Comité Science et métrologie Académie des sciences

Comité Science et métrologie Académie des sciences

Jean Kovalevsky Christian Bordé Christian Amatore Alain AspectFrançois Bacelli Roger BalianAlain Benoit Claude Cohen-TannoudjiJean Dalibard Thibault DamourDaniel Estève Pierre FayetBernard Guinot Theodor HänschSerge Haroche Yves JeanninPierre Perrier Gabriele VenezianoMarc Himbert Ian MillsTerry Quinn Christophe Salomon

Claudine Thomas

Jean Kovalevsky Christian Bordé Christian Amatore Alain AspectFrançois Bacelli Roger BalianAlain Benoit Claude Cohen-TannoudjiJean Dalibard Thibault DamourDaniel Estève Pierre FayetBernard Guinot Theodor HänschSerge Haroche Yves JeanninPierre Perrier Gabriele VenezianoMarc Himbert Ian MillsTerry Quinn Christophe Salomon

Claudine Thomas

COMITÉ « SCIENCE ET MÉTROLOGIE »DE L’ACADÉMIE DES SCIENCES

Effet Hall quantique et métrologie

Colloque organisé par Christian Glattli

Quantum Hall effect and the reform of the SI

Quantum Hall effect and the reform of the SI

Christian J. Bordé

Christian J. Bordé

0

5000

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0 2 4 6 8 10

B(T)

Rxy()

0

2000

4000

6000

8000

10000

RXX()

Rxy

Rxx

i=2

i=3

i=4Rxy

0 10Magnetic Induction B (T)

Rxx

i=2

i=3i=4

2K

H

1

e

h

ii

RR

Quantum Hall effect

Metrological triangle Quantum Ohm law

fe

hU

2

Rh

e

R

R

K

2

'2 ffRIU

I

Josephsoneffect

SET effect

Quantum Halleffect

'efI

212122

4)//()2/( ff

hffehehUI

Watt balance: principle

A) Static mode: B) Dynamical mode:

Radialfield

U

I

Interferometer Position Interferometer

UE.m.f.

UVelocity

Masscomparator

IUmg v

Mechanical Power = Electrical Power

gm

F

v

)/(4

1

4

22121

22

cv

Tff

gv

ffc

h

cMC

K

?or0 e

On electrical units:In the present SI, the values of μ0 and ε0 are fixed and

thus the propagation properties of the electromagnetic field in the vacuum are also fixed:

- propagation velocity

- vacuum impedance 000 /Z

000 /1 c

- electric and magnetic energy densities and

2/20E

2/20H

This system is perfectly adapted to the propagation of lightin vacuum: no charges but also no ether.

20E gives the radiation pressure and

20Ec gives the intensity and the number of photons

Let us now introduce charges.

dimensionless constant imposed by nature, extraordinarily well-known today since its present uncertainty is 0.7x10-9.

The free electromagnetic field is coupled to charges through this constant, which thus appears as a property of electrons and not as a property of the free electromagnetic field.

The values of μ0 and ε0 are related to the positron charge e

by the fine structure constant:

is just another way to write the positron charge choice adopted by field-theory experts.

Maxwell Equations

JF 0

CGSG:

J

cF

4

SI:

eJhcFq /2/P

2

Validity of expressions for RK and KJ

hchh

eK 0J 2

22?

02K 2

1?Z

e

hR

3.10-8

2.10-7

On electrical units:It clarifies future issues to introduce a specific notation for the approximate theoretical expressions of RK and KJ : heKehR /2/ )0(

J2)0(

K in order to distinguish them from the true experimental constants RK and KJ  which are related to the previous ones by:

)1()1( J)0(

JJK)0(

KK KKRRFix h and e would fix the constants

)0(J

)0(K and KR

but not RK and KJ which would keep an uncertainty.

This uncertainty is not that related to the determination of e and h in the SI but to our lack of knowledge of the correction terms to the expressions of RK and KJ.

Let us recall that the present estimate of the value of εK

is of the order of 2.10-8 and that of εJ of the order of 2.10-7

with important uncertainties.

The fact that the universality of these constants has been demonstrated to a much better level simply suggests that possible corrections would involve other combinations of fundamental constants: functions of α, mass ratios, … The hydrogen spectrum provides an illustrating example of a similar situation. The energy of the levels of atomic hydrogen is given to the lowest order by Bohr formula, which can also be derived through a topological argument. Nevertheless there are many corrections to this first term involving various fundamental constants. It is not because the spectrum of hydrogen is universal that we may ignore these corrections and restrict ourselvesto Bohr formula.

...9

14ln

9

28

48

111

4

321

2

23

22/12/1

C

P

P

eH

R

m

mcRSS

243 nm

21

2em c

Rh

HYDROGEN ATOM

cRSSH 4

321 2/12/1

...

9

14ln

9

28

48

111

2

23

2

C

P

P

e R

m

m

Raccordement des Centres d’étalonnages

SECONDE

METRE

h /e 2

Pont de capacités 2 paires de bornes

Pont de capacités 4 paires de bornes

Pont de quadrature 4 paires de bornes

CCC

AC Résistance calculable coaxiale

200

10 k ou

DC

i=1 ou 2

1, 10 et 100 pF

100 à 1000 pF

1000 à 10000 pF

D

R

C k k

k 1 600 Hz

800 Hz

400 Hz

R( ).C. =1

calculable Capacité

1 2

3 4 5

0 ln pF/m 2 5 - 1

QHE

H R (i) = R

K i

h i.e 2

100

et

RK determination with the Lampard

RK determination with the Lampard

21

0

K Z

R

Determination of h/mat byRamsey-Bordé atom interferometry

16

2 2 p at

e p at

m mR h

c m m m

uncertainties (x 10-9) 0.008 2.1 0.2 15

2

04

e

c

Determination of the fine structure constant

atm

hT2

2

10 Janvier 2006

Académie des Sciences

17

Validation of the expression of RK from the fine structure constant

Conclusion on electrical units:

Even if e is fixed, there remains a large uncertainty for RK and KJ  and in addition

vacuum properties acquire an uncertainty. There seems to be no real advantage in fixing the value of e rather than that of μ0.

Les effets quantiques de la métrologie électriqueLes effets quantiques de la métrologie électrique

2

1

e

h

ii

RR K

H

UJ nK J 1 f n

h

2ef

Effet Hall quantiqueEffet Josephson

0

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B(T)

Rxy()

0

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RXX()

Rxy

Rxx

i=2

i=3

i=4

tension

courant

0f1

f