Methods in Theoretical Quantum Optics,9780198563624

Methods in Theoretical Quantum Optics

by ;
ISBN13: 9780198563624
ISBN10: 0198563620
Format: Hardcover
Pub. Date: 1997-12-04
Publisher(s): Clarendon Press
List Price: $245.33

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Summary

This work presents the mathematical methods widely used by workers in the field of quantum optics. It deals with the physical assumptions which lead to the models and approximations employed, but the text is meant to give a firm grounding in those techniques needed to derive analytical solutions to problems. Based on teachings by the authors, most of the text has been tested on students.

Table of Contents

1 Foundations
1(13)
1.1 Introduction
1(1)
1.2 Basic quantum theory
1(8)
1.3 Atoms and fields
9(5)
2 Coherent interactions
14(20)
2.1 Introduction
14(1)
2.2 Interaction pictures
14(4)
2.3 Two-state dynamics
18(5)
2.4 The Jaynes-Cummings model
23(4)
2.5 The Bixon-Jortner quasi-continuum
27(2)
2.6 Interactions between field modes
29(5)
3 Operators and states
34(53)
3.1 Introduction
34(1)
3.2 Atom and field operators
34(5)
3.3 Functions of operators and ordering theorems
39(11)
3.4 Number states
50(3)
3.5 Thermal states
53(4)
3.6 Coherent states
57(10)
3.7 Squeezed states
67(13)
3.8 Angular momentum coherent states
80(7)
4 Quantum statistics of fields
87(43)
4.1 Introduction
87(2)
4.2 Photon number statistics
89(6)
4.3 Optical phase
95(11)
4.4 Characteristic functions
106(8)
4.5 Quasi-probability distributions
114(11)
4.6 Statistics of multimode states
125(5)
5 Dissipative processes
130(52)
5.1 Introduction
130(1)
5.2 Perturbation theory and Fermi's golden rule
130(2)
5.3 Weisskopf-Wigner decay
132(8)
5.4 Final value theorem and spectra
140(5)
5.5 Damping in the Heisenberg picture
145(16)
5.6 Master equations
161(15)
5.7 Evolution of field statistics
176(6)
6 Dressed states
182(40)
6.1 Introduction
182(1)
6.2 Two-state systems
182(7)
6.3 Three-state systems
189(7)
6.4 Dressing the Bixon-Jortner model
196(4)
6.5 Dressing dissipative systems: Fano theory
200(13)
6.6 Dressed operators
213(9)
Appendix 1 Kronecker delta and the permutation symbol 222(3)
Appendix 2 The Dirac delta function 225(3)
Appendix 3 Special functions 228(6)
Appendix 4 Quadrature eigenstates 234(2)
Appendix 5 Operator ordering theorems 236(4)
Appendix 6 The pole approximation 240(3)
Appendix 7 Principal part integrals 243(2)
Appendix 8 Contour integrals 245(5)
Appendix 9 Laplace transforms and the final value theorem 250(5)
Appendix 10 Operator ordering in the Heisenberg equations 255(3)
Appendix 11 The method of characteristics for partial differential equations 258(4)
Appendix 12 Transformation of master equations into partial differential equations 262(4)
Appendix 13 Fokker-Planck equations 266(10)
Appendix 14 Cubic equations 276(1)
Selected bibliography 277(2)
Index 279

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