Mesoscopic Quantum Optics

This new work presents an eclectic treatment of quantum optics, quantum measurements, and mesoscopic physics. Beginning with the fundamentals of quantum optics, the book then provides scientists and engineers with the latest experimental work in the area of optical measurements.

Professor Yoshihisa Yamamoto has performed his research at Tokyo University, MIT, Stanford and other prestigious institutions before he became professor at Stanford. He teaches various courses on quantum optics and has published more than 350 papers and two books.

Atac Imamoglu is the author of Mesoscopic Quantum Optics, published by Wiley.

Preface

xi

Basic Concepts

1

(28)

Probability Interpretation of Quantum Mechanics

1

(3)

Heisenberg Uncertainty Principle

4

(10)

Commutator Bracket and the Minimum Uncertainty State

5

(3)

Quantum Interference and Wave-Particle Duality

8

(1)

Time Evolution of a Minimum Uncertainty State

9

(2)

Coherent State and Squeezed State

11

(3)

von Neumann's Projection Postulate

14

(11)

Measurement Error and Back Action Noise

15

(3)

Pauli's First-Kind and Second-Kind Measurements

18

(1)

Density Operator and Liouville-von Neumann Equation

19

(2)

General Description of Indirect Quantum Measurements

21

(3)

Quantum Nondemolition Measurement

24

(1)

Simultaneous Measurement of Two Conjugate Observables

25

(4)

References

28

(1)

Canonical Quantization

29

(15)

Minimum Action Principle and Lagrangian Formalism

29

(5)

Quantization of the Electromagnetic Field

34

(4)

Second Quantization of the Schrodinger Field

38

(6)

References

42

(2)

Quantum States of the Electromagnetic Fields

44

(32)

Photon Number Eigenstates

45

(8)

Properties of Photon Number Eigenstates

46

(5)

Generation of Photon Number Eigenstates

51

(2)

Coherent States

53

(7)

Properties of Coherent States

53

(5)

Generation of Coherent States

58

(2)

Squeezed States

60

(7)

Properties of Quadrature Amplitude Squeezed States

60

(1)

Generation of Quadrature Amplitude Squeezed States

61

(2)

Properties of Number-Phase Squeezed States

63

(2)

Generation of Number-Phase Squeezed States

65

(2)

Correlated Twin Photons and Quantum Entanglement

67

(4)

Generation of Arbitrary Quantum States by Projective Measurements

68

(2)

Nonlocal Quantum Entanglement

70

(1)

Probability Distribution Functions for a Density Operator

71

(5)

References

74

(2)

Coherence of the Electromagnetic Fields

76

(25)

Photodetection

76

(1)

Young's Interference Experiment and First-Order Coherence

77

(4)

Hanbury--Brown--Twiss Experiment and Second-Order Coherence

81

(4)

Photon Counting

85

(4)

Classical Theory of Photon Count Distribution

86

(2)

Quantum Theory of Photon Count Distribution

88

(1)

Phase Operator of the Quantized Electromagnetic Field

89

(3)

Quantum Limits of Optical Interferometry

92

(9)

Standard Quantum Limits of Optical Interferometry

92

(1)

Squeezed State Interferometer

93

(3)

Photon Number Eigenstate Interferometer

96

(1)

Photonic de Broglie Wave Interferometer

97

(3)

References

100

(1)

Quantum States of Atoms

101

(13)

Angular Momentum Algebra

102

(3)

Quantization of Angular Momentum

102

(1)

Angular Momentum Operators and Eigenstates

103

(2)

Assembly of Two-Level Atoms

105

(9)

Pauli Spin Operators

105

(1)

Collective Angular Momentum Operators

106

(2)

Angular Momentum Eigenstates (Dicke States)

108

(1)

Coherent Atomic States (Bloch States)

109

(4)

References

113

(1)

Interaction between Atoms and Fields

114

(23)

Atom-Field Interaction in the Length Gauge

114

(4)

Jaynes--Cummings Hamiltonian

118

(1)

Two-Level Atom and Single-Mode Photon Number State

119

(3)

Vacuum Rabi Oscillation

119

(2)

Normal Mode Splitting

121

(1)

N Two-Level Atoms and a Single-Mode Photon Number State

122

(6)

Collective Rabi Oscillation and Normal Mode Splitting

122

(2)

Dressed Fermions and Dressed Bosons

124

(1)

Atomic Cavity Quantum Electrodynamics (QED)

125

(2)

Mollow's Triplet

127

(1)

Radiation Trapped State

128

(1)

Cummings Collapse and Revival

128

(3)

Two-Level Atoms with a Continuum of Radiation Fields

131

(3)

Superradiance

134

(3)

References

136

(1)

Mathematical Methods for System-Reservoir Interaction

137

(25)

Noise Operator Method

139

(6)

Field Damping by Field Reservoirs

139

(5)

Einstein Relation between Drift and Diffusion Coefficients

144

(1)

Density Operator Method

145

(7)

Derivation of the Master Equation

145

(1)

Field Damping by Atomic Reservoirs

146

(4)

Atom Damping by Field Reservoirs

150

(1)

Field Damping by Field Reservoirs

151

(1)

The Fokker-Planck Equation

152

(2)

Glauber-Sudarshan P Representation

152

(1)

Stochastic Differential Equations

153

(1)

Quantum Regression Theorem

154

(8)

References

161

(1)

Stochastic Wavefunction Methods

162

(13)

Monte Carlo Wavefunction Approach

163

(8)

Description and Equivalence to Master Equation

164

(2)

Two-Time Correlation Functions

166

(1)

Two-Level Atom Driven by a Laser Field

167

(1)

Single-Mode Cavity Driven by a Thermal Field

168

(3)

Quantum State Diffusion Model

171

(4)

References

174

(1)

Quantum Nondemolition Measurements

175

(11)

QND Measurement of Photon Number

175

(5)

Heisenberg Picture

175

(3)

Schrodinger Picture

178

(2)

Experimental QND Measurements

180

(2)

QND Measurement of Quadrature Amplitudes

182

(4)

References

184

(2)

Semiconductor Bloch Equations

186

(16)

Field Theory of Semiconductors

186

(8)

Semiconductor Bloch Equations

194

(3)

Semiconductor Bloch Equations in the Non-interacting Limit

195

(1)

Semiconductor Bloch Equations with Interactions

196

(1)

Excitons

197

(1)

Nonlinear Response of Excitons

198

(4)

References

200

(2)

Excitons and Polaritons

202

(18)

Non-interacting Excitons

202

(1)

Bulk Exciton Polaritons

203

(3)

Quantum-Well Excitons and Cavity Polaritons

206

(5)

Excitons as Bosons

211

(5)

Bosonization

211

(1)

Bose Condensation of Excitons

212

(1)

Stimulated Scattering of Excitons

213

(3)

Stimulated Scattering Experiment With Excitons

216

(4)

References

219

(1)

Coulomb Blockade and Squeezing

220

(15)

Coulomb Blockade of Tunneling

220

(4)

Macroscopic Coulomb Blockade of Electron Injection

224

(4)

AC-Voltage-Driven Mesoscopic p-i-n Junctions

228

(7)

References

234

(1)

Current Noise in Mesoscopic and Macroscopic Conductors

235

(18)

Suppression of Electrical Current Noise in Dissipative Conductors

236

(10)

Equilibrium and Nonequilibrium Transport Noise in Mesoscopic Conductors

236

(3)

Suppression of Nonequilibrium Partition Noise by Inelastic Scattering

239

(3)

Microscopic Model for Suppression of Nonequilibrium Partition Noise and Loss of Electron Wave Coherence

242

(4)

Quantum Interference in Electron Collision

246

(4)

Negative Correlation in Electron Partition

250

(3)

References

252

(1)

Nonequilibrium Green's Function Formalism

253

(12)

Green's Function and Self-Energy

253

(3)

Correlation and Scattering Functions

256

(1)

Current Flow

257

(8)

Noninteracting Transport

257

(1)

Strongly Interacting Transport

258

(4)

Conductance through a Single Site

262

(2)

References

264

(1)

Quantum Statistical Properties of a Laser

265

(34)

Density Operator Master Equation

266

(12)

Derivation of the Master Equation

266

(3)

Fast Dephasing Case

269

(1)

Lifetime Broadened Laser System

269

(2)

Threshold Characteristics

271

(2)

Photon Statistics

273

(3)

Spectral Linewidth

276

(2)

Fokker-Planck Equation

278

(2)

Langevin Equation

280

(4)

Derivation of the Langevin Equation

280

(1)

Linearization of the Langevin Equations

281

(2)

Quantum Noise at Well Above Threshold

283

(1)

Sub-Poissonian Lasers

284

(5)

Standard Quantum Limit of the Output Field

285

(2)

Photon Number Noise and Phase Noise of Pump-Noise-Suppressed Lasers

287

(1)

Commutator Bracket Conservation

288

(1)

Squeezing in Semiconductor Lasers

289

(5)

Observation of Mode Partition Noise

294

(5)

References

297

(2)

Index

299

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Mesoscopic Quantum Optics

Summary

Author Biography

Table of Contents

Supplemental Materials