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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 | |