Quantum Phenomena in Simple Optical Systems

This book explores the modern problems of quantum optics, and shows that, in simple optical systems, it is possible to obtain quantum states that are interesting from the point of view of modern quantum physics and quantum optics. In particular, the quantum behavior of the second and third harmonics and subharmonics generation processes is investigated, highlighting that, in subharmonic processes, it is possible to obtain Schrödinger's cat-type states of light, which are one of the main problems of quantum physics. The book uses few formulas and mathematical conclusions, opting instead for a large amount of graphic material, in order to make the concepts explored easier to understand. It will be of interest to scientists working in quantum optics, as well as teachers and students of physics. 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