Quantum Field Theory With Application to Quantum Nonlinear Optics

by Prikarpatskii, A. K.; Taneri, Ufuk; Bogoliubov, N. N.

• ISBN13: 9789812381644
• ISBN10: 9812381643
• Format: Paperback
• Copyright: 2003-02-01
• Publisher: World Scientific Pub Co Inc

Summary

Multi-photon excitation states of poly-atomic molecules undergoing a self-interaction via Kerr effect related processes are of great interest today. Their successful study must be both analytical and by means of modern quantum field theoretical tools. This book deals with these and related topics by developing modern quantum field theory methods for the analysis of radiative states in a nonlinear quantum-optical system.These lecture notes are ideally suited to graduate mathematical physics and physics students, but can also be of interest to mathematicians involved in applied physics problems, and physicists and chemists studying phenomena related with modern quantum-optical devices.

Table of Contents

Preface	p. v
Acknowledgements	p. vii
Methods of Studying Quantum Optical Phenomena	p. 1
Introduction to Quantum Mechanics in Microworld	p. 3
Quantum States and Statistics	p. 9
Creation and Annihilation Operators	p. 11
Some Second Quantized Quantum Models of Interacting Particles and Fields (Bosons and Fermions)	p. 15
The Rayleigh-Schrodinger Approach to the Ground State Spectrum Calculations	p. 21
The One-Particle Green's Function	p. 27
The Ground States of Noninteracting Fermi- and Bose-Many Particle Systems	p. 29
The Wick Theorem and Feynman Diagrammatic Expansion	p. 33
The Dyson Equations	p. 39
Polarization Operators	p. 47
The Hartree-Fock Approximation	p. 49
The Correlation Energy of Electron Gas at High Density	p. 53
Nonlinear Quantum Optics Models and Their Applications	p. 61
Nonlinear Quantum Optics Bose-Systems	p. 63
The Dicke Model	p. 77
The Bloch-Maxwell Super-Radiance Quantum Optical Model	p. 81
A Degenerate Parametric Quantum Optical Amplifier	p. 87
Two-Mode Nonlinear Quantum Optics System: A Non-degenerate Parametric Quantum Optical Amplifier	p. 95
A Nonlinear Quantum-Optical System at Equilibrium Radiative State	p. 103
The Green's Function	p. 107
The Feynman Diagram Approach: Perturbation Series Expansion	p. 109
The Equilibrium State Analysis	p. 113
Bibliography	p. 117
Index	p. 119
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