Electrical Metrology and the Revised SI

Part 1: Murray Early, Electrical Metrology, MSL, New Zealand Part 2: Ilya Budovsky, Electricity Section, NMI, Australia

14 September 2017 The 2019 SI Revision of Electrical Metrology…Overview Part 1: Murray The need for change to the SI electrical units The challenge of electrical units Part 2: Ilya Preparations for change Support for stakeholders Questions

Metrology: the science of measurement

2 Proposed Changes to the SI A revised SI, not new – same units, different definitions Based on 7 fixed constants (values to be finalised)

To be fixed in 2019 Already fixed 1 h = 6.626 070 04 ×10–34J s 5 c = 299 792 548 m s-1

–19 2 e = 1.602 176 621 ×10 C 6 ΔνCs = 9 192 631 770 Hz

–23 –1 -1 3 k = 1.380 648 5 ×10 J K 7 Kcd= 683 lm W

23 –1 4 NA= 6.022 140 857 ×10 mol

3 Why Change? 1. Concern over stability of the IPK (international prototype kilogram) 2. Link to the IPK limits accuracy of electrical units 3. Present base units are a mix of definition and realisation 4. Base the system on the most stable quantities available 5. Opportunity to base mole on Avogadro’s constant 6. Opportunity to base on Boltzmann’s constant

NB: , metre and candela will not change in 2019

4 Electrical Units – quantum effects

Electrical measurements revolutionised by quantum effects:

Year Equation Constant ℎ Josephson 2푒 1962 Josephson effect 푉=푛 푓 퐾 = 2푒 constant ℎ 1 ℎ von Klitzing ℎ 휇 푐 1980 Quantum Hall effect 푅 = 푅 = = 푖 푒 constant 푒 2훼

1987 Single electron counting 퐼 = 푛푒푓 Electronic charge 푒

NB: α≅ 1/137, is the fine structure constant 1990 - Conventional values defined:

• KJ–90 = 483 597.9 GHz/V (ur = 0.4 ppm)

• RK–90 = 25 812.807 Ω (ur = 0.1 ppm) • uncertainties dominated by link to mechanical units (, energy, power) reproducibility > 1000 times better! • best calibrations not strictly traceable to the SI?  h  The Josephson Effect   f  0.14 mV  2e  Josephson SIS junction: (for f = 70 GHz, step n = 1) • Superconductor-Insulator-Superconductor sandwich • radiated by microwaves, frequency f • small dc voltage generated 1990s key advance: put 104 to > 105 in a series array – 10 V output! Mature technology: > 20(?) arrays in use in North America (industry and the military) Various kinds of junctions (SNS, SINIS,…) Various array designs (conventional, programmable, pulse) Programmable AC voltages – applied to impedance and power standards 10 V SIS array 6 h The Quantum Hall Effect  25.8 k Klaus von Klitzing (1985) e2 Quantum Hall Resistor: “for the discovery of the quantized Hall effect” • 2D electron layer • Large magnetic field (~10 T) • Low temperatures (< 2.3 K)

Laughlin, Stormer and Tsui (1998) “for their discovery of a new form of quantum fluid with fractionally charged excitations”

Directly compare Graphene and GaAs devices: (Janssen et al, NPL) Thouless, Haldane, Kosterlitz (2016) ”for theoretical discoveries of topological phase 2 -11 7 (RGaAs/AlGaAs-RGraphene) / (h/2e ) = (-4.7 ± 8.6) x 10 transitions and topological phases of matter” Quantum Current Source ef  1.6 pA SOLID STATE ENTANGLER Clocking electrons one by one (for f = 10 MHz) • Currents still too small for high accuracy - ongoing research challenges Various device technologies • SET (single electron tunneling) turnstile

V/2 -V/2 • SAW (surface acoustic wave) U1 U2 • Tunable barrier pumps, carbon nanotubes etc

3-e 1-e 2-e These technologies have strong relevance to: Tunnelling rate vs gate voltage • future electronic devices (impedance (e.g. memory) suppresses unwanted • new physics (e.g. qubits for processes quantum computing) • manipulation of entanglement –fully quantum Hybrid superconductor-normal-metal turnstile 8 Pekola et al, Nature Physics 4 (2008) 120 Linking Electricity to - The Kibble Balance Mechanical versus electrical force (power) • Two modes: weighing and calibration (static & dynamic) • Weighing current I, induced voltage U, coil velocity  • Geometric factor , magnetic field B – eliminated by combining the 2 modes

Weighing mode Calibration mode

        F I dl  B I m g U  B  dl    dl  B  v     v mg U UI    so m  (these all known to < 10-8) I v gv 9 UI The Kibble Balance m  gv

Equivalence of Electrical and Mechanical Power: UI  Pelec  Pmech  mg U 2 U Virtual electrical power:P ~ since: I  s elec R R h Measure resistance in terms of quantum Hall effect: R ~ e2 h Measure voltages in terms of Josephson effect: U ~ f 2e MSL Kibble Balance Project h 2 • Designed by Chris Sutton Then the electrical power is related to Planck’s constant:  2e • Based on twin -balance (actually a measure of the Planck constant h) P ~ ~ h concept elec h 2 • May be used in an oscillatory mode Redefinition: define h and derive mass scale e

10 Current Status of NA (h) Measurement Results

퐴 푒 푀푐훼 푁 = 2푅ℎ

-9 uR = 33 x 10 NRC 2017: h = 6.626 070 133 (60) Js standard relative uncertainty: 9.1 x 10-9 (58 terms in uncertainty budget)

11 Improving Accuracy in Electrical Measurements

∆ ∆ Metrological Moore’s Law: = 10 (i.e. improve accuracy by about a factor of 10 every 15 years) Sustained incremental improvements + ‘quantum’ jumps from breakthrough discoveries

Why bother – do we need it? (multiple manufacturers make 8.5 digit DMMs) 10-4

10-5 Single -6 Junctions 10 Weston Cells KJ-90 uncertainty Arrays (conventional value of 2e/h) 10-7

10-8 Between Labs

Change in Voltage Voltage / Within Labs -9 ∆푢 ∆ 10 = 10 1920 1940 1960 1980 2000 푢 Year 12 From Bachmair, 1988 and Hamilton, 1998 The Particular Challenge of Electrical Units

The discovery of electromagnetism (Faraday 1812, Ørsted 1820) • Multiple units systems e.g. Electrostatic-CGS, Electromagnetic-CGS, Gaussian, Heaviside… • Freedom in choice of unit, numbers and constants in equations (e.g. 4)

• Controversy involving some great names (, Weber, , Heaviside, Lorentz, ….) Michael Faraday Other systems used • e.g. the CGS (cm second) developed by Gauss, Maxwell… (< 1874) • Force 1 dyne = 1 gm x 1 cm/s2 = 10-3 kg x 10-2 m/s2 = 10-5 N CGS has certain advantages – some prefer to teach electromagnetism in CGS

8 • battery: 1.5 volt = 0.005 (ESU) = 1.5 x 10 (EMU) James Clerk Maxwell Consistent use of SI works well, but …

“Scientists have spent almost a century disagreeing about the units for electromagnetism” (J H Williams)

13 Electrical Units – the

Force laws – link to mechanical quantities (also via energy or power)

푞푞 푑퐹 퐼 퐼 Coulomb’s Law:퐹 =푘 Ampere’s Force Law: = 2푘 푟 푑푙 푑 푑푞 푘 linked by:퐼 = requiring: = 푐 푑푡 푘 d = 1 m I1 = I2 = 1 ampere [c is large hence for unit quantities, electric >> magnetic forces] dF/dl = 2x10-7 N/m 1881: electrolytic method • 1 ampere deposits silver at the rate of 0.001118 g/s CGS-EMU: 1 = 10 A

MKSA (SI) ampere 1949 – based on Ampere’s force law, defines µ0 휇 1 1 푘 = 2푘 = = 푐 푍 = 4휋휀 휇휀 휀 14 Curious about the ‘permeability of free space’ µ0?

Using CGS-EMU: d = 1 cm I = I = 1 abampere 푑퐹 퐼 퐼 1 2 푘 =1 =2 dF/dl = 2 dyne/cm 푑푙 푑

For I1 = I2 = 1 abampere, d = 1 cm then dFmCGS /dl = 2 dyne/cm

-5 -2 -3 Convert to SI: (1 dyne = 10 N, 1 cm = 10 m) so dFmSI /dl = 2 x10 N/m

Now using the SI formula: 푑퐹 퐼 퐼 = 2푘 푑푙 푑

-2 -7 2 Since I1 = I2 = 10 ampere (using 1 abampere = 10 A), d = 10 m, then 2km = 2 x10 N/A

휇 To avoid factors of π in field relationships, write: 2푘 = 2휋 Then: µ = 4π x10-7 N/A2 (the magnetic constant, conversion factor for the SI) 0 15 Proposed Changes to the SI 2푒 퐾 = KJ will change by ~0.1 ppm –will affect voltage references slightly ℎ ℎ RK will change by ~0.02 ppm – only affect QHR realisations? 푅 = 푒 휇 μ0, Ɛ0, and Z0 will become experimentally determined 푍 = 휀 –10 –7 –2 • μ0 = 4π [1 + 0.0(2.3) ×10 ] ×10 N A 2ℎ • Uncertainty:푢 휇 =푢 훼 since: 휇 =훼 푐푒 Timeline: • July 1, 2017: Deadline of acceptance of new data. • Sept 4, 2017: CODATA TGFC meeting, manuscripts must be already accepted and publicly available. • Sept 5-6, 2017: CCU reviews values recommends digits etc. • Oct 16-20, 2017: CIPM meeting – recommendation to the CGPM. • Nov 13-24, 2018: CGPM approves the ‘Revised SI’. • May 20, 2019: Implementation day. 16 Murray Early T: 04 931 3192 E: [email protected]

www.measurement.govt.nz Resources 8th edition of SI Brochure (2014): http://www.bipm.org/en/publications/si-brochure/ Draft 9th edition: http://www.bipm.org/utils/common/pdf/si-brochure-draft-2016b.pdf Brandbook: http://www.bipm.org/utils/common/pdf/SI-Brand-Book.pdf

18 Precision Measurement…

…brings the world into focus (concept: Michael de Podesta, NPL)