Comité Science et métrologie Académie des sciences
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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
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B(T)
Rxy()
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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
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tension
courant
0f1
f
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