Table of contents for Quantum optics : an introduction / Mark Fox.

Bibliographic record and links to related information available from the Library of Congress catalog.

Note: Contents data are machine generated based on pre-publication provided by the publisher. Contents may have variations from the printed book or be incomplete or contain other coding.


Counter
Contents
List of symbols xv
I Introduction and background 1
1 Introduction 3
1.1 What is quantum optics ?; 3
1.2 A brief history of quantum optics 4
1.3 How to use this book 7
2 Classical optics 9
2.1 Maxwell's equations and electromagnetic waves 9
2.1.1 Electromagnetic fields 9
2.1.2 Maxwell's equations 10
2.1.3 Electromagnetic waves 11
2.1.4 Polarization 13
2.2 Diffraction and interference 14
2.2.1 Diffraction 14
2.2.2 Interference 15
2.3 Coherence 17
2.4 Nonlinear optics 20
2.4.1 The nonlinear susceptibility 20
2.4.2 Second-order nonlinear phenomena 21
2.4.3 Phase matching 24
3 Quantum mechanics 27
3.1 Formalism of quantum mechanics 27
3.1.1 The Schrödinger equation 27
3.1.2 Properties of wave functions 29
3.1.3 Measurements and expectation values 31
3.1.4 Commutators and the uncertainty principle 32
3.1.5 Angular momentum 33
3.1.6 Dirac notation 35
3.2 Quantized states in atoms 36
3.2.1 The gross structure 36
3.2.2 Fine and hyperfine structure 41
3.2.3 The Zeeman effect 42
3.3 The harmonic oscillator 43
3.4 The Stern-Gerlach experiment 45
3.5 The band theory of solids 47
4 Radiative transitions in atoms 50
4.1 Einstein coefficients 50
4.2 Radiative transition rates 53
4.3 Selection rules 56
4.4 The width and shape of spectral lines 58
4.4.1 The spectral lineshape function 58
4.4.2 Lifetime broadening 58
4.4.3 Collisional (pressure) broadening 59
4.4.4 Doppler broadening 60
4.5 Line broadening in solids 60
4.6 Optical properties of semiconductors 61
4.7 Lasers 63
4.7.1 Laser oscillation 63
4.7.2 Laser modes 66
4.7.3 Laser properties 69
II Photons 75
5 Photon statistics 77
5.1 Introduction 77
5.2 Photon counting statistics 78
5.3 Coherent light: Poissonian photon statistics 80
5.4 Classification of light by photon statistics 84
5.5 Super-Poissonian light 85
5.5.1 Thermal light 85
5.5.2 Chaotic (partially coherent) light 88
5.6 Sub-Poissonian light 89
5.7 Degradation of photon statistics by losses 90
5.8 Theory of photodetection 91
5.8.1 Semi-classical theory of photodetection 92
5.8.2 Quantum theory of photodetection 95
5.9 Shot noise in photodiodes 96
5.10 Observation of sub-Poissonian photon statistics 101
5.10.1 Sub-Poissonian counting statistics 101
5.10.2 Sub-shot-noise photocurrent 103
6 Photon antibunching 107
6.1 Introduction: the intensity interferometer 107
6.2 HBT experiments and classical intensity fluctuations 110
6.3 The second-order correlation function g(2)(r) 112
6.4 HBT experiments with photons 115
6.5 Photon bunching and antibunching 117
6.5.1 Coherent light 118
6.5.2 Bunched light 118
6.5.3 Antibunched light 119
6.6 Experimental demonstrations of photon antibunching 119
6.7 Single-photon sources 122
7 Coherent states and squeezed light 127
7.1 Light waves as classical harmonic oscillators 127
7.2 Phasor diagrams and field quadratures 130
7.3 Light as a quantum harmonic oscillator 132
7.4 The vacuum field 133
7.5 Coherent states 135
7.6 Shot noise and number-phase uncertainty 136
7.7 Squeezed states 139
7.8 Detection of squeezed light 140
7.8.1 Detection of quadrature squeezed vacuum states 140
7.8.2 Detection of amplitude squeezed light 143
7.9 Generation of squeezed states 143
7.9.1 Squeezed vacuum states 143
7.9.2 Amplitude-squeezed light 145
7.10 Quantum noise in amplifiers 147
8 Photon number states 151
8.1 Operator solution of the harmonic oscillator 151
8.2 The number state representation 154
8.3 Photon number states 156
8.4 Coherent states 158
8.5 Quantum theory of Hanbury Brown-Twiss experiments 160
III Atom-photon interactions 165
9 Resonant light-atom interactions 167
9.1 Introduction 167
9.2 Preliminary concepts 168
9.2.1 The two-level atom approximation 168
9.2.2 Coherent superposition states 169
9.2.3 The density matrix 171
9.3 The time-dependent Schrödinger equation 172
9.4 The weak field limit: Einstein's B coefficient 174
9.5 The strong field limit: Rabi oscillations 177
9.5.1 Basic concepts 177
9.5.2 Damping 180
9.5.3 Experimental observations of Rabi oscillations 182
9.6 The Bloch sphere 187
10 Atoms in cavities 195
10.1 Optical cavities 195
10.2 Atom-cavity coupling 197
10.3 Weak coupling 200
10.3.1 Preliminary considerations 200
10.3.2 Free-space spontaneous emission 201
10.3.3 Spontaneous emission in a single-mode cavity: the Purcell effect 202
10.3.4 Experimental demonstrations of the Purcell effect 204
10.4 Strong coupling 206
10.4.1 Cavity quantum electrodynamics 206
10.4.2 Experimental observations of strong coupling 209
10.5 Applications of cavity effects 211
11 Cold atoms 216
11.1 Introduction 216
11.2 Laser cooling 218
11.2.1 Basic principles of Doppler cooling 218
11.2.2 Optical molasses 221
11.2.3 Sub-Doppler cooling 224
11.2.4 Magneto-optic atom traps 226
11.2.5 Experimental techniques for laser cooling 227
11.2.6 Cooling and trapping of ions 229
11.3 Bose-Einstein condensation 229
11.3.1 Bose-Einstein condensation as a phase transition 230
11.3.2 Microscopic description of Bose-Einstein condensation 232
11.3.3 Experimental techniques for Bose-Einstein Condensation 233
11.4 Atom lasers 236
IV Quantum information processing 241
12 Quantum cryptography 243
12.1 Classical cryptography 243
12.2 Basic principles of quantum cryptography 245
12.3 Quantum key distribution according to the BB84 protocol 249
12.4 System errors and identity verification 253
12.4.1 Error correction 253
12.4.2 Identity verification 254
12.5 Single-photon sources 255
12.6 Practical demonstrations of quantum cryptography 256
12.6.1 Free-space quantum cryptography 257
12.6.2 Quantum cryptography in optical fibres 258
13 Quantum computing 264
13.1 Introduction 264
13.2 Quantum bits (qubits) 268
13.2.1 The concept of qubits 268
13.2.2 Bloch vector representation of single qubits 270
13.2.3 Column vector representation of qubits 270
13.3 Quantum logic gates and circuits 270
13.3.1 Preliminary concepts 270
13.3.2 Single qubit gates 272
13.3.3 Two qubit gates 275
13.3.4 Practical implementations of qubit operations 276
13.4 Decoherence and error correction 280
13.5 Applications of quantum computers 282
13.5.1 Deutsch's algorithm 282
13.5.2 Grover's algorithm 285
13.5.3 Shor's algorithm 287
13.5.4 Simulation of quantum systems 288
13.5.5 Quantum repeaters 288
13.6 Experimental implementations of quantum computation 289
13.7 Outlook 293
14 Entangled states and quantum teleportation 297
14.1 Entangled states 297
14.2 Generation of entangled photon pairs 299
14.3 Single photon interference experiments 302
14.4 Bell's theorem 305
14.4.1 Introduction 305
14.4.2 Bell's inequality 306
14.4.3 Experimental confirmation of Bell's theorem 309
14.5 Principles of teleportation 311
14.6 Experimental demonstration of teleportation 314
14.7 Discussion 316
A Appendix A: Poisson statistics 321
B Appendix B: Parametric amplification 324
B.1 Wave propagation in a nonlinear medium 324
B.2 Degenerate parametric amplification 326
C Appendix C: The density of states 329
D Appendix D: Low-dimensional semiconductor structures 332
D.1 Quantum confinement 332
D.2 Quantum wells 335
D.3 Quantum dots 335
E Appendix E: Nuclear magnetic resonance 338
E.1 Basic principles 338
E.2 The rotating frame transformation 340
E.3 The Bloch equations 343
F Appendix F: Bose-Einstein condensation 345
F.1 Classical and quantum statistics 345
F.2 Statistical mechanics of Bose-Einstein condensation 347
F.3 Bose-Einstein condensed systems 349
Solutions and hints to the exercises 352
Bibliography 360
Index 369

Library of Congress Subject Headings for this publication:

Quantum optics.