Table of Contents
Acknowledgements xi
1 Introduction 1
1.1 A note to the reader 1
1.2 Quantum theory 3
1.2.1 Axioms 3
1.2.2 Quantum statistics 7
1.2.3 Schrödinger and Heisenberg pictures 10
1.3 On the questions and homework problems 12
1.4 Further reading 13
2 Quantum field theory of light 14
2.1 Light in media 14
2.1.1 Maxwell's equations 14
2.1.2 Quantum commutator 16
2.2 Light modes 19
2.2.1 Modes and their scalar product 20
2.2.2 Bose commutation relations 22
2.2.3 Interference 23
2.2.4 Monochromatic modes 25
2.3 Zero-point energy and Casimir force 27
2.3.1 An attractive cavity 27
2.3.2 Reflections 30
2.4 Questions 32
2.5 Homework problem 33
2.6 Further reading 35
3 Simple quantum states of light 37
3.1 The electromagnetic oscillator 37
3.2 Single-mode states 40
3.2.1 Quadrature states 40
3.2.2 Fock states 41
3.2.3 Thermal states 45
3.2.4 Coherent states 48
3.3 Uncertainty and squeezing 53
3.4 Questions 60
3.5 Homework problem 61
3.6 Further reading 62
4 Quasiprobability distributions 63
4.1 Wigner representation 63
4.1.1 Wigner's formula 64
4.1.2 Basic properties 68
4.1.3 Examples 73
4.2 Other quasiprobability distributions 79
4.2.1 Q function 80
4.2.2 P function 81
4.2.3 s-parameterized quasiprobability distributions 82
4.3 Examples 85
4.4 Questions 89
4.5 Homework problem 90
4.6 Further reading 91
5 Simple optical instruments 92
5.1 Beam splitter 92
5.1.1 Heisenberg picture 92
5.1.2 Schrödinger picture 96
5.1.3 Fock representation and wave-particle dualism 103
5.2 Detection 106
5.2.1 Photodetector 107
5.2.2 Balanced homodyne detection 110
5.2.3 Quantum tomography 113
5.2.4 Simultaneous measurement of conjugate variables 119
5.3 Questions 131
5.4 Homework problem 133
5.5 Further reading 134
6 Irrevesible processes 135
6.1 Lindblad's theorem 135
6.1.1 Irreversibility 135
6.1.2 Reversible dynamics 137
6.1.3 Irreversible dynamics 137
6.2 Loss and gain 140
6.2.1 Absorption and amplification 140
6.2.2 Absorber 144
6.2.3 Amplifier 147
6.2.4 Eavesdropper 150
6.3 Continuous quantum measurements 151
6.4 Questions 155
6.5 Homework problem 156
6.6 Further reading 158
7 Entanglement 159
7.1 Parametric amplifier 159
7.1.1 Heisenberg picture 159
7.1.2 Schrödinger picture 160
7.1.3 Einstein-Podolski-Rosen state 167
7.1.4 Quantum teleportation 171
7.2 Polarization correlations 175
7.2.1 Singlet state 175
7.2.2 Polarization 178
7.2.3 Bell's theorem 182
7.3 Questions 185
7.4 Homework problem 187
7.5 Further reading 188
8 Horizons 189
8.1 Minkowski space 189
8.1.1 Locality and relativity 191
8.1.2 Space-time geometry 195
8.1.3 Light 197
8.2 Accelerated observers 199
8.2.1 Rindler coordinates 200
8.2.2 Accelerated modes 203
8.2.3 Unruh effect 205
8.3 Moving media 209
8.3.1 Motivation 211
8.3.2 Trans-Planckian problem 214
8.3.3 Light in moving media 217
8.3.4 Geometry of light 219
8.3.5 Hawking radiation 221
8.4 Questions 227
8.5 Homework problem 229
8.6 Further reading 229
Appendix A Stress of the quantum vacuum 231
Appendix B State reconstruction in quantum mechanics 250
References 262
Index 274
