Entangled State Representations in Quantum Optics

✍ Scribed by Xiang-Guo Meng, Ji-Suo Wang, Bao-Long Liang

• Publisher: Springer
• Year: 2023
• Tongue: English
• Leaves: 289
• Category: Library

✦ Synopsis

This book highlights the applications of continuous-variable entangled state representations in the research areas of quantum optics via the integration method within an ordered product of operators (IWOP). As a way to develop the Dirac’s symbolic method, the IWOP method has made the integration of non-commutative operators possible by arranging non-commutable operators within an ordered product symbol. It not only deals with many existent quantum optics problems but also explores new research fields. The book also establishes a theoretical framework for solving important quantum optics subjects by taking full advantage of the entangled state representations. With original methods and detailed descriptions, the book is suitable for researchers, instructors, and students interested in quantum mechanics, quantum optics, and quantum information science.

✦ Table of Contents

Preface
Contents
1 Integration Method Within an Ordered Product of Operators and Continuous-Variable Entangled State Representations
1.1 Integration Method Within an Ordered Product of Operators
1.1.1 Normal Ordering Case
1.1.2 Anti-normal Ordering Case
1.1.3 Weyl Ordering Case
1.2 Two-Particle Entangled State Representation
1.3 Thermal Entangled State Representation
1.3.1 Bosonic Case
1.3.2 Fermionic Case
References
2 Dynamics of Two-Body Hamiltonian Systems
2.1 Energy-Level Distribution and Wave Function of Two-Body Hamiltonian System
2.1.1 Two Moving Charged Particles with Elastic Coupling
2.1.2 Two Moving Charged Particles with Coulomb Coupling
2.2 Path Integral Theory in Entangled State Representation
2.3 Evolution of Atomic Coherent State Governed by the Hamiltonian …
2.4 Atomic Coherent States as Energy Eigenstates of the Hamiltonian …
References
3 New Bipartite Entangled States in Two-Mode Fock Space
3.1 Coherent-Entangled States
3.2 Entangled States Describing Parametric Down Conversion
3.3 Parameterized Entangled States Induced by the Common Eigenstates …
3.4 Parameterized Entangled States as the Common Eigenstates …
References
4 Solutions of Density Operator Master Equations
4.1 Solutions of Several Boson Master Equations
4.1.1 Diffusion Master Equation Under Linear Resonance Force
4.1.2 Master Equation for Single-Mode Cavity Driven by Oscillating External Field in a Heat Reservoir
4.1.3 Master Equation for Damped Harmonic Oscillator Acted by Linear Resonance Force in a Squeezed Heat Reservoir
4.1.4 Master Equation Describing a Diffusive Anharmonic Oscillator
4.2 Solutions of Several Fermi Quantum Master Equations
4.2.1 Fermi Master Equations for Amplitude Damping and Phase Damping
4.2.2 Master Equation for Fermi Heat Reservoir
4.3 Generation of Displaced Thermal State
References
5 Wigner Distribution Function and Quantum Tomogram via Entangled State Representations
5.1 Wigner Distribution Functions
5.1.1 Wigner Operator Theory
5.1.2 Wigner Distribution Functions for Quantum States
5.2 Quantum-state Tomography
5.2.1 Quantum Tomography
5.2.2 Quantum Tomograms of Quantum States
References
6 Evolution and Decoherence of Quantum States in Open Systems
6.1 Evolution of Quantum States in the Amplitude Damping Channel
6.1.1 Displaced Thermal States
6.1.2 Thermal-State Superpositions
6.1.3 Two-Mode Squeezed Vacuum States
6.2 Evolution of Quantum States in the Laser Process
6.2.1 Squeezed Number States
6.2.2 Squeezed Thermal States
6.2.3 Multi-photon Subtracted Squeezed Vacuum States
6.2.4 Multi-photon Added Two-Mode Squeezed Thermal States
References
7 Generalized Binomial Theorems and Multi-variable Special Polynomials Involving Hermite Polynomials
7.1 Generalized Binomial Theorems Involving Hermite Polynomials
7.2 Multi-variable Special Polynomials and Their Generating Functions
7.2.1 Three-variable Case
7.2.2 Six-variable Case
7.2.3 New Operator Identity and Integral Formula
7.2.4 Applications
References
8 Quantum Theory of Mesoscopic Circuit Systems
8.1 Quantum Theory of Mesoscopic LC Circuits
8.1.1 Single Mesoscopic LC Circuit
8.1.2 Mutual Inductance Coupling Mesoscopic LC Circuit
8.2 Quantum Theory of Mesoscopic Circuits Containing Josephson Junction
8.2.1 Mutual-Inductance Coupling Mesoscopic Circuit Including Josephson Junction
8.2.2 Mesoscopic LC Circuit with Josephson Junction Coupled by Mutual Inductance
References