Quantum Phenomena in Simple Optical Systems

Quantum Phenomena in Simple Optical Systems
Table of Contents
Preface
1 Quantum Theory of Unstable Behavior of the Intracavity Second Harmonic Generation Process
	Introduction
	1.1 Nonlinear System, Langevin Equations, and Quantum Noise
	1.2 Semiclassical and Quantum Solutions of Langevin Equations
	1.3 Quantum Dynamics of Photon Numbers of the Modes
	1.4 Distribution Functions for Photon Numbers of the Modes
	1.5 Joint Distribution Functions for Photon Numbers of the Modes
	1.6 Dynamics of Phase Fluctuations
	1.7 Dynamics of Joint Phase Fluctuations of the Modes and Self-Phase Matching
	1.8 Dynamics of Joint Fluctuations in Photon Numbers and Phases
	1.9 Dynamics of Wigner Function and Quantum Entropy of the Modes
	1.10 Correlation of Quadrature Amplitude Fluctuations and Entangled States of the Field
	References
2 Quantum Theory of Unstable Behaviour of Intracavity Third Harmonic Generation Process
	Introduction
	2.1 Basic Equations and Third-Order Noise
	2.2 Semiclassical Steady States and Instability
	2.3.Higher-Order Moments and Third-Order Noise
	2.4. Langevin Equations in a Differential Form
	2.5 Quantum Dynamics of Photon Numbers
	2.6 Distribution functions for the number of photons
	2.7. Quantum Fluctuations of Phases of the Modes
	2.8 Joint Fluctuations in Photon Numbers and Phases of the Modes
	2.9 Quantum Dynamics of the Field in the Case of Evolution from Initial Vacuum States
	2.10 Quantum Dynamics of the Field in the Case of Evolution from Initial Coherent States
	2.11. Correlation Dynamics of Quadrature Amplitude Fluctuations and Entangled States
	References
3 Dynamics of Formation of Superposition States of Light in an Absorbing Medium
	Introduction
	3.1. Model of the Nonlinear System and Basic Equations
	3.2. Quantum Dynamics of the Field in the Absence of One-Photon Absorption
	3.3. Quantum Dynamics of the Field in the Presence of Weak One-Photon Absorption. Quantum Coherence and Dissipation
	3.4. Possibility of Formation of a Schrödinger Cat Type Nonstationary Field State
	References
4 Three-Component Coherent Superposition States of Light
	Introduction
	4.1. Model of the Nonlinear System and Basic Equations
	4.2. Formation and Decay of Coherent Superposition States
	4.3. Evolution from Multicomponent Mixed Initial States
	4.4. Steady states of the System and the Eigenstates of the Field Amplitude Cube
	4.5. Quantum-Mechanical Interference Between Superposition States
	4.6 Quantum Properties of Three-Component Coherent Superposition States of Light
	4.7. System Behaviour in the Absence of One-Photon Absorption
	4.8. System Behaviour in the Presence of Weak One-Photon Absorption, Quantum Coherence, and Dissipation
	References
5 Quantum Dynamics of Intracavity Second Subharmonic Generation
	Introduction
	5.1. Nonlinear System, Main Equations, and Calculation Algorithms
	5.2. System Dynamics in the Case of Weak Coupling of the Modes: Squeezed Vacuum State
	5.3. System Dynamics in the Case of Strong Coupling of the Modes: Two-Component and Entangled States
	5.4. System Dynamics in the Case of Very Strong Couplingof the Modes: Two-Component State with Quantum-Mechanical Interference between State Components
	References
6 Quantum Dynamics of Intracavity Third Subharmonic Generation
	Introduction
	6.1. Nonlinear System, Basic Equations, and Calculation Algorithms
	6.2. System Dynamics in the Case of Weak Coupling of the Modes: Symmetry of Vacuum
	6.3. System Dynamics in the Case of Strong Coupling of the Modes: Squeezed State, Statistical Mixture of Three Squeezed States, and Entangled State
	6.4. System Dynamics in the Case of Very Strong Coupling of the Modes: Three-Component State with Quantum-Mechanical Interference between State Components
	References