Electrical determinations of αand impact on the SI

Transcription

1 Electrical determinations of αand impact on the SI F Piquemal 1, O Thévenot 1, and P Gournay 2 1: LNE 2: BIPM Laboratoire national de métrologie et d essais

2 Outline 1) Introduction 2) The fine structure constant αand the SI 2.1) Past determinations of α: a convergence of atomic and condensed matter physics 2.2) αand the new definitions of ampere and kilogram 2.3) Realisations of the impedance units (farad, ohm) in the SI 3) Towards new electrical determinations of alpha 3.1) Thompson Lampard theorem and implementation conditions 3.2) LNE calculable capacitor and impedance chain 3.3) NMIA-BIPM calculable capacitor and impedance chain 3.4) NIM calculable capacitor 4) Conclusion and outlooks CODATA Workshop, Elville, 2 6 February

3 Introduction Key dates and known faces 1916: Sommerfeld introduced αto explainthe structure in hydrogen atoms Now, αisa measureof the strengthof the electromagnetic field! A. Sommerfeld 1956Theoremin electrostatic discoveredby A. Thompson and D.G. Lampard 1962: Josephson predictions First accessfor electricalmetrologistto estimate αvia the gyromagnetic ratio of the proton + Lampard standard D.G. Lampard 1980: Quantum Hall effect discovered by Klaus von Klitzing Most precise determination of α from condensed matter physics(qhe+lampard) B. Josephson 2018: Birthof a quantum SI? K. vonklitzing 3

4 Uncertainty of LSA based values of h, e, α 1E-02 u r 1E-03 1E-04 1E-05 h e α 1E-06 1E-07 1E-08 1E-09 New SI Rendez vous 1E

5 Towards a quantum SI Present SI Futur SI Conditions to be fulfilled: Validitytests at 10-8 level QHE : R K = h/e 2 JE: K J = 2e/h 5

6 Outline 1) Introduction 2) The fine structure constant αand the SI 2.1) Past determinations of α: a convergence of atomic and condensed matter physics 2.2) αand the new definitions of ampere and kilogram 2.3) Realisations of the impedance units (farad, ohm) in the SI 3) Towards new electrical determinations of alpha 3.1) Thompson Lampard theorem and implementation conditions 3.2) LNE calculable capacitor and impedance chain 3.3) NMIA-BIPM calculable capacitor and impedance chain 3.4) NIM calculable capacitor 4) Conclusion and outlooks 6

7 2.1) Past determinations of α Validity tests of QED at a few parts in 10 8 thanks to QHE α 1 (a e ) α 1 (R K ) NIST-90/97 NMIA-97 LNE-01 NPL-88 NIM (α -1 / ) x

8 Then determinations of α(h/m) come! 1E-02 1E-03 LSA values 1E-04 α(r K ) α(γ' p,h ) α(q SET ) 1E-05 u r 1E-06 1E-07 1E-08 1E-09 α(a e ) α(h/m) 1E

9 Present situation on α a e h/m Γ' p,h-90 (lo) R K ν Mu ν H,ν D Q S (α -1 / ) x

10 α from quantum Hall effect 2 μ SinceR K = h/e 2 by theory QED corrections on R K = h/e 2 at 10-19! A. Penin, PRB, 2009 R K = h/e 2 experimentally tested at parts in 10 8 by implementing calculable capacitors LNE i R H (i) independent of devices Si-MOSFET GaAs/AlGaAs NPL 1991, METAS Graphene GaAs/AlGaAs NPL 2012 LNE GaAs/AlGaAs GaAs/AlGaAs LNE Ribeiro-Palau et al, condmat 10

11 α from Nuclear Magnetic Resonance(1/2) Measurement of the proton/helion spin precession frequency in a calculated uniform magnetic field. ω, ( ) ( ) ( ) γ p,h (lo) : shieldedgyromagneticratio at low magnetic field μ 2μ μ, R : Rydberg constant µ P /µ B : magneticmoment of the proton in unitsof the Bohr magneton / Sphericalsampleof Xat 25 C surroundedby vacuum -Proton: X= pure H 2 O liquid(withoutbubble!) -Helion: X= pure He 3 gasat lowpressure NIST experiment B= 1 mt, single-layer solenoidof 1 m length, 1 turn/mm Compensation techniques Buniformwithin2 parts in 10 8 in 6 cm diam. sphere E. Williams et al, IEEE TIM,

12 α from Nuclear Magnetic Resonance(2/2) Values E. Williams et al, IEEE TIM, 1989 P. Park et al, J. Korean Phys. Soc, 1999 NIST 1989: Γ KV 1999: Γ u r (α) Limitations Geometricfactor k sol - Pitch measurements - Radius correction Frequency shifts - Magnetic susceptibility - Temperature - Sample shape dependence - Chemical impurities Improvement axes? J. Flowers, B. Petley, 2001 New method to determine experimentallyk sol Mul -layer high currentsolenoid 12

13 α from single electron transport (1/2) Electron counting capacitance standard 1st stage: Pumpingelectronson and off cryogenic capacitor E. Williams et al, J. of NIST, 1992 M. Keller et al, Science nd stage: comparingcapacitances withc ref at room temperature C cryo = Ne/ V 4 μ 1 A 1 : dimensionless factor N:number of pumped electrons to charge the ECCS during a given period C cryo : capacitance compared to a capacitance C ref itself compared to ΔC of the calculable capacitor. n J, Voltage step number f J, Josephson irradiation frequency 13

14 α from single electron transport (2/2) Values NIST PTB Q S /e 1 = (-0.09 ±0.92) 10-6 Q S /e 1 = (-0.3 ±1.7) 10-6 M. Keller et al, Metrologia 2007 B. Camarota et al, Metrologia 2012 Limitations A few parts in 10 7 wouldbethe ultimatelimit - Relative electrontransfererror: Type A uncertainty: Freq. dependenceof Capa.10 mhzto 1 khz: 210-8! - Findthe good electronpump, operating at the right time! 14

15 2.2) αand the new definitionsof ampereand kilogram Increased knowledge of α: a key contribution for revising the SI in near future Watt balance experiments give hbased on the strong confidence that R K = h/e 2, but also that K J = 2e/h. Place of αin the discussion aroundthe new definitionof ampere 15

16 α: a rolein the new definitionof ampere CIPM 2006: Report of a committeeof the Académie des Sciences about the future SI J. Kovalevsky et al, 2006 Two possibilities as the base for the new definition of ampere: -The charge on the positron, e -The Planck charge q P = 2ε 0 hc = 2h/Z 0 = e/ α eor not e? This isno more the question! 16

17 Two versions of physics(1/2) αisa propertyof vacuum eas the base constant Based on the string theory, αcan be interpreted as the vacuum expectation valueof a scalar field related to the dilaton, a predicted particle which interacts with the ordinary matter. The values of the constants observed in our 4 dimension world depend on the dilaton. The dilatonand the volume of the supplementary dimensions are dynamic parameters which might vary in space and time. Therefore our observed constants are also expected to vary, including α.! If αdepends on time, the invariance by jaugetransformation in E&M will be complicated to be fulfiledif eis not chosen as the base constant. T. Damour, 2005 Another argument for e!? Equality between the absolute values of the charge on the electron and on the positron The neutrality of the world??? 17

18 Two versions of physics(2/2) α represents a property of the electron q P as the base constant The free electromagnetic field is coupled to charges through α, which thus appears as a property of electrons and not as a property of the free electromagnetic field. The string theory is not fully defined and no experimental evidence for a varying α Once hand cwith fixed values, fixing the numerical value of ewould imply that the so called electrical units are no more purely mechanical units and even no more geometrical units. P. Fayet,

19 Practical considerations(1/2) Fixing the numerical value of the elementary charge e The simplicityof the definitionfor the «man in the street» An easiesteducationalwayto explainthe new SI (comparedto Z 0?!) OK but the case of hfor kg?! The new SI with fixed values of h and e is obviously well adapted to quantum electrical metrology based on QHE and JE Definitions of the second and the electrical units could be coherent in thefarfutureifthesecondisredefinedbasedonthefixedvalueofthe electronmassm e (throughrydbergconstant) length (meter) c 0 Laser mass (kilogram) h Watt balance time (second) m e Optical clock current (ampere) e JE/QHE, SET? 19

20 Practical considerations(2/2) Towards an electronic colouring of the SI The choicefor e: - essentially based on outstanding results of collective phenomena (JE, QHE) reflecting a wave dominance of electron behaviour; -keepsampereunit at the first place, witha «mise en pratique» possiblybasedon SET deviceworkingon corpuscularaspect of the electron. 20

21 2.3) Realisationsof farad and ohm in the SI New Thompson Lampard calculable cross capacitors: Possible determinationof αat one part in 10 8 uncertainty An accurate standard of capacitance 21

22 ε 0 Calculable capacitor exact R K U r =110-7 QHE In the present SI 1 pf 10 pf 100 pf U r(lne) =310-8 TP: Terminal pair CCC: Cryogenic Current Comparator Quad.: Quadrature 2 TP coaxial Bridge U r(lne) = Ω 10 kω 100 kω 10 kω 100 kω 10 nf 1 nf 100 pf 10 pf CCC bridge Calculable resistor Quad. Bridge RCω= 1 4 TP coaxial Bridge 2 TP coaxial Bridge

23 ε 0 U r = R K exact In the new SI Calculable capacitor QHE 1 pf 10 pf 2 TP coaxial Bridge 100 Ω 10 kω 100 kω CCC bridge Calculable resistor 100 pf 10 kω 100 kω 10 nf 1 nf 100 pf 10 pf Quad. Bridge RCω= 1 4 TP coaxial Bridge 2 TP coaxial Bridge

24 ε 0 Calculable capacitor U r = R K AC QHE exact In the near future 10 pf 100 pf 2 TP coaxial Bridge 10 nf 1 nf Quad. Bridge RCω= 1 4 TP coaxial Bridge U r(lne) = pf 10 pf 2 TP coaxial Bridge

25 Outline 1) Introduction 2) The fine structure constant αand the SI 2.1) Past determinations of α: a convergence of atomic and condensed matter physics 2.2) αand the new definitions of ampere and kilogram 2.3) Realisations of the impedance units (farad, ohm) in the SI 3) Towards new electrical determinations of alpha 3.1) Thompson Lampard theorem and implementation conditions 3.2) LNE calculable capacitor and impedance chain 3.3) NMIA-BIPM calculable capacitor and impedance chain 3.4) NIM calculable capacitor 4) Conclusion and outlooks 25

26 Thompson Lampard calculable capacitor Douglas Geoffrey Lampard vonklitzingconstantr K and α Klaus von Klitzing

27 3.1) Thompson Lampard theorem Theorem(1956): For a cylindrical system of 4 isolated electrodes (by means of infinitesimally small gaps) of infinite length and placed in vacuum, 1 4 γ 13 γ exp(-π γ 13 /ε 0 )+exp(-π γ 24 /ε 0 )=1and γ 13 = γ 24 = γ=(ε 0 ln2)/πifperfectsymmetry Theorem extended to a system of 5 electrodes N. Elnekavé(LCIE ) If one successivelyconnectstwoadjacent electrodes, the five-electrodessystem isequivalentto five different four-electrodes capacitors by circular permutation. - Redundant values - Information on the degree of perfection Electrode axis are on the vertices of a regular pentagon if 5 π γ = ln ε γ 25 γ 14 γ γ γ = γ = γ 13 = pf/m

28 3.1) Implementation conditions of the theorem 3challenges to betackled! 1) Infinite length of the electrodes The theoremisvalidonlyfor a uniformfieldrepartition(out of extremityeffect) 1 3 Thompson finds out a solution consisting in introducing a movable guard electrode in the inter-electrode cavity C 1 = L 1 γ+ δ extr(1) 1 C 2 = L 2 γ+ δ extr(2) L 1 C= C 1 C 2 = (L 1 L 2 ) γ if δ extr(1) = δ extr(2) L 2 28

29 = = = z z C C k δ π α α z α=0 0, 1 0, = = = n z z C C n n k n δ α π α z 2) Null thickness inter-electrodes insulator It can be demonstrated that the error δ due to the non null thickness z of the insulator, variesasafunctionofangle, α,betweenthe electrodes tangents, at their contact to the insulator z α 3.1) Implementation conditions of the theorem

30 3.1) Implementation conditions of the theorem 3) Cylindrical system Electrodes withstraightness< 100 nm over the usefullength(σ< ) dedicated apparatus for the measurement of the cylindricality defect Electrodes in vertical position, with a positionning better than 50 nm Lateralshiftingof the movableguard< 50 nm (σ< ) Coaxialitybetweencross section & movableaxis < 0.1 µrad Calculable capacitorin vacuum chamber

31 3.2) LNE calculable capacitor and impedance chain Objective: determiner K (thus α) withan uncertaintydown to one part in 10 8 Uncertainty budget in 2000 Uncertainty components 1σ relative uncertainty x 10-8 Laser wavelenght Air refractive index Laser alignment 0.09 Defect of the movable corner cube reflector 0.02 Deformation of the pentagon 0.02 Cylindrical defect 2.4 Efficiency of the movable guard 0.2 Lateral shifting of the spike 3 Bridge ratio (used 5 times) 1.5 Injection signal 0.3 Bridge coaxiality defect 0.5 Loading 0.3 Voltage effect (10 pf, 100 pf, 1000 pf) nf connection effect 0.3 Frequency (quad bridge) 0.02 Resistor frequency effect 1.5 DC QHE 0.3 Total type B uncertainties 4.6 Specifications of the new calculable capacitor Realization of a new set of electrodes Fabrication of a new standard in vertical position Realization of capacitance variation of 1pF New ratio-transformers Optimized coaxial calculable resistors and resistance transfer standards G. Trapon and al, Metrologia, 2003

32 Architecture of the new LNE calculable capacitor Hexapodal frame Driving plate Metrological plate Measuring machine Calculable capacitor Bottom of the vacuum container 2.4 mhigh and 1.2 mwidth 5electrodes See poster O. Thevenot et al Capacitance variation of 1 pf L= 370 mm Motorwithencoder (resolution55 nm) and displacementmeasuredwitha Michelson interferometer(resolution 0.3 nm) 532 nm laser source tunedon an I 2 line August, 27th 2014 CPEM

33 New set of electrodeswithstraightness< 100 nm Amagnetic stainless steel Diameter75.5mm,length:450mm Cylindricality defect about 1.5 µm after grinding To reduce this defect to 100 nm, the cylinders are manually lapped and polished. Fabrication of specific lapping-tool Best results with grinding-tool made of corundum (abrasive) withshellacand rosinfor bonding. The toolisshapedto fit the cylinders.

34 Measurementsof the straightnessand the parallelismof the generatinglinesof electrodeswith σ< 25 nm Measuring machine specifically built nm electrode completely finished: 98% of the generating lines have straightness defects lower than100nm(80%lowerthan50nm) andtheroughnessparameterrqisabout 7 nm(similar to mass standards); The 4 other electrodes: straightness defects between 100 nm and 300 nm; Around4to6monthswillbenecessarytofinishtheseelectrodes.

35 Improved electrical measurement chain ω tare: 1,25 pf (for LVb) quad. AT pf a b Mobile guard a : in b : out phase wagner 7 or 0 D 1pF inj. -1 LVb or 10 pf New resistors 10 kωto 40 kωwith very low parameters freq. coeff. < per khz; temp coeff= ± C -1, drift /day. New calculable Haddad type resistors 1 kω New two stage transformers have been built, compared to the previous ones: increased maximum operating voltage (240 V, 400 Hz) and a lower ratio corrections ( ).

36 3.3) The new NMIA-BIPM capacitor design (1) Calculable capacitance variation 0.4 pf for a guard electrode displacement of mm Four main cylindrical electrodes in vertical position: diameter 50 mm and length 470 mm Main electrodes are geometrically accurate to within 100 nm over the central 370 mm Fixed lower guard electrode and moving upper guard electrode both ended by a nosepiece Fabry-Perot interferometer (532 nm laser source)

37 The new NMIA-BIPM capacitor design (2) The cross section of the capacitor has been designed for gap corrections less than 1 x 10-9 of the measured capacitance The nosepiece of the guard electrode has been designed for a sensitivity of 1 x 10-9 of the measured capacitance for a smooth change of 100 nmin diagonal spacing ( implying geometrical accuracy of the electrode bars of the same order of magnitude and sub-micrometric positioning systems) The initial spacing between guard electrodes has been designed for close approach correction of less than 1 x 10-9 of the measured capacitance If the ultimatedesign expectations are met, thenbridges becomethe limitingparts of the linkbetweenthe calculable capacitor and the quantum Hall effect

38 The chain from R K to 0.4 pf

39 3.4) New NIM calculable capacitor Collaboration NIM & NMIA Capacitance Bridge Calculable Capacitor Laser Interferometry The SI unit of capacitance of 1 pf was reproduced from the calculable capacitor within an uncertainty of 20 parts in 10 9

40 Outline 1) Introduction 2) The fine structure constant αand the SI 2.1) Past determinations of α: a convergence of atomic and condensed matter physics 2.2) αand the new definitions of ampere and kilogram 2.3) Realisations of the impedance units (farad, ohm) in the SI 3) Towards new electrical determinations of alpha 3.1) Thompson Lampard theorem and implementation conditions 3.2) LNE calculable capacitor and impedance chain 3.3) NMIA-BIPM calculable capacitor and impedance chain 3.4) NIM calculable capacitor 4) Conclusion and outlooks 40

41 Conclusion and outlooks (1/2) α, a fundamental dimensionless parameter -a key rolein the revisingof the SI throughits determinations both in atomic and condensed matter physics; -a stumblingblock in the choicefor the new definitionof ampere Limitations on electrical determinations of α QHE + calculable capacitor: u r >10-9 NMR + QHE&JE: u r > 10-8 ECCS&JE + calculable capacitor: u r >

42 Conclusion and outlooks (2/2) Future determinations of α based on new calculable capacitors - Expected better agreement between α(r K ) and α(h/m, a e ) New determinationof γ p,h!? - What s wrong in the past measurements? - γ will be the electromagnetic constant with the highest uncertaintyin the new SI withhand efixed (u r = , basedon CODATA2002) I. Mills et al,

43 Acknowledgements Gaël Thuillier, Ralf Sindjui, Olivier Séron, Saïf Khan (LNE) Lu Zuliang, Huang Lu, Yang Yan (NIM) 43

44 Thanksa lot for yourattention! 44