1．From Geometry to the Quantum 1
2．Introduction to Lasers 13
2.1 Normal Modes in a Cavity 14
2.2 Basic Properties of Lasers 17
3．Properties of Light:Blackbody Radiation 19
3.1 Planck's Quantum Derivation 20
3.2 The Proper Derivation of Planck's Formula 24
3.3 Fluctuations of Light 26
3.4 Maxwell's Lucifer 32
4．Interaction of Light with Matter Ⅰ 37
4.1 Stimulated and Spontaneous Emission 39
4.2 Optical Excitation of Two Level Atoms 41
4.3 Life-Time and Amplification 43
5．Basic Optical Processes—Still Classical 45
5.1 Interference and Coherence 45
5.2 Light Pressure 48
5.3 Optical Absorption 51
5.4 Amplification:Three Level Systems 53
5.5 Classical Treatment of Atom-Light Interaction 55
5.5.1 Dipole radiation 56
5.5.2 Radiation damping 57
5.6 Spectral Lines 60
6．More Detailed Principles of Laser 63
6.1 Basic Theory:Classical Electrodynamics 63
6.2 Mode-Locking 68
6.3 Non-linear Optics 70
6.4 Phase Matching 73
6.4.1 Rigorous derivation 73
6.4.2 Heuristic derivation 76
6.5 Multiphoton Processes 78
7．Interactions of Light with Matter Ⅱ 81
7.1 Vector Spaces 81
7.2 Dirac Formalism 84
7.3 Time Dependent Perturbation Theory 87
7.4 Alternative Derivation of Perturbation 92
7.5 The Wigner-Weisskopf Theory 94
7.5.1 Constant perturbation 94
7.5.2 Harmonic perturbation 95
7.6 Digression:Entropy and the Second Law 97
7.7 Einstein's B Coefficient 100
7.8 Multiphoton Processes Revisited 102
8．Two Level Systems 105
8.1 Operator Matrix Algebra 105
8.2 Two Level Systems:Rabi Model 107
8.3 Other Issues with Two Level Systems 114
8.4 The Berry Phase 116
8.4.1 Parallel transport 117
8.4.2 The Bloch sphere 119
8.4.3 Implementation 121
8.4.4 Generalization of the phase 124
8.5 Gauge Principle 126
9．Field Quantization 131
9.1 Quantum Harmonic Oscillator 133
9.2 What Are Photons？ 137
9.3 Blackbody Spectrum from Photons 139
9.4 Quantum Fluctuations and Zero Point Energy 140
9.5 Coherent States 142
9.6 Composite Systems—Tensor Product Spaces 146
9.6.1 Beam splitters 147
9.6.2 Generation of coherent states 150
9.7 Bosonic Nature of Light 151
9.8 Polarization:The Quantum Description 153
9.8.1 Unpolarized light—mixed states 154
10．Interaction of Light with Matter Ⅲ 157
10.1 Fully Quantized Treatment 157
10.2 Jaynes-Cummings Model 158
10.3 Spontaneous Emission—At Last 163
10.4 The Lamb Shift 164
10.5 Parametric Down Conversion 166
10.6 Quantum Measurement:A Brief Discussion 167
11．Some Recent Applications of Quantum Optics 171
11.1 Laser Cooling 171
11.1.1 Bose-Einstein condensation 173
11.2 Quantum Information Processing 176
11.2.1 Quantum teleportation 177
12．Closing Lines 181
13．Problems and Solutions 183
13.1 Problem and Solutions 1 183
13.1.1 Problem set 1 183
13.1.2 Solutions 1 185
13.2 Problem and Solutions 2 190
13.2.1 Problem set 2 190
13.2.2 Solutions 2 193
13.3 Problems and Solutions 3 197
13.3.1 Problem set 3 197
13.3.2 Solutions 3 199
13.4 Problems and Solutions 4 203
13.4.1 Problem set 4 203
13.4.2 Solutions 4 205
13.5 Problems and Solutions 5 210
13.5.1 Problem set 5 210
13.5.2 Solutions 5 212
Bibliography 217
Index 219