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

271 Pages·2019·5.943 MB·English

by  Göbel, Ernst O., Siegner, Uwe

TheNewInternationalSystemofUnits(SI)

The New International System of Units (SI)
QuantumMetrologyandQuantumStandards
ErnstO.GöbelandUweSiegner
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10 9 8 7 6 5 4 3 2 1
v
Contents
Foreword ix
Preface xi
ListofAbbreviations xv
1 Introduction 1
References 3
2 SomeBasics 5
2.1 Measurement 5
2.1.1 LimitationsofMeasurementUncertainty 5
2.1.1.1 TheFundamentalQuantumLimit 6
2.1.1.2 Noise 7
2.2 TheSI(SystèmeInternationald’Unités) 9
2.2.1 TheSecond:UnitofTime 11
2.2.2 TheMeter:UnitofLength 13
2.2.3 TheKilogram:UnitofMass 14
2.2.4 TheAmpere:UnitofElectricCurrent 15
2.2.5 TheKelvin:UnitofThermodynamicTemperature 16
2.2.6 TheMole:UnitofAmountofSubstance 18
2.2.7 TheCandela:UnitofLuminousIntensity 19
2.2.8 Summary:BaseandDerivedUnitsoftheSI 21
References 21
3 RealizationoftheSISecond:ThermalBeamCsClock,Laser
Cooling,andtheCsFountainClock 23
3.1 TheThermalBeamCsClock 25
3.2 TechniquesforLaserCoolingandTrappingofAtoms 28
3.2.1 DopplerCooling,OpticalMolasses,andMagneto-OpticalTraps 29
3.2.2 CoolingBelowtheDopplerLimit 31
3.3 TheCsFountainClock 32
References 35
4 FluxQuanta,JosephsonEffect,andtheSIVolt 39
4.1 JosephsonEffectandQuantumVoltageStandards 39
vi Contents
4.1.1 BasicsofSuperconductivity 39
4.1.2 BasicsoftheJosephsonEffect 41
4.1.2.1 ACandDCJosephsonEffect 42
4.1.2.2 MixedDCandACVoltages:ShapiroSteps 43
4.1.3 BasicPhysicsofRealJosephsonJunctions 44
4.1.4 JosephsonVoltageStandards 46
4.1.4.1 GeneralOverview:MaterialsandTechnologyofJosephsonArrays 47
4.1.4.2 SISJosephsonVoltageStandards 48
4.1.4.3 ProgrammableBinaryJosephsonVoltageStandards 50
4.1.4.4 Pulse-DrivenACJosephsonVoltageStandards 53
4.1.5 MetrologywithJosephsonVoltageStandards 57
4.1.5.1 DCVoltage,theSIVolt 57
4.1.5.2 TheConventionalVoltinthePreviousSI 59
4.1.5.3 ACMeasurementswithJosephsonVoltageStandards 59
4.2 FluxQuantaandSQUIDs 62
4.2.1 SuperconductorsinExternalMagneticFields 62
4.2.1.1 Meissner–OchsenfeldEffect 63
4.2.1.2 FluxQuantizationinSuperconductingRings 65
4.2.1.3 JosephsonJunctionsinExternalMagneticFieldsandQuantum
Interference 66
4.2.2 BasicsofSQUIDs 67
4.2.3 ApplicationsofSQUIDsinMeasurement 71
4.2.3.1 RealDCSQUIDs 71
4.2.3.2 SQUIDMagnetometersandMagneticPropertyMeasurement
Systems 73
4.2.3.3 CryogenicCurrentComparators:CurrentandResistanceRatios 74
4.2.3.4 BiomagneticMeasurements 76
4.3 TraceableMagneticFluxDensityMeasurements 77
References 80
5 QuantumHallEffect,theSIOhm,andtheSIFarad 87
5.1 BasicPhysicsofThree-andTwo-DimensionalSemiconductors 88
5.1.1 Three-DimensionalSemiconductors 88
5.1.2 Two-DimensionalSemiconductors 90
5.2 Two-DimensionalElectronSystemsinRealSemiconductors 91
5.2.1 BasicPropertiesofSemiconductorHeterostructures 92
5.2.2 EpitaxialGrowthofSemiconductorHeterostructures 93
5.2.3 SemiconductorQuantumWells 94
5.2.4 ModulationDoping 95
5.3 TheHallEffect 97
5.3.1 TheClassicalHallEffect 97
5.3.1.1 TheClassicalHallEffectinThreeDimensions 97
5.3.1.2 TheClassicalHallEffectinTwoDimensions 98
5.3.2 PhysicsoftheQuantumHallEffect 99
5.4 MetrologyUsingtheQuantumHallEffect 103
5.4.1 DCQuantumHallResistanceStandards,theSIOhm 103
5.4.2 TheConventionalOhminthePreviousSI 104
Contents vii
5.4.3 TechnologyofDCQuantumHallResistanceStandardsandResistance
Scaling 106
5.4.4 ACQuantumHallResistanceStandards,theSIFarad 108
5.4.5 RelationBetweenElectricalMetrologyandtheFine-Structure
Constant 110
5.5 GrapheneforResistanceMetrology 111
5.5.1 BasicPropertiesofGraphene 111
5.5.2 FabricationofGrapheneMonolayersforResistanceMetrology 113
5.5.3 QuantumHallEffectinMonolayerGraphene 115
References 117
6 Single-ChargeTransferDevicesandtheSIAmpere 123
6.1 BasicPhysicsofSingle-ElectronTransport 124
6.1.1 Single-ElectronTunneling 124
6.1.2 CoulombBlockadeinSETTransistors 125
6.1.3 CoulombBlockadeOscillationsandSingle-ElectronDetection 127
6.1.4 ClockedSingle-ElectronTransfer 129
6.2 QuantizedCurrentSources 130
6.2.1 MetallicSingle-ElectronPumps 131
6.2.2 SemiconductingQuantizedCurrentSources 133
6.2.2.1 GaAs-BasedSETDevices 133
6.2.2.2 Silicon-BasedSETDevices 137
6.2.3 SuperconductingQuantizedCurrentSources 138
6.2.4 Self-ReferencedQuantizedCurrentSources 140
6.3 RealizationoftheSIAmpere 142
6.3.1 AmpereRealizationviatheSIVoltandSIOhm 142
6.3.2 DirectAmpereRealizationwithQuantizedCurrentSources 144
6.4 ConsistencyTests:QuantumMetrologyTriangle 144
References 146
7 TheSIKilogram,theMole,andthePlanckConstant 153
7.1 From“MonitoringtheStabilityoftheKilogram”tothePlanck
Constant 156
7.2 TheAvogadroExperiment 158
7.3 TheKibbleBalanceExperiment 165
7.4 TheMole:UnitofAmountofSubstance 169
7.5 TheCODATAEvaluationoftheValueoftheDefiningPlanckConstant
andtheMaintenanceandDisseminationoftheKilogram 170
7.5.1 TheCODATAEvaluationandtheFinalValueoftheDefiningPlanck
Constant,h 170
7.5.2 Realization,Maintenance,andDisseminationoftheKilogram 172
References 173
8 TheSIKelvinandtheBoltzmannConstant 181
8.1 PrimaryThermometers 182
8.1.1 DielectricConstantGasThermometry 183
8.1.2 AcousticGasThermometry 184
viii Contents
8.1.3 RadiationThermometry 186
8.1.4 DopplerBroadeningThermometry 187
8.1.5 JohnsonNoiseThermometry 189
8.1.6 CoulombBlockadeThermometry 191
8.2 TheCODATAEvaluationoftheValueoftheDefiningBoltzmann
Constant,RealizationandDisseminationoftheNewKelvin 193
8.2.1 TheCODATAEvaluationoftheFinalValueoftheDefiningBoltzmann
Constant 193
8.2.2 RealizationandDisseminationoftheKelvin 194
References 194
9 BeyondthePresentSI:OpticalClocksandQuantum
Radiometry 201
9.1 OpticalClocksandaNewSecond 201
9.1.1 FemtosecondFrequencyCombs 204
9.1.2 TrappingofIonsandNeutralAtomsforOpticalClocks 209
9.1.2.1 IonTraps 209
9.1.2.2 OpticalLattices 211
9.1.3 NeutralAtomicclocks 211
9.1.4 AtomicIonClocks 214
9.1.5 PossibleVariationoftheFine-StructureConstant,𝛼 217
9.2 Single-PhotonMetrologyandQuantumRadiometry 220
9.2.1 Single-PhotonSources 222
9.2.1.1 (NV)ColorCentersinDiamond 223
9.2.1.2 SemiconductorQuantumDots 225
9.2.2 Single-PhotonDetectors 227
9.2.2.1 Nonphoton-Number-ResolvingDetectors 227
9.2.2.2 Photon-Number-ResolvingDetectors 228
9.2.3 MetrologicalChallenge 229
References 230
10 Outlook 245
References 246
Index 247