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Introduction | |

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Quantisation of the Electromagnetic Field | |

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Field Quantisation | |

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Fock or Number States | |

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Coherent States | |

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Squeezed States | |

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Two-Photon Coherent States | |

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Variance in the Electric Field | |

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Multimode Squeezed States | |

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Phase Properties of the Field | |

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Exercises | |

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References | |

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Further Reading | |

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Coherence Properties of the Electromagnetic Field | |

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Field-Correlation Functions | |

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Properties of the Correlation Functions | |

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Correlation Functions and Optical Coherence | |

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First-Order Optical Coherence | |

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Coherent Field | |

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Photon Correlation Measurements | |

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Quantum Mechanical Fields | |

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Squeezed State | |

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Squeezed Vacuum | |

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Phase-Dependent Correlation Functions | |

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Photon Counting Measurements | |

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Classical Theory | |

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Constant Intensity | |

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Fluctuating Intensity-Short-Time Limit | |

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Quantum Mechanical Photon Count Distribution | |

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Coherent Light | |

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Chaotic Light | |

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Photo-Electron Current Fluctuations | |

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Exercises | |

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References | |

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Further Reading | |

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Representations of the Electromagnetic Field | |

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Expansion in Number States | |

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Expansion in Coherent States | |

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P Representation | |

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Wigner's Phase-Space Density | |

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Q Function | |

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R Representation | |

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Generalized P Representations | |

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Positive P Representation | |

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Exercises | |

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References | |

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Quantum Phenomena in Simple Systems in Nonlinear Optics | |

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Single-Mode Quantum Statistics | |

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Degenerate Parametric Amplifier | |

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Photon Statistics | |

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Wigner Function | |

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Two-Mode Quantum Correlations | |

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Non-degenerate Parametric Amplifier | |

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Squeezing | |

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Quadrature Correlations and the Einstein-Podolsky-Rosen Paradox | |

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Wigner Function | |

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Reduced Density Operator | |

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Quantum Limits to Amplification | |

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Amplitude Squeezed State with Poisson Photon Number Statistics | |

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Exercises | |

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References | |

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Stochastic Methods | |

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Master Equation | |

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Equivalent c-Number Equations | |

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Photon Number Representation | |

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P Representation | |

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Properties of Fokker-Planck Equations | |

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Steady State Solutions - Potential Conditions | |

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Time Dependent Solution | |

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Q Representation | |

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Wigner Function | |

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Generalized P Representation | |

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Stochastic Differential Equations | |

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Use of the Positive P Representation | |

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Linear Processes with Constant Diffusion | |

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Two Time Correlation Functions in Quantum Markov Processes | |

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Quantum Regression Theorem | |

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Application to Systems with a P Representation | |

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Stochastic Unravellings | |

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Simulating Quantum Trajectories | |

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Exercises | |

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References | |

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Further Reading | |

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Input-Output Formulation of Optical Cavities | |

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Cavity Modes | |

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Linear Systems | |

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Two-Sided Cavity | |

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Two Time Correlation Functions | |

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Spectrum of Squeezing | |

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Parametric Oscillator | |

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Squeezing in the Total Field | |

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Fokker-Planck Equation | |

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Exercises | |

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References | |

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Further Reading | |

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Generation and Applications of Squeezed Light | |

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Parametric Oscillation and Second Harmonic Generation | |

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Semi-Classical Steady States and Stability Analysis | |

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Parametric Oscillation | |

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Second Harmonic Generation | |

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Squeezing Spectrum | |

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Parametric Oscillation | |

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Experiments | |

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Twin Beam Generation and Intensity Correlations | |

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Second Harmonic Generation | |

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Experiments | |

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Applications of Squeezed Light | |

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Interferometric Detection of Gravitational Radiation | |

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Sub-Shot-Noise Phase Measurements | |

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Quantum Information | |

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Exercises | |

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References | |

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Further Reading | |

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Nonlinear Quantum Dissipative Systems | |

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Optical Parametric Oscillator: Complex P Function | |

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Optical Parametric Oscillator: Positive P Function | |

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Quantum Tunnelling Time | |

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Dispersive Optical Bistability | |

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Comment on the Use of the Q and Wigner Representations | |

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Exercises | |

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Appendix | |

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Evaluation of Moments for the Complex P function for Parametric Oscillation (9.17) | |

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Evaluation of the Moments for the Complex P Function for Optical Bistability (9.48) | |

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References | |

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Further Reading | |

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Interaction of Radiation with Atoms | |

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Quantization of the Many-Electron System | |

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Interaction of a Single Two-Level Atom with a Single Mode Field | |

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Spontaneous Emission from a Two-Level Atom | |

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Phase Decay in a Two-Level System | |

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Resonance Fluorescence | |

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Exercises | |

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References | |

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Further Reading | |

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CQED | |

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Cavity QED | |

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Vacuum Rabi Splitting | |

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Single Photon Sources | |

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Cavity QED with N Atoms | |

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Circuit QED | |

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Exercises | |

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References | |

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Further Reading | |

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Quantum Theory of the Laser | |

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Master Equation | |

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Photon Statistics | |

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Spectrum of Intensity Fluctuations | |

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Laser Linewidth | |

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Regularly Pumped Laser | |

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Appendix: Derivation of the Single-Atom Increment | |

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Exercises | |

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References | |

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Bells Inequalities in Quantum Optics | |

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The Einstein-Podolsky-Rosen (EPR) Argument | |

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Bell Inequalities and the Aspect Experiment | |

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Violations of Bell's Inequalities Using a Parametric Amplifier Source | |

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One-Photon Interference | |

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Exercises | |

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References | |

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Quantum Nondemolition Measurements | |

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Concept of a QND Measurement | |

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Back Action Evasion | |

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Criteria for a QND Measurement | |

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The Beam Splitter | |

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Ideal Quadrature QND Measurements | |

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Experimental Realisation | |

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A Photon Number QND Scheme | |

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Exercises | |

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References | |

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Quantum Coherence and Measurement Theory | |

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Quantum Coherence | |

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The Effect of Dissipation | |

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Experimental Observation of Coherence Decay | |

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Quantum Measurement Theory | |

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General Measurement Theory | |

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The Pointer Basis | |

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Examples of Pointer Observables | |

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Model of a Measurement | |

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Conditional States and Quantum Trajectories | |

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Homodyne Measurement of a Cavity Field | |

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Exercises | |

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References | |

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Quantum Information | |

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Introduction | |

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The Qubit | |

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Entanglement | |

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Quantum Key Distribution | |

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Quantum Teleportation | |

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Quantum Computation | |

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Linear Optical Quantum Gates | |

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Single Photon Sources | |

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Exercises | |

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References | |

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Further Reading | |

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Ion Traps | |

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Introduction | |

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Trapping and Cooling | |

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Novel Quantum States | |

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Trapping Multiple Ions | |

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Ion Trap Quantum Information Processing | |

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Exercises | |

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References | |

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Light Forces | |

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Radiative Forces in the Semiclassical Limit | |

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Mean Force for a Two-Level Atom Initially at Rest | |

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Friction Force for a Moving Atom | |

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Laser Standing Wave-Doppler Cooling | |

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Dressed State Description of the Dipole Force | |

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Atomic Diffraction by a Standing Wave | |

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Optical Stern-Gerlach Effect | |

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Quantum Chaos | |

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Dynamical Tunnelling | |

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Dynamical Localisation | |

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The Effect of Spontaneous Emission | |

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References | |

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Further Reading | |

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Bose-Einstein Condensation | |

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Hamiltonian: Binary Collision Model | |

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Mean-Field Theory - Gross-Pitaevskii Equation | |

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Single Mode Approximation | |

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Quantum State of the Condensate | |

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Quantum Phase Diffusion: Collapses and Revivals of the Condensate Phase | |

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Interference of Two Bose-Einstein Condensates and Measurement-Induced Phase | |

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Interference of Two Condensates Initially in Number States | |

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Quantum Tunneling of a Two Component Condensate | |

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Semiclassical Dynamics | |

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Quantum Dynamics | |

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Coherence Properties of Bose-Einstein Condensates | |

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1st Order Coherence | |

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Higher Order Coherence | |

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Exercises | |

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References | |

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Further Reading | |

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Index | |