Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics

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Springer Science & Business Media, Aug 27, 2004 - Science - 449 pages
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This book offers a systematic and comprehensive exposition of the quantum stochastic methods that have been developed in the field of quantum optics. It includes new treatments of photodetection, quantum amplifier theory, non-Markovian quantum stochastic processes, quantum input--output theory, and positive P-representations. It is the first book in which quantum noise is described by a mathematically complete theory in a form that is also suited to practical applications. Special attention is paid to non-classical effects, such as squeezing and antibunching. Chapters added to the previous edition, on the stochastic Schrödinger equation, and on cascaded quantum systems, and now supplemented, in the third edition by a chapter on recent developments in various pertinent fields such as laser cooling, Bose-Einstein condensation, quantum feedback and quantum information.

 

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Contents

A Historical Introduction
1
12 The Spectrum of Quantum Noise
4
13 Emission and Absorption of Light
7
14 Consistency Requirements for Quantum Noise Theory
10
15 Quantum Stochastic Processes and the Master Equation
13
Quantum Statistics
21
22 Quantum Theory of Measurement
24
23 Multitime Measurements
33
Amplifiers and Measurement
212
72 Amplifiers
213
73 The Macroscopic Limit in Open Quantum Systems
222
Photon Counting
230
82 Photodetection and Photon Counting
238
83 Photon Counting Formulae
243
84 Homodyne and Heterodyne Detection
259
85 InputOutput Formulations of Photodetection
264

24 Quantum Statistical Mechanics
35
25 System and Heat Bath
39
3 Quantum Langevin Equations
42
31 The Harmonic Oscillator Heat Bath
44
32 The Field InterpretationNoise Inputs and Outputs
51
33 The Noise Interpretation
57
34 Examples and Applications
61
35 The Adjoint Equation
71
36 The Master Equation
76
Phase Space Methods
90
41 The Harmonic Oscillator in One Variable
91
42 Coherent States and the Classical Limit
96
43 Coherent States
99
44 Phase Space Representations
106
45 Operator Correspondences and Equations of Motion
122
The BakerHausdorff Formula
128
Quantum Markov Processes
130
51 The Physical Basis of the Master Equation
131
52 Multitime Structure of Quantum Markov Processes
143
and Quantum Stochastic Differential Equations
148
54 The Master Equation
161
Applying the Master Equation
169
62 Quantum Classical Correspondence
172
63 Some Amplifier Models
176
64 Generalized PRepresentations
183
65 Applications of the Generalized PRepresentations
194
66 Applications of the Positive PRepresentation
195
67 The Anharmonic Oscillator
203
68 Theoretical Framework of the Problem
205
69 Conclusions
209
610 ExampleQuantum Noise in the Parametric Oscillator
210
Interaction of Light with Atoms
276
92 Two Level Atom in the Electromagnetic Field
278
93 The Laser
289
94 Optical Bistability
306
95 Other Phase Space Methods
310
Squeezing
322
102 The Degenerate Parametric Amplifier
324
103 Squeezed Light on a Single Atom
332
104 Simulation Methods Based on the Adjoint Equation
334
The Stochastic Schrodinger Equation
341
111 Quantum Stochastic Schrodinger Equation
343
112 QSDE for Time Evolution Operators and State Vectors
345
113 Number Processes and Photon Counting
351
114 Diffusion Processes and Homodyne Detection
371
115 Applications and Illustrations
376
Cascaded Quantum Systems
397
121 Coupling Equations
398
122 Application to Harmonic Oscillator Systems
404
123 Two Level Atom Driven by Antibunched Light
407
124 Characterizing NonClassical Light
412
Supplement
418
132 BoseEinstein Condensation
419
133 Phase Space Methods
420
136 NonMarkovian QSDEs
421
138 Implementing Quantum Information Using Atoms and Ions
422
References
429
Bibliography
434
Author Index
437
Subject Index
438
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