## Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum OpticsThis 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 |

434 | |

Author Index | 437 |

438 | |

### Other editions - View all

Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic ... Crispin Gardiner,Peter Zoller No preview available - 2010 |

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Quantum Communication and Information Technologies Alexander S. Shumovsky,Valery I. Rupasov Limited preview - 2003 |