Quantum Optics

ISBN-13: 9783540588313 / Angielski / Miękka / 1995 / 351 str.

Opis

Quantum Optics gives a comprehensive coverage of developments in quantum optics over the past twenty 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.

Spis treści

1. Introduction.- 2. Quantisation of the Electromagnetic Field.- 2.1 Field Quantisation.- 2.2 Fock or Number States.- 2.3 Coherent States.- 2.4 Squeezed States.- 2.5 Two-Photon Coherent States.- 2.6 Variance in the Electric Field.- 2.7 Multimode Squeezed States.- 2.8 Phase Properties of the Field.- Exercises.- 3. Coherence Properties of the Electromagnetic Field.- 3.1 Field-Correlation Functions.- 3.2 Properties of the Correlation Functions.- 3.3 Correlation Functions and Optical Coherence.- 3.4 First-Order Optical Coherence.- 3.5 Coherent Field.- 3.6 Photon Correlation Measurements.- 3.7 Quantum Mechanical Fields.- 3.7.1 Squeezed States.- 3.7.2 Squeezed Vacuum.- 3.8 Phase-Dependent Correlation Functions.- 3.9 Photon Counting Measurements.- 3.9.1 Classical Theory.- 3.9.2 Constant Intensity.- 3.9.3 Fluctuating Intensity — Short-Time Limit.- 3.10 Quantum Mechanical Photon Count Distribution.- 3.10.1 Coherent Light.- 3.10.2 Chaotic Light.- 3.10.3 Photo-Electron Current Fluctuations.- Exercises.- 4. Representations of the Electromagnetic Field.- 4.1 Expansion in Number States.- 4.2 Expansion in Coherent States.- 4.2.1 P Representation.- a) Correlation Functions.- b) Covariance Matrix.- c) Characteristic Function.- 4.2.2 Wigner’s Phase-Space Density.- a) Coherent State.- b) Squeezed State.- c) Number State.- 4.2.3 Q Function.- 4.2.4 R Representation.- 4.2.5 Generalized P Representations.- a) Number State.- b) Squeezed State.- 4.2.6 Positive P Representation.- Exercises.- 5. Quantum Phenomena in Simple Systems in Nonlinear Optics.- 5.1 Single-Mode Quantum Statistics.- 5.1.1 Degenerate Parametric Amplifier.- 5.1.2 Photon Statistics.- 5.1.3 Wigner Function.- 5.2 Two-Mode Quantum Correlations.- 5.2.1 Non-degenerate Parametric Amplifier.- 5.2.2 Squeezing.- 5.2.3 Quadrature Correlations and the Einstein- Podolsky-Rosen Paradox.- 5.2.4 Wigner Function.- 5.2.5 Reduced Density Operator.- 5.3 Quantum Limits to Amplification.- 5.4 Amplitude Squeezed State with Poisson Photon Number Statistics.- Problems.- 6. Stochastic Methods.- 6.1 Master Equation.- 6.2 Equivalent c-Number Equations.- 6.2.1 Photon Number Representation.- 6.2.2 P Representation.- 6.2.3 Properties of Fokker-Planck Equations.- 6.2.4 Steady State Solutions — Potential Conditions.- 6.2.5 Time Dependent Solution.- 6.2.6 Q Representation.- 6.2.7 Wigner Function.- 6.2.8 Generalized P Represention.- a) Complex P Representation.- b) Positive P Representation.- 6.3 Stochastic Differential Equations.- 6.3.1 Use of the Positive P Representation.- 6.4 Linear Processes with Constant Diffusion.- 6.5 Two Time Correlation Functions in Quantum Markov Processes.- 6.5.1 Quantum Regression Theorem.- 6.6 Application to Systems with a P Representation.- Exercises.- 7. Input-Output Formulation of Optical Cavities.- 7.1 Cavity Modes.- 7.2 Linear Systems.- 7.3 Two-Sided Cavity.- 7.4 Two Time Correlation Functions.- 7.5 Spectrum of Squeezing.- 7.6 Parametric Oscillator.- 7.7 Squeezing in the Total Field.- 7.8 Fokker-Planck Equation.- Exercises.- 8. Generation and Applications of Squeezed Light.- 8.1 Parametric Oscillation and Second Harmonic Generation.- 8.1.1 Semi-classical Steady States and Stability Analysis.- 8.1.2 Parametric Oscillation.- 8.1.3 Second Harmonic Generation.- 8.1.4 Squeezing Spectrum.- 8.1.5 Parametric Oscillation.- 8.1.6 Experiments.- 8.2 Twin Beam Generation and Intensity Correlations.- 8.2.1 Second Harmonic Generation.- 8.2.2 Experiments.- 8.2.3 Dispersive Optical Bistability.- 8.3 Applications of Squeezed Light.- 8.3.1 Interferometric Detection of Gravitational Radiation.- 8.3.2 Sub-Shot-Noise Phase Measurements.- Exercises.- 9. Nonlinear Quantum Dissipative Systems.- 9.1 Optical Parametric Oscillator: Complex P Function.- 9.2 Optical Parametric Oscillator: Positive P Function.- 9.3 Quantum Tunnelling Time.- 9.4 Dispersive Optical Bistability.- 9.5 Comment on the Use of the Q and Wigner Representations.- Exercises.- 9.A Appendix.- 9.A.1 Evaluation of Moments for the Complex P function for Parametric Oscillation (9.17).- 9.A.2 Evaluation of the Moments for the Complex P Function for Optical Bistability (9.48).- 10. Interaction of Radiation with Atoms.- 10.1 Quantization of the Electron Wave Field.- 10.2 Interaction Between the Radiation Field and the Electron Wave Field.- 10.3 Interaction of a Two-Level Atom with a Single Mode Field.- 10.4 Quantum Collapses and Revivals.- 10.5 Spontaneous Decay of a Two-Level Atom.- 10.6 Decay of a Two-Level Atom in a Squeezed Vacuum.- 10.7 Phase Decay in a Two-Level System.- Exercises.- 11. Resonance Fluorescence.- 11.1 Master Equation.- 11.2 Spectrum of the Fluorescent Light.- 11.3 Photon Correlations.- 11.4 Squeezing Spectrum.- Exercises.- 12. Quantum Theory of the Laser.- 12.1 Master Equation.- 12.2 Photon Statistics.- 12.2.1 Spectrum of Intensity Fluctuations.- 12.3 Laser Linewidth.- 12.4 Regularly Pumped Laser.- 12. A Appendix: Derivation of the Single-Atom Increment.- Exercises.- 13. Intracavity Atomic Systems.- 13.1 Optical Bistability.- 13.2 Nondegenerate Four Wave Mixing.- 13.3 Experimental Results.- Exercises.- 14. Bells Inequalities in Quantum Optics.- 14.1 The Einstein-Podolsky-Rosen (EPR) Argument.- 14.2 Bell Inequalities and the Aspect Experiment.- 14.3 Violations of Bell’s Inequalities Using a Parametric Amplifier Source.- 14.4 One-Photon Interference.- Exercises.- 15. Quantum Nondemolition Measurements.- 15.1 Concept of a QND measurement.- 15.2 Back Action Evasion.- 15.3 Criteria for a QND Measurement.- 15.4 The Beam Splitter.- 15.5 Ideal Quadrature QND Measurements.- 15.6 Experimental Realisation.- 15.7 A Photon Number QND Scheme.- Exercises.- 16. Quantum Coherence and Measurement Theory.- 16.1 Quantum Coherence.- 16.2 The Effect of Fluctuations.- 16.3 Quantum Measurement Theory.- 16.4 Examples of Pointer Observables.- 16.5 Model of a Measurement.- Exercises.- 17. Atomic Optics.- 17.1 Young’s Interference with Path Detectors.- 17.1.1 The Feynman Light Microscope.- 17.2 Atomic Diffraction by a Standing Light Wave.- 17.3 Optical Stern-Gerlach Effect.- 17.4 Quantum Non-Demolition Measurement of the Photon Number by Atomic Beam Deflection.- 17.5 Measurement of Atomic Position.- 17.5.1 Atomic Focussing and Contractive States.- Exercises.- 17.A Appendix.- References.