Fine structure constant determinations F. Nez Laboratoire Kastler Brossel, UPMC,ENS,CNRS “Metrology of simple systems and fundamental tests” Quantum metrology and fundamental constants S. Galtier, F. Nez, L. Julien, P. Cladé, S. Guellati-Khélifa, F. Biraben, R. Bouchendira
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Fine structure constant determinationsF. Nez
Laboratoire
Kastler
Brossel, UPMC,ENS,CNRS“Metrology of simple systems and fundamental tests”
Quantum metrology and fundamental constants
S. Galtier, F. Nez, L. Julien, P. Cladé, S. Guellati-Khélifa, F. Biraben, R. Bouchendira
Present status of the knowledge of the fine structure constant
CODATA 10
Codata
2010 arXiv:1203.5425v1 [physics.atom-ph]
22
111pn
R
Optical spectrum(Balmer
1885)
Balmer-Rydberg
formula(1889)
A brief history : 19th century
R
: Rydberg
constantn
and p
integers
A bit of history
re-
p
Bohr (1913)
energy
2n nhcRE
n=3
n=2
n=1
n=5n=4
Balmer
lines : n= 2
Hα
Hα
Hβ
Hβ
etc.
etc
22
111pn
R
Optical spectrum(Balmer
1885)
Balmer-Rydberg
formula(1889)
A brief history : 19th century
A bit of history
re-
p
Bohr (1913)
energy
2n nhcRE
n=3
n=2
n=1
n=5n=4
Hα
Hα
Hβ
Hβ
etc.
etc
R
: Rydberg
constantn
and p
integers
sketch
Fine structure : two lines !!
Balmer
lines : n= 2
1905
: Special theory of relativity1913
: Bohr model description of H atom1916 : A. Sommerfeld
tried to include special relativity in the Bohr model to explain the fine structure observed in H
A bit of history
Rydberg
constant
Fine Structure constant
Hg
(Paschen
series)
Codata
2012
e x
c =4.8032…10-10
abs.e.m.u.
h = 6.62606957(29) x
10-34
J s
2= 5.3251354528 x
10-3
ΔnH = 0.36551…cm-1
Value of
from f.s.
f.s. scaled as 4
1995
2000
2005
2010
2015
1960197019801990200020102020
1910 1930 1950 1970 1990 2010 2030History of
determinations
(from “CODATA xxxx”)
10-2
10-4
10-6
10-8
10-10
α-1-137.0359990 59995 60000
α-1
QED 8th order (2002)
QED 8th order(2007)
2×10-9
g-2 (Washington)
new g-2 (Harvard)
5×10-7
10 0
QED 10th order + new 8th order (May 2012)
History of
determinations Sommerfeld 1916 (~ 10-2)
:
-1
=137,4 (1,3)
H f.s.
+ indirect
Birge
1929 (~ 8.10-4)
:
-1=137,29 (11)
indirect (e, h, c)
Birge
1941 (~ 1.10-4)
:
-1=137,030 (16)
indirect (R¶
, e/m, F, NA
)
LSA 1952 (~ 1.10-5)
: -1=137,037 7 (16) (LSA D f.s., ae
)
LSA 1965 (~ 4.10-6)
:
-1=137,038 8 (6)
(H Lamb shift, muonium
hfs, ae
)(H Ls
137,037, H hfs137,03552)
B.N.T. 1969 (~ 1.10-7)
: -1=137,036 02 (21)
(H hfs, gp
, Josephson) mainly
without
QED (H Ls, ae
)codata
1973 (~ 8.10-8)
: -1=137,036 04 (11)
(data selection
+ uncert. expansion)
codata
1986 (~ 4.10-8)
:
-1= 137,035 989 5 (61)
(data selection
+ uncert. expansion)
codata
1998 (~ 4.10-9)
:
-1=137,035 999 76 (50)
(mainly, ae-WS
)
codata
2002 (~ 4.10-9)
:
-1=137,035 999 11 (50)
(ae-Ws
, h/mCs
)
codata
2006 (~ 7.10-10)
:
-1=137,035 999 679 (94)
(ae-Hd
)
codata
2010 (~ 3.10-10)
:
-1=137,035 999 074 (44)
(ae-Hd
, h/mRb
)
latest
QED 2012 (~ 2.5.10-10)
-1
=137,035 999 166 (34)
(ae-Hd
, 10th order
QED)
Determinations of the fine structure constant
c4e
0
2
α
dimension less (free of units) scales electromagnetic interaction (common to all methods : charge particle in e.m
field )
137.035 990 137.036 000 137.036 010
h/m
(neutron)
-1
quantum Hall effectSolid state
physics’p,h-90
hfs muonium
QEDg –
2 of the electron
(UW)g –
2 of the electron
(Harvard)
h/m
(Cs)
h / mh/m (Rb)
20062008
He fine structure
2010
mv=h/λDB
vr
=ћk/m
General outline
Lecture I : less accurate determinations of
Quantum Hall effect
Hydrogen fine and hyperfine structure
Helium fine structure
Exotic hydrogen-like atoms
Lecture II : most accurate determinations of
g-2 (lepton)
h/m
contribution of
in new SI
Quantum Hall effect
(see
v.K.
Wed. 18th
July) (1.8×10-8)
2
cehR 02K
RH Rxx
2K
H eih
iR)i(R
Q.H.E.
VH
Ix
VxxB
Nobel prize 1985
0.5m
2
0 cRK
NIST 97NML 97
NIM 97
NPL 88
BNM 01
15 2
34
CalculableCapacitor
m/F15
2ln0
1, 10 and 100pF
100 -1000pF
1000 -
10000pF
R
CDR()C()=1 1600 Hz
800 Hz400 Hz
10 k20 k40 k
2)(eih
iRiR K
H
100
200 ou
k
Meter
Second
Q.H.E.
AC
DC
10-7-1
Quantum Hall effect
(see
v.K.
Wed. 18th
July) (1.8×10-8)
137.035 990 137.036 000 137.036 010
h/m
(neutron)
-1
quantum Hall effectSolid state
physics’p,h-90
hfs
muonium
QEDg –
2 of the electron (UW)g –
2 of the electron (Harvard)
h/m
(Cs)
h / mh/m (Rb)
20062008
He fine structure
2010
mv=h/λDB
vr
=ћk/m
Quantum Hall effect (see v.K. Wed. 18 July) (1.8×10-8)
2012 : → Universality of RK
: Graphene, GaAs/AlGaAs
(see Tzalenchuk
talk Thurs 19 July)→ QED correction negligible
General outline
Lecture I : less accurate determinations of
Quantum Hall effect
Hydrogen fine and hyperfine structure
Helium fine structure
Exotic hydrogen-like atoms
Lecture II : most accurate determinations of
g-2 (lepton)
h/m
contribution of
in new SI
Hydrogen fine structurer
e-p
e-
spinrelativity
Dirac
43.5 GHz
Bohr
n= 1
n= 2
n= 3
energy
1S1/2
2S1/2
, 2P1/2
2P3/2
2n nhcRE
(3/8)mc²α²
~mc²α4
1913: N. Bohr
1916: A Sommerfeld
tried to include special relativity in the Bohr model to explain the fine structure observed in H
→ =ve
/c
velocity of the electron on the 1st orbit of Bohr model to the velocity of light
→ angular momentum quantization k ≠
n→ failed because spin of the electron is missing
1928
: Dirac
equation combines more recent equation describing H spectrum (wave function) (Schrödinger eq.) and the relativity.
positron (anti-electron) spin of the electron
The fine structure constant introduced by A. Sommerfeld
is still the relevant parameter for the H spectroscopy
c4πe2
0
c2mcR
h
22
Fine structure constant
Quantum ElectroDynamics
(QED)
Electrodynamics
: interaction between charge and field
QED
: quantization of the field photon : field quantized in term of quantum harmonic oscillators quantum harmonic oscillators En
=(n+1/2)Ñωground state: zero energy = 1/2 Ñω
renormalization
0 Heisenberg principle Et~ Ñ
fluctuations
QED vacuum
is subject to fluctuations around zero average-field
spontaneous emission : quantum state = atom + field = not a stationary stateVacuum fluctuations→ spontaneous emission
energy (E) carried out by the electron in vacuum = E of electron + E in the e.m. field =electron + cloud of photons = renormalization of the electron mass (self energy~m/m)
Quantum vacuum : continuously appearing and disappearing pair of “virtual”