A Guide to Experiments in Quantum Optics

This revised and broadened second edition provides readers with an insight into this fascinating world and future technology in quantum optics. Alongside classical and quantum-mechanical models, the authors focus on important and current experimental techniques in quantum optics to provide an understanding of light, photons and laserbeams. In a comprehensible and lucid style, the book conveys the theoretical background indispensable for an understanding of actual experiments using photons. It covers basic modern optical components and procedures in detail, leading to experiments such as the generation of squeezed and entangled laserbeams, the test and applications of the quantum properties of single photons, and the use of light for quantum information experiments.

Table of Contents:
Preface XI 1 Introduction 1 1.1 Historical perspective 1 1.2 Motivation: Practical effects of quantum noise 3 1.3 How to use this guide 8 Bibliography 10 2 Classical models of light 12 2.1 Classical waves 13 2.1.1 Mathematical description of waves 13 2.1.2 The Gaussian beam 14 2.1.3 Quadrature amplitudes 16 2.1.4 Field energy, intensity, power 18 2.1.5 A classical mode of light 19 2.1.6 Classical modulations 20 2.2 Statistical properties of classical light 23 2.2.1 The origin of fluctuations 23 2.2.2 Coherence 23 2.2.3 Correlation functions 27 2.2.4 Noise spectra 29 2.2.5 An idealized classical case: Light from a chaotic source 31 Bibliography 36 3 Photons – the motivation to go beyond classical optics 37 3.1 Detecting light 37 3.2 The concept of photons 40 3.3 Light from a thermal source 41 3.4 Interference experiments 43 3.5 Modelling single photon experiments 46 3.5.1 Polarization of a single photon 47 3.5.2 Some mathematics 49 3.5.3 Polarization states 50 3.5.4 The single photon interferometer 51 3.6 Intensity correlation, bunching, anti-bunching 53 3.7 Single photon Rabi frequencies 56 Bibliography 57 4 Quantum models of light 60 4.1 Quantization of light 60 4.1.1 Some general comments on quantum mechanics 60 4.1.2 Quantization of cavity modes 61 4.1.3 Quantized energy 62 4.1.4 The quantum mechanical harmonic oscillator 63 4.2 Quantum states of light 64 4.2.1 Number or Fock states 64 4.2.2 Coherent states 65 4.2.3 Mixed states 68 4.3 Quantum optical representations 68 4.3.1 Quadrature amplitude operators 68 4.3.2 Probability and quasi-probability distributions 70 4.3.3 Photon number distributions, Fano factor 75 4.4 Propagation and detection of quantum optical fields 77 4.4.1 Propagation in quantum optics 77 4.4.2 Detection in quantum optics 81 4.4.3 An example: The beam splitter 82 4.5 Quantum transfer functions 84 4.5.1 A linearized quantum noise description 84 4.5.2 An example: The propagating coherent state 86 4.5.3 Real laser beams 87 4.5.4 The transfer of operators, signals and noise 88 4.5.5 Side band modes as quantum states 90 4.6 Quantum correlations 92 4.6.1 Photon correlations 92 4.6.2 Quadrature correlations 93 4.7 Summary: The different quantum models 95 Bibliography 97 5 Basic optical components 99 5.1 Beam splitters 99 5.1.1 Classical description of a beam splitter 99 5.1.2 The beam splitter in the quantum operator model 102 5.1.3 The beam splitter with single photons 104 5.1.4 The beam splitter and the photon statistics 106 5.1.5 The beam splitter with coherent states 108 5.1.6 The beam splitter in the noise sideband model 110 5.1.7 Comparison between a beam splitter and a classical current junction 111 5.2 Interferometers 112 5.2.1 Classical description of an interferometer 113 5.2.2 Quantum model of the interferometer 115 5.2.3 The single photon interferometer 115 5.2.4 Transfer of intensity noise through the interferometer 116 5.2.5 Sensitivity limit of an interferometer 117 5.3 Cavities 119 5.3.1 Classical description of a linear cavity 121 5.3.2 The special case of high reflectivities 125 5.3.3 The phase response 126 5.3.4 Spatial properties of cavities 128 5.3.5 Equations of motion for the cavity mode 132 5.3.6 The quantum equations of motion for a cavity 133 5.3.7 The propagation of fluctuations through the cavity 133 5.3.8 Single photons through a cavity 137 5.4 Other optical components 138 5.4.1 Lenses 138 5.4.2 Crystals and polarizers 140 5.4.3 Modulators 141 5.4.4 Optical fibres 143 5.4.5 Optical noise sources 143 5.4.6 Nonlinear processes 144 Bibliography 145 6 Lasers and Amplifiers 147 6.1 The laser concept 147 6.1.1 Technical specifications of a laser 148 6.1.2 Rate equations  150 6.1.3 Quantum model of a laser 154 6.1.4 Examples of lasers 156 6.1.5 Laser phase noise 161 6.2 Amplification of optical signals 162 6.3 Parametric amplifiers and oscillators 164 6.3.1 The second-order non-linearity 165 6.3.2 Parametric amplification 167 6.3.3 Optical parametric oscillator 168 6.3.4 Pair production 169 6.4 Summary 171 Bibliography  171 7 Photo detection techniques 173 7.1 Photodetector characteristics 173 7.2 Detecting single photons 174 7.3 Photon sources and analysis 178 7.4 Detecting photocurrents 180 7.4.1 The detector circuit 184 7.5 Spectral analysis of photocurrents 187 Bibliography 197 8 Quantum noise: Basic measurements and techniques 200 8.1 Detection and calibrationo f quantum noise 200 8.1.1 Direct detection and calibration 200 8.1.2 Balanced detection 204 8.1.3 Detection of intensity modulation and SNR 205 8.1.4 Homodyne detection 206 8.1.5 Heterodyne detection 210 8.2 Intensity noise 211 8.3 The intensity noise eater 212 8.3.1 Classical intensity control .213 8.3.2 Quantum noise control 216 8.4 Frequency stabilization, locking of cavities 221 8.4.1 How to mount a mirror 225 8.5 Injection locking 226 Bibliography 229 9 Squeezing experiments 232 9.1 The concept of squeezing 232 9.1.1 Tools for squeezing, two simple examples 232 9.1.2 Properties of squeezed states 238 9.2 Quantum model of squeezed states 242 9.2.1 The formal definition of a squeezed state 242 9.2.2 The generation of squeezed states 245 9.2.3 Squeezing as correlations between noise sidebands 247 9.3 Detecting squeezed light 250 9.3.1 Reconstructing the squeezing ellipse 253 9.3.2 Summary of different representations of squeezed states 254 9.3.3 Propagation of squeezed light 254 9.4 Four wave mixing 260 9.5 Optical parametric processes 263 9.6 Second harmonic generation 267 9.7 Kerr effect 275 9.7.1 The response of the Kerr medium 275 9.7.2 Fibre Kerr Squeezing 277 9.7.3 Atomic Kerr squeezing 279 9.8 Atom-cavity coupling 280 9.9 Pulsed squeezing 283 9.9.1 Quantum noise of optical pulses 283 9.9.2 Pulsed squeezing experiments with Kerr media 285 9.9.3 Pulsed SHG and OPO experiments 287 9.9.4 Soliton squeezing 288 9.9.5 Spectral filtering 289 9.9.6 Nonlinear interferometers 290 9.10 Amplitude squeezed light from diode lasers 292 9.11 Twin photon beams 294 9.12 Polarization squeezing 295 9.13 Quantum state tomography 298 9.14 Summary of squeezing results 300 9.14.1 Loopholes in the quantum description 303 Bibliography 303 10 Applications of squeezed light 310 10.1 Optical communication 310 10.2 Spatial squeezing and quantum imaging 313 10.3 Optical sensors 315 10.4 Gravitational wave detection 321 10.4.1 The origin and properties of GW 321 10.4.2 Quantum properties of the ideal interferometer 323 10.4.3 The sensitivity of real instruments 328 10.4.4 Interferometry with squeezed light 333 Bibliography 338 11 QND 343 11.1 The concept of QND measurements 343 11.2 Classification of QND measurements 346 11.3 Experimental results 348 11.4 Single photon QND 350 Bibliography 353 12 Fundamental tests of quantum mechanics 355 12.1 Wave-Particle duality 355 12.2 Indistinguishability 358 12.3 Nonlocality 362 12.3.1 Einstein-Podolsky-Rosen Paradox 362 12.3.2 Generation of entangled CW beams 365 12.3.3 Bell inequalities 367 12.4 Summary 371 Bibliography 371 13 Quantum Information 374 13.1 Photons as qubits 374 13.2 Post selection and coincidence counting 376 13.3 True single photon sources 377 13.3.1 Heralded single photons 377 13.3.2 Single photons on demand 379 13.4 Characterizing photonic qubits 381 13.5 Quantum key distribution 382 13.5.1 QKD using single photons 383 13.5.2 QKD using continuous variables 385 13.5.3 No cloning 387 13.6 Teleportation 387 13.6.1 Teleportation of photon qubits 388 13.6.2 Continuous variable teleportation 390 13.7 Quantum computation 395 13.8 Summary 400 Bibliography 401 14 Summary and outlook 404 15 Appendices 407 Appendix A: Gaussian functions 407 Appendix B: List of quantum operators, states and functions 408 Appendix C: The full quantum derivation of quantum states 410 Appendix D: Calculation of the quantum properties of a feedback loop 412 Appendix E: Symbols and abbreviations 414 Index 416

About the Author :
Hans-A. Bachor received his degrees in physics from the Universität Hannover, Germany. Since 1981 he has worked and taught at the Australian National University, Canberra, Australia where he is now Professor and Director of the Australian Centre of Excellence in Quantum-Atom Optics. The focus of his work are experiments with nonclassical light. Timothy C. Ralph graduated from Macquarie University, Australia and received his PhD from the Australian National University. He is presently Associate Professor at the University of Queensland, Brisbane, Australia. He is also scientific manager for the Queensland node of the Australian Centre of Excellence for Quantum Computer Technology. The focus of his work is quantum information in optics.

Review :
"...I find it extremely useful and timely, for all the people who have received a solid education in classical optics and who feel the need to understand "what's going on" in quantum optics, what means "below the standard quantum limit" etc... I like very much your approach of starting from experimental schemes. One of the great qualities of this book is that it is "self-contained": the theoretical tools necessary to understand the experiments are given in a concise and useful way. I will recommend it to those of my students who look for an "hands on" introduction to quantum optics." Alain Aspect, Ecole Polytechnique, Orsay, France From the first Edition: "Compared to other books on this topic starting with theoretical background the stress here is put on the actual experiments and the underlying physics is explained in the intuitive way." V. Burjan jun (Praha) Zentralblatt für Mathematik, 27/2000 "The book focuses on a series of quantum optics experiments and what can be learnt from them. It provides a practical background in opto-electronics." ASLIB Book Guide, Vol. 63, No. 11, 1998 This particular book therefore comes as a somewhat refreshing change. Indeed it satisfies a need for a book which describes actual experiments with their limitations and at the same time providing accessible theoretical explanation. ... I certainly recommend postgraduate students in quantum optics to obtain access to this book. D. T. Pegg, Griffith University Australian & New Zealand Physicist, Vol. 35, Number 4, 1998 "Das Buch stellt eine wertvolle Hilfe dar, um einen ersten Einblick in Experimente der Quantenoptik zu erhalten. Viele Messtechniken werden anschaulich erklärt, und wertvolle Details zu den dabei verwendeten Apparaturen werden gegeben. Die zahlreichen Literaturhinweise bieten eine hervorragende Hilfe zur weiteren Vertiefung. ... Das Buch ist für eine erste Einführung in die experimentellen Aspekte der Quantenoptik sehr empfehlenswert." Physik Journal