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- ISBN: 9783540285731 | 3540285733
- Cover: Hardcover
- Copyright: 2/3/2008
Quantum Optics gives a comprehensive coverage of developments in quantum optics over the past years. In the early chapters the formalism of quantum optics is elucidated and the main techniques are introduced. These are applied in the later chapters to problems such as squeezed states of light, resonance fluorescence, laser theory, quantum theory of four-wave mixing, quantum non-demolition measurements, Bell's inequalities, and atom optics. Experimental results are used to illustrate the theory throughout. This yields the most comprehensive and up-to-date coverage of experiment and theory in quantum optics in any textbook.
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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