An Open Systems Approach to Quantum Optics: Lectures Presented at the Université Libre de Bruxelles, October 28 to November 4, 1991, Volume 18

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Springer Science & Business Media, May 27, 1993 - Computers - 179 pages
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This volume contains ten lectures presented in the series ULB Lectures in Nonlinear Optics at the Universite Libre de Bruxelles during the period October 28 to November 4, 1991. A large part of the first six lectures is taken from material prepared for a book of somewhat larger scope which will be published,by Springer under the title Quantum Statistical Methods in Quantum Optics. The principal reason for the early publication of the present volume concerns the material contained in the last four lectures. Here I have put together, in a more or less systematic way, some ideas about the use of stochastic wavefunctions in the theory of open quantum optical systems. These ideas were developed with the help of two of my students, Murray Wolinsky and Liguang Tian, over a period of approximately two years. They are built on a foundation laid down in a paper written with Surendra Singh, Reeta Vyas, and Perry Rice on waiting-time distributions and wavefunction collapse in resonance fluorescence [Phys. Rev. A, 39, 1200 (1989)]. The ULB lecture notes contain my first serious atte~pt to give a complete account of the ideas and their potential applications. I am grateful to Professor Paul Mandel who, through his invitation to give the lectures, stimulated me to organize something useful out of work that may, otherwise, have waited considerably longer to be brought together.
 

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Contents

Introduction
1
Lecture 1 Master Equations and Sources I
5
12 Master equations
6
13 Master equation for a cavity mode driven by thermal light
9
14 The cavity output field
13
15 Correlations between the free field and the source field
16
Lecture 2 Master Equations and Sources II
22
22 Master equation for a twostate atom in thermal equilibrium
24
the spectrum of squeezing
100
63 Vacuum fluctuations
103
64 Squeezing spectra for the degenerate parametric oscillator
107
65 Photoelectron counting for the degenerate parametric oscillator
110
Lecture 7 Quantum Trajectories I
113
71 Exclusive and nonexclusive photoelectron counting probabilities
114
72 The distribution of waiting times
116
73 Quantum trajectories from the photoelectron counting distribution
117

23 Phase destroying processes
28
24 The radiated field
33
resonance fluorescence lasers parametric oscillators
35
Lecture 3 Standard Methods of Analysis I
39
the quantum regression theorem
41
33 Optical spectra
46
34 The HanburyBrownTwiss effect
52
35 Photon antibunching
53
Lecture 4 Standard Methods of Analysis II
58
42 FokkerPlanck equation for a cavity mode driven by thermal light
64
43 Stochastic differential equations
67
44 Linearization and the system size expansion
68
45 The degenerate parametric oscillator
73
Lecture 5 Photoelectric Detection I
78
52 Photoelectron counting for a general classical field
80
53 Moments of the counting distribution
82
54 The waitingtime distribution
86
55 Photoelectron counting for quantized fields
88
Lecture 6 Photoelectric Detection II
93
74 Unravelling the master equation for the source
121
75 Stochastic wavefunctions
122
Lecture 8 Quantum Trajectories II
126
82 Resonance fluorescence
130
83 Cavity mode driven by thermal light
134
84 The degenerate parametric oscillator
136
85 Complementary unravellings
138
Lecture 9 Quantum Trajectories III
140
92 Homodyne detection
143
93 Nonclassical photoelectron correlations
146
94 Stochastic Schrodinger equation for the degenerate parametric oscillator
148
95 Nonlocality
152
Lecture 10 Quantum Trajectories IV
155
cavity QED
160
103 Spontaneous dressedstate polarization
162
104 Semiclassical analysis
164
105 Quantum stability phase switching and Schrodinger cats
166
Postscript
174
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