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.1 Introduction.1.1 Historical perspective.1.2 Motivation: Practical effects of quantum noise.1.3 How to use this guide.Bibliography.2 Classical models of light.2.1 Classical waves.2.1.1 Mathematical description of waves.2.1.2 The Gaussian beam.2.1.3 Quadrature amplitudes.2.1.4 Field energy, intensity, power.2.1.5 A classical mode of light.2.1.6 Classical modulations.2.2 Statistical properties of classical light.2.2.1 The origin of fluctuations.2.2.2 Coherence.2.2.3 Correlation functions.2.2.4 Noise spectra.2.2.5 An idealized classical case: Light from a chaotic source.Bibliography.3 Photons - the motivation to go beyond classical optics.3.1 Detecting light.3.2 The concept of photons.3.3 Light from a thermal source.3.4 Interference experiments.3.5 Model ling single photon experiments.3.5.1 Polarization of a single photon.3.5.2 Some mathematics.3.5.3 Polarization states.3.5.4 The single photon interferometer.3.6 Intensity correlation, bunching, anti-bunching.3.7 Single photon Rabi frequencies.Bibliography.4 Quantum models of light.4.1 Quantization of light.4.1.1 Some general comments on quantum mechanics.4.1.2 Quantization of cavity modes.4.1.3 Quantized energy.4.1.4 The quantum mechanical harmonic oscillator.4.2 Quantum statesof light.4.2.1 Number or Fock states.4.2.2 Coherent states.4.2.3 Mixed states.4.3 Quantum optical representations.4.3.1 Quadrature amplitude operators.4.3.2 Probability and quasi-probability distributions.4.3.3 Photon number distributions, Fano factor.4.4 Propagation and detection of quantum optical fields.4.4.1 Propagation in quantum optics.4.4.2 Detection in quantum optics.4.4.3 An example: The beam splitter.4.5 Quantum transfer functions.4.5.1 A linearized quantum noise description.4.5.2 An example: The propagating coherent state.4.5.3 Real laser beams.4.5.4 The transfer of operators, signals and noise.4.5.5 Side band modes as quantum states.4.6 Quantum correlations.4.6.1 Photon correlations.4.6.2 Quadrature correlations.4.7 Summary: The different quantum models.Bibliography.5 Basic optical components.5.1 Beamsplitters.5.1.1 Classical description of a beamsplitter.5.1.2 The beamsplitter in the quantum operator model.5.1.3 The beamsplitter with single photons.5.1.4 The beamsplitter and the photon statistics.5.1.5 The beamsplitter with coherent states.5.1.6 The beamsplitter in the noise sideband model.5.1.7 Comparison between a beamsplitter and a classical current junction.5.2 Interferometers.5.2.1 Classical description of an interferometer.5.2.2 Quantum model of the interferometer.5.2.3 The single photon interferometer.5.2.4 Transfer of intensity noise through the interferometer.5.2.5 Sensitivity limit of an interferometer.5.3 Cavities.5.3.1 Classical description of a linear cavity.5.3.2 The special case of high reflectivities.5.3.3 The phase response.5.3.4 Spatial properties of cavities.5.3.5 Equations of motion for the cavity mode.5.3.6 The quantum equations of motion for a cavity.5.3.7 The propagation of fluctuations through the cavity.5.3.8 Single photons through a cavity.5.4 Other optical components.5.4.1 Lenses.5.4.2 Crystals and polarizers.5.4.3 Modulators.5.4.4 Optical fibres.5.4.5 Optical noise sources.5.4.6 Nonlinear processes.Bibliography.6 Lasers and Amplifiers.6.1 The laser concept.6.1.1 Technical specifications of a laser.6.1.2 Rate equations.6.1.3 Quantum model of a laser.6.1.4 Examples of lasers.6.1.5 Laser phase noise.6.2 Amplification of optical signals.6.3 Parametric amplifiers and oscillators.6.3.1 The second-order non-linearity.6.3.2 Parametric amplification.6.3.3 Optical parametric oscillator.6.3.4 Pair production.6.4 Summary.Bibliography.7 Photodetection techniques.7.1 Photodetector characteristics.7.2 Detecting single photons.7.3 Photon sources and analysis.7.4 Detecting photocurrents.7.4.1 The detector circuit.7.5 Spectral analysis of photocurrents.Bibliography.8 Quantum noise: Basic measurements and techniques.8.1 Detection and calibration of quantum noise.8.1.1 Direct detection and calibration.8.1.2 Balanced detection.8.1.3 Detection of intensity modulation and SNR.8.1.4 Homodyne detection.8.1.5 Heterodyne detection.8.2 Intensity noise.8.3 The intensity noise eater.8.3.1 Classical intensity control.8.3.2 Quantum noise control.8.4 Frequency stabilization, locking of cavities.8.4.1 How to mount a mirror.8.5 Injection locking.Bibliography.9 Squeezing experiments.9.1 The concept of squeezing.9.1.1 Tools for squeezing, two simple examples.9.1.2 Properties of squeezed states .9.2 Quantum model of squeezed states.9.2.1 The formal definition of a squeezed state.9.2.2 The generation of squeezed states.9.2.3 Squeezing as correlations between noise sidebands.9.3 Detecting squeezed light.9.3.1 Reconstructing the squeezing ellipse.9.3.2 Summary of different representations of squeezed states.9.3.3 Propagation of squeezed light.9.4 Four wave mixing.9.5 Optical parametric processes.9.6 Second harmonic generation.9.7 Kerr effect.9.7.1 The response of the Kerr medium.9.7.2 Fibre Kerr Squeezing.9.7.3 Atomic Kerr squeezing.9.8 Atom-cavity coupling.9.9 Pulsed squeezing.9.9.1 Quantum noise of optical pulses.9.9.2 Pulsed squeezing experiments with Kerr media.9.9.3 Pulsed SHG and OPO experiments.9.9.4 Soliton squeezing.9.9.5 Spectral filtering.9.9.6 Nonlinear interferometers.9.10 Amplitude squeezed light from diode lasers.9.11 Twin photon beams.9.12 Polarization squeezing.9.13 Quantum state tomography.9.14 Summary of squeezing results.9.14.1 Loopholes in the quantum description.Bibliography.10 Applications of squeezed light.10.1 Optical communication.10.2 Spatial squeezing and quantum imaging.10.3 Optical sensors.10.4 Gravitational wave detection.10.4.1 The origin and properties of GW.10.4.2 Quantum properties of the ideal interferometer.10.4.3 The sensitivityof real instruments.10.4.4 Interferometry with squeezed light.Bibliography.11 QND.11.1 The concept of QND measurements.11.2 Classification of QND measurements.11.3 Experimental results.11.4 Single photon QND.Bibliography.12 Fundamental tests of quantum mechanics.12.1 Wave-Particle duality.12.2 Indistinguishability.12.3 Nonlocality.12.3.1 Einstein-Podolsky-Rosen Paradox.12.3.2 Generation of entangled CW beams.12.3.3 Bell inequalities.12.4 Summary.Bibliography.13 Quantum Information.13.1 Photons asqubits.13.2 Postselection and coincidence counting.13.3 True single photon sources.13.3.1 Heralded single photons.13.3.2 Single photons on demand.13.4 Characterizing photonic qubits.13.5 Quantum key distribution.13.5.1 QKD using single photons.13.5.2 QKD using continuous variables.13.5.3 Nocloning.13.6 Teleportation.13.6.1 Teleportation of photon qubits.13.6.2 Continuous variable teleportation.13.7 Quantum computation.13.8 Summary.Bibliography.14 Summary and outlook.15 Appendices.Appendix A: Gaussian functions.Appendix B: List of quantum operators, states and functions.Appendix C: The full quantum derivation of quantum states.Appendix D: Calculation of the quantum properties of a feedback loop.Appendix E: Symbols and abbreviations.Index.