2 An Example: The Propagating Coherent State 1234.5.3 Real Laser Beams 1234.5.4 The Transfer of Operators, Signals, and Noise 1244.5.5 Sideband Modes as Quantum States 1264.5.6 Another Example: A Coherent State Pulse Through a Frequency Filter 1294.5.7 Transformation of the Covariance Matrix 1304.6 Quantum Correlations 1314.6.1 Photon Correlations 1314.6.2 Quadrature Correlations 1324.6.3 Two-Mode Covariance Matrix 1334.7 Summary 1344.7.1 The Photon Number Basis 1344.7.2 Quadrature Representations 1354.7.3 Quantum Operators 1354.7.4 The Quantum Noise Limit 136References 136Further Reading 1375 Basic Optical Components 1395.1 Beamsplitters 1405.1.1 Classical Description of a Beamsplitter 1405.1.1.1 Polarization Properties of Beamsplitters 1425.1.2 The Beamsplitter in the Quantum Operator Model 1435.1.3 The Beamsplitter with Single Photons 1445.1.4 The Beamsplitter and the Photon Statistics 1465.1.5 The Beamsplitter with Coherent States 1495.1.5.1 Transfer Function for a Beamsplitter 1495.1.6 Comparison Between a Beamsplitter and a Classical Current Junction 1515.1.7 The Beamsplitter as a Model of Loss 1525.2 Interferometers 1535.2.1 Classical Description of an Interferometer 1545.2.2 Quantum Model of the Interferometer 1555.2.3 The Single-Photon Interferometer 1565.2.4 Transfer of Intensity Noise Through the Interferometer 1565.2.5 Sensitivity Limit of an Interferometer 1575.2.6 Effect of Mode Mismatch on an Interferometer 1605.3 Optical Cavities 1625.3.1 Classical Description of a Linear Cavity 1645.3.2 The Special Case of High Reflectivities 1695.3.3 The Phase Response 1705.3.4 Spatial Properties of Cavities 1725.3.4.1 Mode Matching 1725.3.4.2 Polarization 1745.3.4.3 Tunable Mirrors 1755.3.5 Equations of Motion for the Cavity Mode 1755.3.6 The Quantum Equations of Motion for a Cavity 1765.3.7 The Propagation of Fluctuations Through the Cavity 1775.3.8 Single Photons Through a Cavity 1805.3.9 Multimode Cavities 1815.3.10 Engineering Beamsplitters, Interferometers, and Resonators 1825.4 Other Optical Components 1845.4.1 Lenses 1845.4.2 Holograms and Metasurfaces 1855.4.3 Crystals and Polarizers 1875.4.4 Optical Fibres and Waveguides 1885.4.5 Modulators 1895.4.5.1 Phase and Amplitude Modulators 1915.4.6 Spatial Light Modulators 1935.4.7 Optical Noise Sources 1955.4.8 Non-linear Processes 195References 1966 Lasers and Amplifiers 1996.1 The Laser Concept 1996.1.1 Technical Specifications of a Laser 2016.1.2 Rate Equations 2036.1.3 Quantum Model of a Laser 2076.1.4 Examples of Lasers 2096.1.4.1 Classes of Lasers 2096.1.4.2 Dye Lasers and Argon Ion Lasers 2096.1.4.3 The CW Nd: YAG Laser 2106.1.4.4 Diode Lasers 2136.1.4.5 Limits of the Single-Mode Approximation in Diode Lasers 2136.1.5 Laser Phase Noise 2146.1.6 Pulsed Lasers 2156.2 Amplification of Optical Signals 2156.3 Parametric Amplifiers and Oscillators 2186.3.1 The Second-Order Non-linearity 2196.3.2 Parametric Amplification 2206.3.3 Optical Parametric Oscillator 2216.3.3.1 Noise Spectrum of the Parametric Oscillator 2226.3.4 Pair Production 2236.4 Measurement-Based Amplifiers 2246.4.1 Deterministic Measurement-Based Amplifiers 2256.4.2 Heralded Measurement-Based Amplifiers 2286.5 Summary 230References 2317 Photon Generation and Detection 2337.1 Photon Sources 2367.1.1 Deterministic Photon Sources 2397.2 Photon Detection 2407.2.1 Detecting Individual Photons 2407.2.1.1 Photochemical Detectors 2417.2.1.2 Photoelectric Detectors 2417.2.1.3 Photo-thermal Detectors 2437.2.1.4 Multipixel and Imaging Devices 2437.2.2 Recording Electrical Signals from Individual Photons 2457.3 Generating, Detecting, and Analysing Photocurrents 2477.3.1 Properties of Photocurrents 2477.3.1.1 Beat Measurements 2477.3.1.2 Intensity Noise and the Shot Noise Level 2487.3.1.3 Quantum Efficiency 2497.3.1.4 Photodetector Materials 2507.3.2 Generating Photocurrents 2517.3.2.1 Photodiodes and Detector Circuit 2517.3.2.2 Amplifiers and Electronic Noise 2527.3.2.3 Detector Saturation 2547.3.3 Recording of Photocurrents 2557.3.4 Spectral Analysis of Photocurrents 2577.3.4.1 Digital Fourier Transform 2577.3.4.2 Analogue Fourier Transform 2587.3.4.3 From Optical Sidebands to the Current Spectrum 2587.3.4.4 The Operation of an Electronic Spectrum Analyser 2597.3.4.5 Detecting Signal and Noise Independently 2607.3.4.6 The Decibel Scale 2617.3.4.7 Adding Electronic AC Signals 2627.4 Imaging with Photons 263References 264Further Reading 2678 Quantum Noise: Basic Measurements and Techniques 2698.1 Detection and Calibration of Quantum Noise 2698.1.1 Direct Detection and Calibration 2698.1.1.1 White Light Calibration 2738.1.2 Balanced Detection 2738.1.3 Detection of Intensity Modulation and SNR 2758.1.4 Homodyne Detection 2758.1.4.1 The Homodyne Detector for Classical Waves 2758.1.5 Heterodyne Detection 2798.1.5.1 Measuring Other Properties 2808.2 Intensity Noise 2818.2.1 Laser Noise 2818.3 The Intensity Noise Eater 2828.3.1 Classical Intensity Control 2828.3.2 Quantum Noise Control 2858.3.2.1 Practical Consequences 2898.4 Frequency Stabilization and Locking of Cavities 2908.4.1 Pound–Drever–Hall Locking 2928.4.2 Tilt Locking 2938.4.3 The PID Controller 2948.4.4 How to Mount a Mirror 2958.4.5 The Extremes of Mirror Suspension: GW Detectors 2968.5 Injection Locking 296References 2999 Squeezed Light 3039.1 The Concept of Squeezing 3039.1.1 Tools for Squeezing: Two Simple Examples 3039.1.1.1 The Kerr Effect 3049.1.1.2 Four-Wave Mixing 3079.1.2 Properties of Squeezed States 3109.1.2.1 What Are the Uses of These Various Types of Squeezed Light? 3129.2 Quantum Model of Squeezed States 3149.2.1 The Formal Definition of a Squeezed State 3149.2.2 The Generation of Squeezed States 3179.2.3 Squeezing as Correlations Between Noise Sidebands 3199.3 Detecting Squeezed Light 3229.3.1 Detecting Amplitude Squeezed Light 3229.3.2 Detecting Quadrature Squeezed Light 3229.3.3 Using a Cavity to Measure Quadrature Squeezing 3249.3.4 Summary of Different Representations of Squeezed States 3259.3.5 Propagation of Squeezed Light 3259.4 Early Demonstrations of Squeezed Light 3309.4.1 Four Wave Mixing 3309.4.2 Optical Parametric Processes 3339.4.3 Second Harmonic Generation 3399.4.4 The Kerr Effect 3439.4.4.1 The Response of the Kerr Medium 3439.4.4.2 Optimizing the Kerr Effect 3459.4.4.3 Fibre Kerr Squeezing 3469.4.4.4 Atomic Kerr Squeezing 3489.4.4.5 Atomic Polarization Self-Rotation 3499.5 Pulsed Squeezing 3499.5.1 Quantum Noise of Optical Pulses 3499.5.2 Pulsed Squeezing Experiments with Kerr Media 3529.5.3 Pulsed SHG and OPO Experiments 3539.5.4 Soliton Squeezing 3549.5.5 Spectral Filtering 3559.5.6 Non-linear Interferometers 3569.6 Amplitude Squeezed Light from Diode Lasers 3589.7 Quantum State Tomography 3609.8 State of the Art of CW Squeezing 3639.9 Squeezing of Multiple Modes 3659.9.1 Twin-Photon Beams 3659.9.2 Polarization Squeezing 3679.9.3 Degenerate Multimode Squeezers 3689.10 Summary: Quantum Limits and Enhancement 370References 371Further Reading 37610 Applications of Quantum Light 37710.1 Quantum Enhanced Sensors 37710.1.1 Coherent Sensors and Sensitivity Scaling 37710.1.2 Practical Examples of Sensors 38010.1.3 Ultimate Sensing Limits 38210.1.4 Adaptive Phase Estimation 38410.2 Optical Communication 38410.3 Gravitational Wave Detection 38910.3.1 The Origin and Properties of GW 38910.3.1.1 Concept and Design of an Optical GW Detector 39210.3.2 Quantum Properties of the Ideal Interferometer 39310.3.2.1 Configurations of Interferometers 39610.3.2.2 Recycling 39710.3.2.3 Modulation Techniques 39810.3.3 The Sensitivity of GW Observatories 40010.3.3.1 Enhancement Below the SQL 40210.3.4 Interferometry with Squeezed Light 40510.3.4.1 Quantum Enhancement Beyond the SQL 41010.4 Quantum Enhanced Imaging 41110.4.1 Imaging with Photons on Demand 41110.4.2 Quantum Enhanced Coincidence Imaging 41210.5 Multimode Squeezing Enhancing Sensors 41410.5.1 Spatial Multimode Squeezing 41410.6 Summary and Outlook 419References 41911 QND 42511.1 QND Measurements of Quadrature Amplitudes 42511.2 Classification of QND Measurements 42711.3 Experimental Results 43011.4 Single-Photon QND 43211.4.1 Measurement-Based QND 434References 43712 Fundamental Tests of Quantum Mechanics 44112.1 Wave–Particle Duality 44112.2 Indistinguishability 44612.3 Non-locality 45312.3.1 Einstein–Podolsky–Rosen Paradox 45312.3.2 Characterization of Entangled Beams via Homodyne Detection 45812.3.2.1 Logarithmic Negativity and Two-Mode Squeezing 45912.3.2.2 Entanglement of Formation 46012.3.3 Bell Inequalities 46112.3.3.1 Long-Distance Bell Inequality Violations 46612.3.3.2 Loophole-Free Bell Inequality Violations 46612.4 Summary 468References 46813 Quantum Information 47313.1 Photons as Qubits 47313.1.1 Other Quantum Encodings 47513.2 Post-selection and Coincidence Counting 47513.3 True Single-Photon Sources 47713.3.1 Heralded Single Photons 47713.3.2 Single Photons on Demand 48013.4 Characterizing Photonic Qubits 48213.5 Quantum Key Distribution 48413.5.1 QKD Using Single Photons 48513.5.2 QKD Using Continuous Variables 48913.5.3 No Cloning 49213.6 Teleportation 49213.6.1 Teleportation of Photon Qubits 49313.6.2 Continuous Variable Teleportation 49513.6.3 Entanglement Swapping 50213.6.4 Entanglement Distillation 50213.7 Quantum Computation 50513.7.1 Dual-Rail Quantum Computing 50613.7.1.1 Quantum Circuits with Linear Optics 50713.7.1.2 Cluster States 51113.7.1.3 Quantum Gates with Non-linear Optics 51313.7.2 Single-Rail Quantum Computation 51413.7.2.1 Quantum Random Walks 51513.7.2.2 Boson Sampling 51613.7.3 Continuous Variable Quantum Computation 51813.7.3.1 Cat State Quantum Computing 51913.7.3.2 Continuous Variable Cluster States 52113.7.4 Large-Scale Quantum Computation 52213.8 Summary 525References 526Further Reading 53114 The Future: From Q-demonstrations to Q-technologies 53314.1 Demonstrating Quantum Effects 53314.2 Matter Waves and Atoms 53514.3 Q-Technology Based on Optics 53714.3.1 Applications of Squeezed Light 53714.3.2 Quantum Communication and Logic with Photons 53914.3.3 Cavity QED 54214.3.4 Extending to Other Wavelengths: Microwaves and Cryogenic Circuits 54214.3.5 Quantum Optomechanics 54214.3.6 Transfer of Quantum Information Between Different Physical Systems 54314.3.7 Transferring and Storing Quantum States 54414.4 Outlook 544References 545Further Reading 547Appendices 549Appendix A: List of Quantum Operators, States, and Functions 549Appendix B: Calculation of the Quantum Properties of a Feedback Loop 551Appendix C: Detection of Signal and Noise with an ESA 552Reference 554Appendix D: An Example of Analogue Processing of Photocurrents 554Appendix E: Symbols and Abbreviations 556Index 559

Hans Bachor, PhD, is Professor at the Australian National University and the Director of the ARC Centre of Excellence for Quantum-Atom Optics. He is a Fellow of the AIP, IOP, and AOS, and has won several Humboldt prizes, an ARC Federation fellow, and the Australian Institute of Physics Award for Outstanding Services to Physics. Tim Ralph, PhD, is an Australian Research Council Professorial Fellow and Node Director and Program Manager of the Queensland Node of the ARC Centre of Excellence for Quantum Computation and Communication Technology.

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• Preface xvAcknowledgments xix1 Introduction 11.1 Optics in Modern Life 11.2 The Origin and Progress of Quantum Optics 31.3 Motivation Through Simple and Direct Teaching Experiments 71.4 Consequences of Photon Correlations 121.5 How to Use This Guide 14References 162 Classical Models of Light 192.1 Classical Waves 202.1.1 Mathematical Description of Waves 202.1.2 The Gaussian Beam 212.1.3 Quadrature Amplitudes 242.1.4 Field Energy, Intensity, and Power 252.1.5 A Classical Mode of Light 262.1.6 Light Carries Information 282.1.7 Modulations 302.2 Optical Modes and Degrees of Freedom 322.2.1 Lasers with Single and Multiple Modes 322.2.2 Polarization 332.2.2.1 Poincaré Sphere and Stokes Vectors 352.2.3 Multimode Systems 362.3 Statistical Properties of Classical Light 372.3.1 The Origin of Fluctuations 372.3.1.1 Gaussian Noise Approximation 382.3.2 Noise Spectra 392.3.3 Coherence 402.3.3.1 Correlation Functions 442.4 An Example: Light from a Chaotic Source as the Idealized Classical Case 462.5 Spatial Information and Imaging 502.5.1 State-of-the-Art Imaging 502.5.2 Classical Imaging 522.5.3 Image Detection 552.5.4 Scanning 562.5.5 Quantifying Noise and Contrast 582.5.6 Coincidence Imaging 592.5.7 Imaging with Coherent Light 602.5.8 Image Reconstruction with Structured Illumination 602.5.9 Image Analysis and Modes 612.5.10 Detection Modes and Displacement 612.6 Summary 62References 63Further Reading 643 Photons: The Motivation to Go Beyond Classical Optics 653.1 Detecting Light 653.2 The Concept of Photons 683.3 Light from a Thermal Source 703.4 Interference Experiments 733.5 Modelling Single-Photon Experiments 783.5.1 Polarization of a Single Photon 793.5.1.1 Some Mathematics 803.5.2 Polarization States 813.5.3 The Single-Photon Interferometer 833.6 Intensity Correlation, Bunching, and Anti-bunching 843.7 Observing Photons in Cavities 883.8 Summary 90References 90Further Reading 924 Quantum Models of Light 934.1 Quantization of Light 934.1.1 Some General Comments on Quantum Mechanics 934.1.2 Quantization of Cavity Modes 944.1.3 Quantized Energy 954.1.4 The Creation and Annihilation Operators 974.2 Quantum States of Light 974.2.1 Number or Fock States 974.2.2 Coherent States 994.2.3 Mixed States 1014.3 Quantum Optical Representations 1024.3.1 Quadrature Amplitude Operators 1024.3.2 Probability and Quasi-probability Distributions 1044.3.3 Photon Number Distributions 1084.3.4 Covariance Matrix 1114.3.4.1 Summary of Different Representations of Quantum States and Quantum Noise 1124.4 Propagation and Detection of Quantum Optical Fields 1134.4.1 Quantum Optical Modes in Free Space 1144.4.2 Propagation in Quantum Optics 1154.4.3 Detection in Quantum Optics 1174.4.4 An Example: The Beamsplitter 1184.5 Quantum Transfer Functions 1204.5.1 A Linearized Quantum Noise Description 1214.5.2 An Example: The Propagating Coherent State 1234.5.3 Real Laser Beams 1234.5.4 The Transfer of Operators, Signals, and Noise 1244.5.5 Sideband Modes as Quantum States 1264.5.6 Another Example: A Coherent State Pulse Through a Frequency Filter 1294.5.7 Transformation of the Covariance Matrix 1304.6 Quantum Correlations 1314.6.1 Photon Correlations 1314.6.2 Quadrature Correlations 1324.6.3 Two-Mode Covariance Matrix 1334.7 Summary 1344.7.1 The Photon Number Basis 1344.7.2 Quadrature Representations 1354.7.3 Quantum Operators 1354.7.4 The Quantum Noise Limit 136References 136Further Reading 1375 Basic Optical Components 1395.1 Beamsplitters 1405.1.1 Classical Description of a Beamsplitter 1405.1.1.1 Polarization Properties of Beamsplitters 1425.1.2 The Beamsplitter in the Quantum Operator Model 1435.1.3 The Beamsplitter with Single Photons 1445.1.4 The Beamsplitter and the Photon Statistics 1465.1.5 The Beamsplitter with Coherent States 1495.1.5.1 Transfer Function for a Beamsplitter 1495.1.6 Comparison Between a Beamsplitter and a Classical Current Junction 1515.1.7 The Beamsplitter as a Model of Loss 1525.2 Interferometers 1535.2.1 Classical Description of an Interferometer 1545.2.2 Quantum Model of the Interferometer 1555.2.3 The Single-Photon Interferometer 1565.2.4 Transfer of Intensity Noise Through the Interferometer 1565.2.5 Sensitivity Limit of an Interferometer 1575.2.6 Effect of Mode Mismatch on an Interferometer 1605.3 Optical Cavities 1625.3.1 Classical Description of a Linear Cavity 1645.3.2 The Special Case of High Reflectivities 1695.3.3 The Phase Response 1705.3.4 Spatial Properties of Cavities 1725.3.4.1 Mode Matching 1725.3.4.2 Polarization 1745.3.4.3 Tunable Mirrors 1755.3.5 Equations of Motion for the Cavity Mode 1755.3.6 The Quantum Equations of Motion for a Cavity 1765.3.7 The Propagation of Fluctuations Through the Cavity 1775.3.8 Single Photons Through a Cavity 1805.3.9 Multimode Cavities 1815.3.10 Engineering Beamsplitters, Interferometers, and Resonators 1825.4 Other Optical Components 1845.4.1 Lenses 1845.4.2 Holograms and Metasurfaces 1855.4.3 Crystals and Polarizers 1875.4.4 Optical Fibres and Waveguides 1885.4.5 Modulators 1895.4.5.1 Phase and Amplitude Modulators 1915.4.6 Spatial Light Modulators 1935.4.7 Optical Noise Sources 1955.4.8 Non-linear Processes 195References 1966 Lasers and Amplifiers 1996.1 The Laser Concept 1996.1.1 Technical Specifications of a Laser 2016.1.2 Rate Equations 2036.1.3 Quantum Model of a Laser 2076.1.4 Examples of Lasers 2096.1.4.1 Classes of Lasers 2096.1.4.2 Dye Lasers and Argon Ion Lasers 2096.1.4.3 The CW Nd: YAG Laser 2106.1.4.4 Diode Lasers 2136.1.4.5 Limits of the Single-Mode Approximation in Diode Lasers 2136.1.5 Laser Phase Noise 2146.1.6 Pulsed Lasers 2156.2 Amplification of Optical Signals 2156.3 Parametric Amplifiers and Oscillators 2186.3.1 The Second-Order Non-linearity 2196.3.2 Parametric Amplification 2206.3.3 Optical Parametric Oscillator 2216.3.3.1 Noise Spectrum of the Parametric Oscillator 2226.3.4 Pair Production 2236.4 Measurement-Based Amplifiers 2246.4.1 Deterministic Measurement-Based Amplifiers 2256.4.2 Heralded Measurement-Based Amplifiers 2286.5 Summary 230References 2317 Photon Generation and Detection 2337.1 Photon Sources 2367.1.1 Deterministic Photon Sources 2397.2 Photon Detection 2407.2.1 Detecting Individual Photons 2407.2.1.1 Photochemical Detectors 2417.2.1.2 Photoelectric Detectors 2417.2.1.3 Photo-thermal Detectors 2437.2.1.4 Multipixel and Imaging Devices 2437.2.2 Recording Electrical Signals from Individual Photons 2457.3 Generating, Detecting, and Analysing Photocurrents 2477.3.1 Properties of Photocurrents 2477.3.1.1 Beat Measurements 2477.3.1.2 Intensity Noise and the Shot Noise Level 2487.3.1.3 Quantum Efficiency 2497.3.1.4 Photodetector Materials 2507.3.2 Generating Photocurrents 2517.3.2.1 Photodiodes and Detector Circuit 2517.3.2.2 Amplifiers and Electronic Noise 2527.3.2.3 Detector Saturation 2547.3.3 Recording of Photocurrents 2557.3.4 Spectral Analysis of Photocurrents 2577.3.4.1 Digital Fourier Transform 2577.3.4.2 Analogue Fourier Transform 2587.3.4.3 From Optical Sidebands to the Current Spectrum 2587.3.4.4 The Operation of an Electronic Spectrum Analyser 2597.3.4.5 Detecting Signal and Noise Independently 2607.3.4.6 The Decibel Scale 2617.3.4.7 Adding Electronic AC Signals 2627.4 Imaging with Photons 263References 264Further Reading 2678 Quantum Noise: Basic Measurements and Techniques 2698.1 Detection and Calibration of Quantum Noise 2698.1.1 Direct Detection and Calibration 2698.1.1.1 White Light Calibration 2738.1.2 Balanced Detection 2738.1.3 Detection of Intensity Modulation and SNR 2758.1.4 Homodyne Detection 2758.1.4.1 The Homodyne Detector for Classical Waves 2758.1.5 Heterodyne Detection 2798.1.5.1 Measuring Other Properties 2808.2 Intensity Noise 2818.2.1 Laser Noise 2818.3 The Intensity Noise Eater 2828.3.1 Classical Intensity Control 2828.3.2 Quantum Noise Control 2858.3.2.1 Practical Consequences 2898.4 Frequency Stabilization and Locking of Cavities 2908.4.1 Pound–Drever–Hall Locking 2928.4.2 Tilt Locking 2938.4.3 The PID Controller 2948.4.4 How to Mount a Mirror 2958.4.5 The Extremes of Mirror Suspension: GW Detectors 2968.5 Injection Locking 296References 2999 Squeezed Light 3039.1 The Concept of Squeezing 3039.1.1 Tools for Squeezing: Two Simple Examples 3039.1.1.1 The Kerr Effect 3049.1.1.2 Four-Wave Mixing 3079.1.2 Properties of Squeezed States 3109.1.2.1 What Are the Uses of These Various Types of Squeezed Light? 3129.2 Quantum Model of Squeezed States 3149.2.1 The Formal Definition of a Squeezed State 3149.2.2 The Generation of Squeezed States 3179.2.3 Squeezing as Correlations Between Noise Sidebands 3199.3 Detecting Squeezed Light 3229.3.1 Detecting Amplitude Squeezed Light 3229.3.2 Detecting Quadrature Squeezed Light 3229.3.3 Using a Cavity to Measure Quadrature Squeezing 3249.3.4 Summary of Different Representations of Squeezed States 3259.3.5 Propagation of Squeezed Light 3259.4 Early Demonstrations of Squeezed Light 3309.4.1 Four Wave Mixing 3309.4.2 Optical Parametric Processes 3339.4.3 Second Harmonic Generation 3399.4.4 The Kerr Effect 3439.4.4.1 The Response of the Kerr Medium 3439.4.4.2 Optimizing the Kerr Effect 3459.4.4.3 Fibre Kerr Squeezing 3469.4.4.4 Atomic Kerr Squeezing 3489.4.4.5 Atomic Polarization Self-Rotation 3499.5 Pulsed Squeezing 3499.5.1 Quantum Noise of Optical Pulses 3499.5.2 Pulsed Squeezing Experiments with Kerr Media 3529.5.3 Pulsed SHG and OPO Experiments 3539.5.4 Soliton Squeezing 3549.5.5 Spectral Filtering 3559.5.6 Non-linear Interferometers 3569.6 Amplitude Squeezed Light from Diode Lasers 3589.7 Quantum State Tomography 3609.8 State of the Art of CW Squeezing 3639.9 Squeezing of Multiple Modes 3659.9.1 Twin-Photon Beams 3659.9.2 Polarization Squeezing 3679.9.3 Degenerate Multimode Squeezers 3689.10 Summary: Quantum Limits and Enhancement 370References 371Further Reading 37610 Applications of Quantum Light 37710.1 Quantum Enhanced Sensors 37710.1.1 Coherent Sensors and Sensitivity Scaling 37710.1.2 Practical Examples of Sensors 38010.1.3 Ultimate Sensing Limits 38210.1.4 Adaptive Phase Estimation 38410.2 Optical Communication 38410.3 Gravitational Wave Detection 38910.3.1 The Origin and Properties of GW 38910.3.1.1 Concept and Design of an Optical GW Detector 39210.3.2 Quantum Properties of the Ideal Interferometer 39310.3.2.1 Configurations of Interferometers 39610.3.2.2 Recycling 39710.3.2.3 Modulation Techniques 39810.3.3 The Sensitivity of GW Observatories 40010.3.3.1 Enhancement Below the SQL 40210.3.4 Interferometry with Squeezed Light 40510.3.4.1 Quantum Enhancement Beyond the SQL 41010.4 Quantum Enhanced Imaging 41110.4.1 Imaging with Photons on Demand 41110.4.2 Quantum Enhanced Coincidence Imaging 41210.5 Multimode Squeezing Enhancing Sensors 41410.5.1 Spatial Multimode Squeezing 41410.6 Summary and Outlook 419References 41911 QND 42511.1 QND Measurements of Quadrature Amplitudes 42511.2 Classification of QND Measurements 42711.3 Experimental Results 43011.4 Single-Photon QND 43211.4.1 Measurement-Based QND 434References 43712 Fundamental Tests of Quantum Mechanics 44112.1 Wave–Particle Duality 44112.2 Indistinguishability 44612.3 Non-locality 45312.3.1 Einstein–Podolsky–Rosen Paradox 45312.3.2 Characterization of Entangled Beams via Homodyne Detection 45812.3.2.1 Logarithmic Negativity and Two-Mode Squeezing 45912.3.2.2 Entanglement of Formation 46012.3.3 Bell Inequalities 46112.3.3.1 Long-Distance Bell Inequality Violations 46612.3.3.2 Loophole-Free Bell Inequality Violations 46612.4 Summary 468References 46813 Quantum Information 47313.1 Photons as Qubits 47313.1.1 Other Quantum Encodings 47513.2 Post-selection and Coincidence Counting 47513.3 True Single-Photon Sources 47713.3.1 Heralded Single Photons 47713.3.2 Single Photons on Demand 48013.4 Characterizing Photonic Qubits 48213.5 Quantum Key Distribution 48413.5.1 QKD Using Single Photons 48513.5.2 QKD Using Continuous Variables 48913.5.3 No Cloning 49213.6 Teleportation 49213.6.1 Teleportation of Photon Qubits 49313.6.2 Continuous Variable Teleportation 49513.6.3 Entanglement Swapping 50213.6.4 Entanglement Distillation 50213.7 Quantum Computation 50513.7.1 Dual-Rail Quantum Computing 50613.7.1.1 Quantum Circuits with Linear Optics 50713.7.1.2 Cluster States 51113.7.1.3 Quantum Gates with Non-linear Optics 51313.7.2 Single-Rail Quantum Computation 51413.7.2.1 Quantum Random Walks 51513.7.2.2 Boson Sampling 51613.7.3 Continuous Variable Quantum Computation 51813.7.3.1 Cat State Quantum Computing 51913.7.3.2 Continuous Variable Cluster States 52113.7.4 Large-Scale Quantum Computation 52213.8 Summary 525References 526Further Reading 53114 The Future: From Q-demonstrations to Q-technologies 53314.1 Demonstrating Quantum Effects 53314.2 Matter Waves and Atoms 53514.3 Q-Technology Based on Optics 53714.3.1 Applications of Squeezed Light 53714.3.2 Quantum Communication and Logic with Photons 53914.3.3 Cavity QED 54214.3.4 Extending to Other Wavelengths: Microwaves and Cryogenic Circuits 54214.3.5 Quantum Optomechanics 54214.3.6 Transfer of Quantum Information Between Different Physical Systems 54314.3.7 Transferring and Storing Quantum States 54414.4 Outlook 544References 545Further Reading 547Appendices 549Appendix A: List of Quantum Operators, States, and Functions 549Appendix B: Calculation of the Quantum Properties of a Feedback Loop 551Appendix C: Detection of Signal and Noise with an ESA 552Reference 554Appendix D: An Example of Analogue Processing of Photocurrents 554Appendix E: Symbols and Abbreviations 556Index 559