| Introduction | p. 1 |
| Quantisation of the Electromagnetic Field | p. 7 |
| Field Quantisation | p. 7 |
| Fock or Number States | p. 10 |
| Coherent States | p. 12 |
| Squeezed States | p. 15 |
| Two-Photon Coherent States | p. 18 |
| Variance in the Electric Field | p. 20 |
| Multimode Squeezed States | p. 22 |
| Phase Properties of the Field | p. 23 |
| Exercises | p. 26 |
| References | p. 26 |
| Further Reading | p. 27 |
| Coherence Properties of the Electromagnetic Field | p. 29 |
| Field-Correlation Functions | p. 29 |
| Properties of the Correlation Functions | p. 31 |
| Correlation Functions and Optical Coherence | p. 32 |
| First-Order Optical Coherence | p. 34 |
| Coherent Field | p. 37 |
| Photon Correlation Measurements | p. 38 |
| Quantum Mechanical Fields | p. 41 |
| Squeezed State | p. 42 |
| Squeezed Vacuum | p. 44 |
| Phase-Dependent Correlation Functions | p. 44 |
| Photon Counting Measurements | p. 46 |
| Classical Theory | p. 46 |
| Constant Intensity | p. 48 |
| Fluctuating Intensity-Short-Time Limit | p. 48 |
| Quantum Mechanical Photon Count Distribution | p. 50 |
| Coherent Light | p. 51 |
| Chaotic Light | p. 51 |
| Photo-Electron Current Fluctuations | p. 52 |
| Exercises | p. 54 |
| References | p. 55 |
| Further Reading | p. 55 |
| Representations of the Electromagnetic Field | p. 57 |
| Expansion in Number States | p. 57 |
| Expansion in Coherent States | p. 58 |
| P Representation | p. 58 |
| Wigner's Phase-Space Density | p. 62 |
| Q Function | p. 65 |
| R Representation | p. 67 |
| Generalized P Representations | p. 68 |
| Positive P Representation | p. 71 |
| Exercises | p. 72 |
| References | p. 72 |
| Quantum Phenomena in Simple Systems in Nonlinear Optics | p. 73 |
| Single-Mode Quantum Statistics | p. 73 |
| Degenerate Parametric Amplifier | p. 73 |
| Photon Statistics | p. 75 |
| Wigner Function | p. 76 |
| Two-Mode Quantum Correlations | p. 77 |
| Non-degenerate Parametric Amplifier | p. 77 |
| Squeezing | p. 80 |
| Quadrature Correlations and the Einstein-Podolsky-Rosen Paradox | p. 82 |
| Wigner Function | p. 83 |
| Reduced Density Operator | p. 84 |
| Quantum Limits to Amplification | p. 86 |
| Amplitude Squeezed State with Poisson Photon Number Statistics | p. 88 |
| Exercises | p. 91 |
| References | p. 91 |
| Stochastic Methods | p. 93 |
| Master Equation | p. 93 |
| Equivalent c-Number Equations | p. 99 |
| Photon Number Representation | p. 99 |
| P Representation | p. 100 |
| Properties of Fokker-Planck Equations | p. 102 |
| Steady State Solutions - Potential Conditions | p. 103 |
| Time Dependent Solution | p. 104 |
| Q Representation | p. 105 |
| Wigner Function | p. 107 |
| Generalized P Representation | p. 109 |
| Stochastic Differential Equations | p. 112 |
| Use of the Positive P Representation | p. 115 |
| Linear Processes with Constant Diffusion | p. 116 |
| Two Time Correlation Functions in Quantum Markov Processes | p. 117 |
| Quantum Regression Theorem | p. 118 |
| Application to Systems with a P Representation | p. 118 |
| Stochastic Unravellings | p. 119 |
| Simulating Quantum Trajectories | p. 123 |
| Exercises | p. 124 |
| References | p. 125 |
| Further Reading | p. 125 |
| Input-Output Formulation of Optical Cavities | p. 127 |
| Cavity Modes | p. 127 |
| Linear Systems | p. 131 |
| Two-Sided Cavity | p. 132 |
| Two Time Correlation Functions | p. 133 |
| Spectrum of Squeezing | p. 135 |
| Parametric Oscillator | p. 136 |
| Squeezing in the Total Field | p. 138 |
| Fokker-Planck Equation | p. 138 |
| Exercises | p. 141 |
| References | p. 141 |
| Further Reading | p. 141 |
| Generation and Applications of Squeezed Light | p. 143 |
| Parametric Oscillation and Second Harmonic Generation | p. 143 |
| Semi-Classical Steady States and Stability Analysis | p. 145 |
| Parametric Oscillation | p. 146 |
| Second Harmonic Generation | p. 146 |
| Squeezing Spectrum | p. 147 |
| Parametric Oscillation | p. 148 |
| Experiments | p. 149 |
| Twin Beam Generation and Intensity Correlations | p. 151 |
| Second Harmonic Generation | p. 156 |
| Experiments | p. 157 |
| Applications of Squeezed Light | p. 158 |
| Interferometric Detection of Gravitational Radiation | p. 158 |
| Sub-Shot-Noise Phase Measurements | p. 171 |
| Quantum Information | p. 173 |
| Exercises | p. 174 |
| References | p. 174 |
| Further Reading | p. 175 |
| Nonlinear Quantum Dissipative Systems | p. 177 |
| Optical Parametric Oscillator: Complex P Function | p. 177 |
| Optical Parametric Oscillator: Positive P Function | p. 181 |
| Quantum Tunnelling Time | p. 186 |
| Dispersive Optical Bistability | p. 190 |
| Comment on the Use of the Q and Wigner Representations | p. 192 |
| Exercises | p. 192 |
| Appendix | p. 193 |
| Evaluation of Moments for the Complex P function for Parametric Oscillation (9.17) | p. 193 |
| Evaluation of the Moments for the Complex P Function for Optical Bistability (9.48) | p. 194 |
| References | p. 195 |
| Further Reading | p. 195 |
| Interaction of Radiation with Atoms | p. 197 |
| Quantization of the Many-Electron System | p. 197 |
| Interaction of a Single Two-Level Atom with a Single Mode Field | p. 201 |
| Spontaneous Emission from a Two-Level Atom | p. 203 |
| Phase Decay in a Two-Level System | p. 204 |
| Resonance Fluorescence | p. 205 |
| Exercises | p. 210 |
| References | p. 210 |
| Further Reading | p. 211 |
| CQED | p. 213 |
| Cavity QED | p. 213 |
| Vacuum Rabi Splitting | p. 217 |
| Single Photon Sources | p. 218 |
| Cavity QED with N Atoms | p. 221 |
| Circuit QED | p. 225 |
| Exercises | p. 227 |
| References | p. 228 |
| Further Reading | p. 229 |
| Quantum Theory of the Laser | p. 231 |
| Master Equation | p. 231 |
| Photon Statistics | p. 233 |
| Spectrum of Intensity Fluctuations | p. 234 |
| Laser Linewidth | p. 237 |
| Regularly Pumped Laser | p. 238 |
| Appendix: Derivation of the Single-Atom Increment | p. 242 |
| Exercises | p. 245 |
| References | p. 245 |
| Bells Inequalities in Quantum Optics | p. 247 |
| The Einstein-Podolsky-Rosen (EPR) Argument | p. 247 |
| Bell Inequalities and the Aspect Experiment | p. 248 |
| Violations of Bell's Inequalities Using a Parametric Amplifier Source | p. 254 |
| One-Photon Interference | p. 259 |
| Exercises | p. 264 |
| References | p. 264 |
| Quantum Nondemolition Measurements | p. 267 |
| Concept of a QND Measurement | p. 268 |
| Back Action Evasion | p. 270 |
| Criteria for a QND Measurement | p. 270 |
| The Beam Splitter | p. 273 |
| Ideal Quadrature QND Measurements | p. 276 |
| Experimental Realisation | p. 277 |
| A Photon Number QND Scheme | p. 279 |
| Exercises | p. 281 |
| References | p. 282 |
| Quantum Coherence and Measurement Theory | p. 283 |
| Quantum Coherence | p. 283 |
| The Effect of Dissipation | p. 288 |
| Experimental Observation of Coherence Decay | p. 291 |
| Quantum Measurement Theory | p. 293 |
| General Measurement Theory | p. 294 |
| The Pointer Basis | p. 296 |
| Examples of Pointer Observables | p. 299 |
| Model of a Measurement | p. 299 |
| Conditional States and Quantum Trajectories | p. 302 |
| Homodyne Measurement of a Cavity Field | p. 303 |
| Exercises | p. 305 |
| References | p. 306 |
| Quantum Information | p. 307 |
| Introduction | p. 307 |
| The Qubit | p. 308 |
| Entanglement | p. 310 |
| Quantum Key Distribution | p. 312 |
| Quantum Teleportation | p. 318 |
| Quantum Computation | p. 324 |
| Linear Optical Quantum Gates | p. 327 |
| Single Photon Sources | p. 336 |
| Exercises | p. 343 |
| References | p. 344 |
| Further Reading | p. 346 |
| Ion Traps | p. 347 |
| Introduction | p. 347 |
| Trapping and Cooling | p. 347 |
| Novel Quantum States | p. 353 |
| Trapping Multiple Ions | p. 356 |
| Ion Trap Quantum Information Processing | p. 359 |
| Exercises | p. 362 |
| References | p. 363 |
| Light Forces | p. 365 |
| Radiative Forces in the Semiclassical Limit | p. 366 |
| Mean Force for a Two-Level Atom Initially at Rest | p. 368 |
| Friction Force for a Moving Atom | p. 371 |
| Laser Standing Wave-Doppler Cooling | p. 372 |
| Dressed State Description of the Dipole Force | p. 374 |
| Atomic Diffraction by a Standing Wave | p. 377 |
| Optical Stern-Gerlach Effect | p. 381 |
| Quantum Chaos | p. 385 |
| Dynamical Tunnelling | p. 387 |
| Dynamical Localisation | p. 389 |
| The Effect of Spontaneous Emission | p. 390 |
| References | p. 394 |
| Further Reading | p. 395 |
| Bose-Einstein Condensation | p. 397 |
| Hamiltonian: Binary Collision Model | p. 398 |
| Mean-Field Theory - Gross-Pitaevskii Equation | p. 399 |
| Single Mode Approximation | p. 400 |
| Quantum State of the Condensate | p. 401 |
| Quantum Phase Diffusion: Collapses and Revivals of the Condensate Phase | p. 401 |
| Interference of Two Bose-Einstein Condensates and Measurement-Induced Phase | p. 405 |
| Interference of Two Condensates Initially in Number States | p. 405 |
| Quantum Tunneling of a Two Component Condensate | p. 409 |
| Semiclassical Dynamics | p. 411 |
| Quantum Dynamics | p. 414 |
| Coherence Properties of Bose-Einstein Condensates | p. 416 |
| 1st Order Coherence | p. 416 |
| Higher Order Coherence | p. 417 |
| Exercises | p. 419 |
| References | p. 419 |
| Further Reading | p. 420 |
| Index | p. 421 |
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