A Guide to Experiments in Quantum Optics

Transcription

1 Hans-A. Bachor and Timothy C. Ralph A Guide to Experiments in Quantum Optics Second, Revised and Enlarged Edition WILEY- VCH WILEY-VCH Verlag CmbH Co. KGaA

2 Contents Preface 1 Introduction 1.1 Historical perspective Motivation: Practical effects of quantum noise How to use this guide... 2 Classical models of light 2.1 Classical waves Mathematical description of waves The Gaussian beam Quadrature amplitudes Field energy, intensity. power A classical mode of light Classical modulations Statistical properties of classical light The origin of fluctuations Coherence Correlation functions Noise spectra An idealized classical case: Light from a chaotic source Photons -the motivation to go beyond classical optics 3.1 Detecting light The concept of photons Light from a thermal source Interference experiments Modelling single photon experiments Polarization of a single photon... Some mathematics Polarization states The single photon interferometer Intensity correlation, bunching, anti-bunching... XI

3 VI Contents 3.7 Single photon Rabi frequencies Quantum models of light 4.1 Quantization of light Some general comments on quantum mechanics Quantization of cavity modes Quantized energy The quantum mechanical harmonic oscillator Quantum states of light Number or Fock states Coherent states Mixed states Quantum optical representations Quadrature amplitude operators Probability and quasi-probability distributions Photon number distributions, Fano factor Propagation and detection of quantum optical fields Propagation in quantum optics Detection in quantum optics An example: The beamsplitter Quantum transfer functions A linearized quantum noise description An example: The propagating coherent state Real laser beams The transfer of operators, signals and noise Sideband modes as quantum states Quantum correlations Photon correlations Quadrature correlations Summary: The different quantum models Basic optical components 5.1 Beamsplitters Classical description of a beamsplitter The beamsplitter in the quantum operator model The beamsplitter with single photons The beamsplitter and the photon statistics The beamsplitter with coherent states The beamsplitter in the noise sideband model Comparison between a beamsplitter and a classical current junction. 5.2 Interferometers Classical description of an interferometer Quantum model of the interferometer

4 Contents VI The single photon interferometer Transfer of intensity noise through the interferometer Sensitivity limit of an interferometer Cavities Classical description of a linear cavity The special case of high reflectivities The phase response Spatial properties of cavities Equations of motion for the cavity mode The quantum equations of motion for a cavity The propagation of fluctuations through the cavity Single photons through a cavity Other optical components Lenses Crystals and polarizers Modulators Optical fibres Optical noise sources Nonlinear processes Lasers and Amplifiers The laser concept Technical specifications of a laser Rate equations Quantum model of a laser Examples of lasers Laser phase noise Amplification of optical signals Parametric amplifiers and oscillators The second-order non-linearity Parametric amplification Optical parametric oscillator Pair production Summary Photodetection techniques Photodetector characteristics Detecting single photons Photon sources and analysis Detecting photocurrents The detector circuit Spectral analysis of photocurrents

5 VI11 Contents 8 Quantum noise: Basic measurements and techniques Detection and calibration of quantum noise Direct detection and calibration Balanced detection Detection of intensity modulation and SNR Homodyne detection Heterodyne detection Intensity noise The intensity noise eater Classical intensity control Quantum noise control Frequency stabilization, locking of cavities How to mount a mirror Injection locking Squeezing experiments The concept of squeezing Tools for squeezing, two simple examples Properties of squeezed states Quantum model of squeezed states The formal definition of a squeezed state The generation of squeezed states Squeezing as correlations between noise sidebands Detecting squeezed light Reconstructing the squeezing ellipse Summary of different representations of squeezed states Propagation of squeezed light Four wave mixing Optical parametric processes Second harmonic generation Kerr effect The response of the Kerr medium Fibre Kerr Squeezing Atomic Kerr squeezing Atom-cavity coupling Pulsed squeezing Quantum noise of optical pulses Pulsed squeezing experiments with Kerr media Pulsed SHG and OPO experiments Soliton squeezing Spectral filtering Nonlinear interferometers Amplitude squeezed light from diode lasers Twin photon beams

6 Contents IX 9.12 Polarization squeezing Quantum state tomography Summary of squeezing results Loopholes in the quantum description Applications of squeezed light Optical communication... 3 IO 10.2 Spatial squeezing and quantum imaging Optical sensors Gravitational wave detection The origin and properties of GW Quantum properties of the ideal interferometer The sensitivity of real instruments Interferometry with squeezed light QND The concept of QND measurements Classification of QND measurements Experimental results Single photon QND Fundamental tests of quantum mechanics Wave-Particle duality Indistinguishability Nonlocality Einstein-Podolsky-Rosen Paradox Generation of entangled CW beams Bell inequalities Summary I 13 Quantum Information Photons as qubits Postselection and coincidence counting True single photon sources Heralded single photons Single photons on demand Characterizing photonic qubits Quantum key distribution QKD using single photons QKD using continuous variables No cloning

7 X Contents 13.6 Teleportation Teleportation of photon qubits Continuous variable teleportation Quantum computation Summary Summary and outlook Appendices 407 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 of the quantum properties of a feedback loop Appendix E: Symbols and abbreviations Index 416