Quantum physics has, on the one hand, drastically changed our theoretical description of the physical world and has, on the other hand, revolutionized everyday life, by allowing us to build lasers, atomic clocks used in GPS, and semiconductor-based devices such as laptop computers and smartphones. The object of this book is to give a self-contained introduction to both aspects. It contains a detailed account of the foundational principles: superposition, entanglement, quantum non-locality, decoherence and measurement theory, and of some selected applications: quantum cryptography and quantum computers, cold atoms, light emitting and laser diodes, and atomic clocks. The book is aimed at a general audience and the only prerequisite is a high-school background in mathematics.

Preface v

Foreword ix

1 An Inconvenient Principle 1

1.1 Waves in classical physics 2

1.2 The Mach–Zehnder interferometer 6

1.3 Photons 81

1.4 Photons in the Mach–Zehnder interferometer 15

1.5 The Mach–Zehnder interferometer revisited 18

1.6 Quantum particles 21

1.7 Delayed choice and interaction-free measurement 24

1.8 Further reading 28

2 Secure Communications 29

2.1 Classical cryptography: Secret key and public key 29

2.2 Light polarization 33

2.3 Photon polarization 35

2.4 The BB84 protocol of quantum cryptography 39

2.5 Further reading 4

3 Einstein, Bohr, and Bell 45

3.1 Superluminal communications? 46

3.2 A remarkable inequality 48

3.3 Quantum physics and entanglement 50

3.4 Bell’s non-locality and experiment 54

3.5 Further reading 59

4 Atoms, Light, and Lasers 61

4.1 Classical particles and classical waves on a line 62

4.2 A quantum particle in a potential well 65

4.3 Heisenberg inequalities and energy levels 67

4.4 Atoms 71

4.5 Lasers 74

4.6 Further reading 80

5 Cold Atoms 81

5.1 What is temperature? 82

5.2 Cooling atoms 86

5.3 Bose–Einstein condensates 97

5.4 Further reading 104

6 The Kingdom of Semiconductors 105

6.1 Conductors and insulators 106

6.2 Semiconductors 112

6.3 Interaction with an electromagnetic field 116

6.4 Heterojunctions 118

6.5 Further reading 123

7 Relativistic Quantum Physics 125

7.1 Relativistic quantum field theory 125

7.2 The standard model of particle physics 135

7.3 Quantum gravity 142

7.4 Further reading 147

8 Towards a Quantum Computer? 149

8.1 Bits and quantum logic gates 150

8.2 Quantum algorithms 156

8.3 Quantum algorithms and algorithmic complexity 161

8.4 Physical realizations 163

8.5 Further reading 165

9 The Environment is Watching 167

9.1 Decoherence: An elementary example 168

9.2 Environment and decoherence 172

9.3 Further reading 179

10 Interpretations 181

10.1 The Copenhagen interpretation 182

10.2 von Neumann’s theory 188

10.3 The measuring apparatus is macroscopic 193

10.4 Non-standard interpretations 196

10.5 Conclusion 200

10.6 Further reading 201

11 Appendices 203

References 231

Index 235

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