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The New International System of Units (SI): Quantum Metrology and Quantum Standards

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The New International System of Units (SI): Quantum Metrology and Quantum Standards

Ernst O. Göbel, Uwe Siegner

ISBN: 978-3-527-81449-7 May 2019 272 Pages

Description

The International System of Units, the SI, provides the foundation for all measurements in science, engineering, economics, and society. The SI has been fundamentally revised in 2019. The new SI is a universal and highly stable unit system based on invariable constants of nature. Its implementation rests on quantum metrology and quantum standards, which base measurements on the manipulation and counting of single quantum objects, such as electrons, photons, ions, and flux quanta. This book explains and illustrates the new SI, its impact on measurements, and the quantum metrology and quantum technology behind it.
The book is based on the book ?Quantum Metrology: Foundation of Units and Measurements? by the same authors.
From the contents:

-Measurement
-The SI (Système International d?Unités)
-Realization of the SI Second: Thermal Beam Cs Clock, Laser Cooling, and the Cs Fountain Clock
-Flux Quanta, Josephson Effect, and the SI Volt
-Quantum Hall Effect, the SI Ohm, and the SI Farad
-Single-Charge Transfer Devices and the SI Ampere
-The SI Kilogram, the Mole, and the Planck constant
-The SI Kelvin and the Boltzmann Constant
-Beyond the present SI: Optical Clocks and Quantum Radiometry
-Outlook

Foreword ix

Preface xi

List of Abbreviations xv

1 Introduction 1

References 3

2 Some Basics 5

2.1 Measurement 5

2.1.1 Limitations of Measurement Uncertainty 5

2.1.1.1 The Fundamental Quantum Limit 6

2.1.1.2 Noise 7

2.2 The SI (Système International d’Unités) 9

2.2.1 The Second: Unit of Time 11

2.2.2 The Meter: Unit of Length 13

2.2.3 The Kilogram: Unit of Mass 14

2.2.4 The Ampere: Unit of Electric Current 15

2.2.5 The Kelvin: Unit of Thermodynamic Temperature 16

2.2.6 The Mole: Unit of Amount of Substance 18

2.2.7 The Candela: Unit of Luminous Intensity 19

2.2.8 Summary: Base and Derived Units of the SI 21

References 21

3 Realization of the SI Second: Thermal Beam Cs Clock, Laser Cooling, and the Cs Fountain Clock 23

3.1 The Thermal Beam Cs Clock 25

3.2 Techniques for Laser Cooling and Trapping of Atoms 28

3.2.1 Doppler Cooling, Optical Molasses, and Magneto-Optical Traps 29

3.2.2 Cooling Below the Doppler Limit 31

3.3 The Cs Fountain Clock 32

References 35

4 Flux Quanta, Josephson Effect, and the SI Volt 39

4.1 Josephson Effect and Quantum Voltage Standards 39

4.1.1 Basics of Superconductivity 39

4.1.2 Basics of the Josephson Effect 41

4.1.2.1 AC and DC Josephson Effect 42

4.1.2.2 Mixed DC and AC Voltages: Shapiro Steps 43

4.1.3 Basic Physics of Real Josephson Junctions 44

4.1.4 Josephson Voltage Standards 46

4.1.4.1 General Overview: Materials and Technology of Josephson Arrays 47

4.1.4.2 SIS Josephson Voltage Standards 48

4.1.4.3 Programmable Binary Josephson Voltage Standards 50

4.1.4.4 Pulse-Driven AC Josephson Voltage Standards 53

4.1.5 Metrology with Josephson Voltage Standards 57

4.1.5.1 DC Voltage, the SI Volt 57

4.1.5.2 The Conventional Volt in the Previous SI 59

4.1.5.3 AC Measurements with Josephson Voltage Standards 59

4.2 Flux Quanta and SQUIDs 62

4.2.1 Superconductors in External Magnetic Fields 62

4.2.1.1 Meissner–Ochsenfeld Effect 63

4.2.1.2 Flux Quantization in Superconducting Rings 65

4.2.1.3 Josephson Junctions in External Magnetic Fields and Quantum Interference 66

4.2.2 Basics of SQUIDs 67

4.2.3 Applications of SQUIDs in Measurement 71

4.2.3.1 Real DC SQUIDs 71

4.2.3.2 SQUID Magnetometers and Magnetic Property Measurement Systems 73

4.2.3.3 Cryogenic Current Comparators: Current and Resistance Ratios 74

4.2.3.4 Biomagnetic Measurements 76

4.3 Traceable Magnetic Flux Density Measurements 77

References 80

5 Quantum Hall Effect, the SI Ohm, and the SI Farad 87

5.1 Basic Physics of Three- and Two-Dimensional Semiconductors 88

5.1.1 Three-Dimensional Semiconductors 88

5.1.2 Two-Dimensional Semiconductors 90

5.2 Two-Dimensional Electron Systems in Real Semiconductors 91

5.2.1 Basic Properties of Semiconductor Heterostructures 92

5.2.2 Epitaxial Growth of Semiconductor Heterostructures 93

5.2.3 Semiconductor Quantum Wells 94

5.2.4 Modulation Doping 95

5.3 The Hall Effect 97

5.3.1 The Classical Hall Effect 97

5.3.1.1 The Classical Hall Effect in Three Dimensions 97

5.3.1.2 The Classical Hall Effect in Two Dimensions 98

5.3.2 Physics of the Quantum Hall Effect 99

5.4 Metrology Using the Quantum Hall Effect 103

5.4.1 DC Quantum Hall Resistance Standards, the SI Ohm 103

5.4.2 The Conventional Ohm in the Previous SI 104

5.4.3 Technology of DC Quantum Hall Resistance Standards and Resistance Scaling 106

5.4.4 AC Quantum Hall Resistance Standards, the SI Farad 108

5.4.5 Relation Between Electrical Metrology and the Fine-Structure Constant 110

5.5 Graphene for Resistance Metrology 111

5.5.1 Basic Properties of Graphene 111

5.5.2 Fabrication of Graphene Monolayers for Resistance Metrology 113

5.5.3 Quantum Hall Effect in Monolayer Graphene 115

References 117

6 Single-Charge Transfer Devices and the SI Ampere 123

6.1 Basic Physics of Single-Electron Transport 124

6.1.1 Single-Electron Tunneling 124

6.1.2 Coulomb Blockade in SET Transistors 125

6.1.3 Coulomb Blockade Oscillations and Single-Electron Detection 127

6.1.4 Clocked Single-Electron Transfer 129

6.2 Quantized Current Sources 130

6.2.1 Metallic Single-Electron Pumps 131

6.2.2 Semiconducting Quantized Current Sources 133

6.2.2.1 GaAs-Based SET Devices 133

6.2.2.2 Silicon-Based SET Devices 137

6.2.3 Superconducting Quantized Current Sources 138

6.2.4 Self-Referenced Quantized Current Sources 140

6.3 Realization of the SI Ampere 142

6.3.1 Ampere Realization via the SI Volt and SI Ohm 142

6.3.2 Direct Ampere Realization with Quantized Current Sources 144

6.4 Consistency Tests: Quantum Metrology Triangle 144

References 146

7 The SI Kilogram, the Mole, and the Planck Constant 153

7.1 From “Monitoring the Stability of the Kilogram” to the Planck Constant 156

7.2 The Avogadro Experiment 158

7.3 The Kibble Balance Experiment 165

7.4 The Mole: Unit of Amount of Substance 169

7.5 The CODATA Evaluation of the Value of the Defining Planck Constant and the Maintenance and Dissemination of the Kilogram 170

7.5.1 The CODATA Evaluation and the Final Value of the Defining Planck Constant, h 170

7.5.2 Realization, Maintenance, and Dissemination of the Kilogram 172

References 173

8 The SI Kelvin and the Boltzmann Constant 181

8.1 Primary Thermometers 182

8.1.1 Dielectric Constant Gas Thermometry 183

8.1.2 Acoustic Gas Thermometry 184

8.1.3 Radiation Thermometry 186

8.1.4 Doppler Broadening Thermometry 187

8.1.5 Johnson Noise Thermometry 189

8.1.6 Coulomb Blockade Thermometry 191

8.2 The CODATA Evaluation of the Value of the Defining Boltzmann Constant, Realization and Dissemination of the New Kelvin 193

8.2.1 The CODATA Evaluation of the Final Value of the Defining Boltzmann Constant 193

8.2.2 Realization and Dissemination of the Kelvin 194

References 194

9 Beyond the Present SI: Optical Clocks and Quantum Radiometry 201

9.1 Optical Clocks and a New Second 201

9.1.1 Femtosecond Frequency Combs 204

9.1.2 Trapping of Ions and Neutral Atoms for Optical Clocks 209

9.1.2.1 Ion Traps 209

9.1.2.2 Optical Lattices 211

9.1.3 Neutral Atomic clocks 211

9.1.4 Atomic Ion Clocks 214

9.1.5 Possible Variation of the Fine-Structure Constant, 𝛼 217

9.2 Single-Photon Metrology and Quantum Radiometry 220

9.2.1 Single-Photon Sources 222

9.2.1.1 (NV) Color Centers in Diamond 223

9.2.1.2 Semiconductor Quantum Dots 225

9.2.2 Single-Photon Detectors 227

9.2.2.1 Nonphoton-Number-Resolving Detectors 227

9.2.2.2 Photon-Number-Resolving Detectors 228

9.2.3 Metrological Challenge 229

References 230

10 Outlook 245

References 246

Index 247