| The Degenerate Parametric Oscillator I: Squeezed States | p. 1 |
| Introduction | p. 1 |
| Degenerate Parametric Amplification and Squeezed States | p. 4 |
| Degenerate Parametric Amplification Without Pump Depletion | p. 4 |
| Quantum Fluctuations and Squeezed States | p. 8 |
| The Degenerate Parametric Oscillator | p. 14 |
| Master Equation for the Degenerate Parametric Oscillator | p. 20 |
| Cavity Output Fields | p. 27 |
| The Spectrum of Squeezing | p. 31 |
| Intracavity Field Fluctuations | p. 32 |
| Definition of the Spectrum of Squeezing | p. 38 |
| Homodyne Detection: The Source-Field Spectrum of Squeezing | p. 40 |
| The Source-Field Spectrum of Squeezing with Unit Efficiency | p. 44 |
| Free-Field Contributions | p. 47 |
| Vacuum Fluctuations | p. 49 |
| Squeezing in the Wigner Representation: A Comment on Interpretation | p. 54 |
| The Degenerate Parametric Oscillator II: Phase-Space Analysis in the Small-Noise Limit | p. 61 |
| Phase-Space Formalism for the Degenerate Parametric Oscillator | p. 61 |
| Phase-Space Equation of Motion in the P Representation | p. 62 |
| Phase-Space Equations of Motion in the Q and Wigner Representations | p. 66 |
| Squeezing: Quantum Fluctuations in the Small-Noise Limit | p. 71 |
| System Size Expansion Far from Threshold | p. 71 |
| Quantum Fluctuations Below Threshold | p. 74 |
| Quantum Fluctuations Above Threshold | p. 83 |
| Quantum Fluctuations at Threshold | p. 86 |
| The Positive P Representation | p. 95 |
| The Positive P Representation | p. 96 |
| The Characteristic Function and Associated Distribution | p. 98 |
| Fokker-Planck Equation for the Degenerate Parametric Oscillator | p. 103 |
| Linear Theory of Quantum Fluctuations | p. 112 |
| Miscellaneous Topics | p. 117 |
| Alternative Approaches to the Linear Theory of Quantum Fluctuations | p. 117 |
| Dynamical Stability of the Classical Phase Space | p. 124 |
| Preservation of Conjugacy for Stochastic Averages | p. 127 |
| The Degenerate Parametric Oscillator III: Phase-Space Analysis Outside the Small-Noise Limit | p. 133 |
| The Degenerate Parametric Oscillator with Adiabatic Elimination of the Pump | p. 134 |
| Adiabatic Elimination in the Stochastic Differential Equations | p. 135 |
| A Note About Superoperators | p. 138 |
| Adiabatic Elimination in the Master Equation | p. 141 |
| Numerical Simulation of the Stochastic Differential Equations | p. 145 |
| Deterministic Dynamics in the Extended Phase Space | p. 151 |
| Steady-State Solution for the Positive P Distribution | p. 156 |
| Quantum Fluctuations and System Size | p. 160 |
| Quantum Dynamics Beyond Classical Trajectories plus "Fuzz" | p. 169 |
| Higher-Order Corrections to the Spectrum of Squeezing at Threshold | p. 178 |
| Difficulties with the Positive P Representation | p. 181 |
| Technical Difficulties: Two-Photon Damping | p. 182 |
| Physical Interpretation: The Anharmonic Oscillator | p. 189 |
| Cavity QED I: Simple Calculations | p. 195 |
| System Size and Coupling Strength | p. 196 |
| Cavity QED in the Perturbative Limit | p. 198 |
| Cavity-Enhanced Spontaneous Emission | p. 202 |
| Cavity-Enhanced Resonance Fluorescence | p. 210 |
| Forwards Photon Scattering in the Weak-Excitation Limit | p. 217 |
| A One-Atom "Laser" | p. 222 |
| Nonperturbative Cavity QED | p. 231 |
| Spontaneous Emission from a Coupled Atom and Cavity | p. 232 |
| Vacuum Rabi Splitting | p. 239 |
| Vacuum Rabi Resonances in the Two-State Approximation | p. 243 |
| Many Atoms in a Cavity: Macroscopic Theory | p. 247 |
| Optical Bistability: Steady-State Transmission of a Nonlinear Fabry-Perot | p. 247 |
| The Mean-Field Limit for a Homogeneously Broadened Two-Level Medium | p. 253 |
| Steady State | p. 254 |
| Maxwell-Bloch Equations | p. 263 |
| Stability of the Steady State | p. 268 |
| Relationship Between Macroscopic and Microscopic Variables | p. 271 |
| Cavity QED with Many Atoms | p. 275 |
| Weak-Probe Transmission Spectra | p. 276 |
| A Comment on Spatial Effects | p. 280 |
| Many Atoms in a Cavity II: Quantum Fluctuations in the Small-Noise Limit | p. 285 |
| Microscopic Model | p. 286 |
| Master Equation for Optical Bistability | p. 286 |
| Fokker-Planck Equation in the P Representation | p. 287 |
| Fokker-Planck Equation in the Q Representation | p. 289 |
| Fokker-Planck Equation in the Wigner Representation | p. 292 |
| Linear Theory of Quantum Fluctuations | p. 298 |
| System Size Expansion for Optical Bistability | p. 299 |
| Linearization About the Steady State | p. 306 |
| Covariance Matrix for Absorptive Bistability | p. 312 |
| Atom-Atom Correlations | p. 317 |
| A Comment on Measures of Squeezing | p. 320 |
| Spectrum of the Transmitted Light in the Weak-Excitation Limit | p. 322 |
| Forwards Photon Scattering in the Weak-Excitation Limit | p. 330 |
| Cavity QED II: Quantum Fluctuations | p. 335 |
| Density Matrix Expansion for the Weak-Excitation Limit | p. 335 |
| Pure-State Factorization of the Density Operator for One Atom | p. 336 |
| Pure-State Factorization of the Density Operator for Many Atoms | p. 339 |
| Forwards Photon Scattering for N Atoms in a Cavity | p. 345 |
| Corrections to the Small-Noise Approximation | p. 350 |
| Antibunching of Fluorescence for One Atom in a Cavity | p. 352 |
| Spectra of Squeezing in the Weak-Excitation Limit | p. 357 |
| Spatial Effects | p. 360 |
| Beyond Classical Trajectories plus "Fuzz": Spontaneous Dressed-State Polarization | p. 368 |
| Maxwell-Bloch Equations for "Zero System Size" | p. 369 |
| Dressed Jaynes-Cummings Eigenstates | p. 376 |
| Secular Approximation in the Basis of Dressed Jaynes-Cummings Eigenstates | p. 383 |
| Spectrum of the Transmitted Light in the Strong-Coupling and Weak-Excitation Limits | p. 385 |
| The [square root]n Anharmonic Oscillator | p. 391 |
| Quantum Fluctuations for Strong Excitation | p. 395 |
| Quantum Trajectories I: Background and Interpretation | p. 401 |
| Density Operators and Scattering Records | p. 403 |
| Generalizing the Bohr-Einstein Quantum Jump | p. 410 |
| The Einstein Stochastic Process | p. 410 |
| Conditional Evolution: Trajectories for Known Initial States | p. 412 |
| Conditional Evolution: Trajectories for "Blind" Realizations | p. 415 |
| The Master Equation | p. 420 |
| Quantum Jumps in the Presence of Coherence | p. 422 |
| Miscellaneous Observations | p. 426 |
| Time Evolution Under Null Measurements | p. 426 |
| Conditional States and Nonlinearity | p. 429 |
| Record Probabilities and Norms | p. 430 |
| Monte Carlo Simulations | p. 431 |
| The Waiting-Time Distribution | p. 433 |
| Quantum Trajectories II: The Degenerate Parametric Oscillator | p. 437 |
| Scattering Records and Photoelectron Counting | p. 437 |
| Record Probabilities | p. 438 |
| Factorization for Pure Initial States | p. 446 |
| Unraveling the Density Operator | p. 447 |
| Photoelectron Counting Records | p. 447 |
| Homodyne-Current Records | p. 451 |
| Heterodyne-Current Records | p. 460 |
| Physical Interpretation | p. 466 |
| Systems, Environments, and Complementarity | p. 466 |
| Modeling Projective Measurements | p. 473 |
| Quantum Trajectories III; More Examples | p. 479 |
| Photon Scattering in the Weak-Excitation Limit | p. 479 |
| Unraveling the Density Operator: Cascaded Systems | p. 484 |
| System-Reservoir Interaction Hamiltonian | p. 486 |
| Reservoir Field | p. 487 |
| The Cascaded Systems Master Equation | p. 488 |
| Photoelectron Counting Unraveling | p. 491 |
| Coherent Driving Fields | p. 492 |
| Symmetric Irreversible Coupling | p. 497 |
| Optical Spectra | p. 499 |
| Optical Spectrum Using a Scanning Interferometer | p. 500 |
| Spontaneous Emission from a Driven Excited-State Doublet | p. 506 |
| Optical Spectrum Using Heterodyne Detection | p. 510 |
| References | p. 515 |
| Index | p. 527 |
| Table of Contents provided by Ingram. All Rights Reserved. |
