Post on 17-Jul-2020
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Improved Determination ofthe Electron Mass in Atomic Mass Units
Wolfgang Quint
GSI Darmstadt and Univ. Heidelberg
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
B
g-Factor of the electron
h
sg
B⋅=
µ
µµ: magnetic moment
g: g-factor
s: spin
µB: Bohr magneton
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
g = 2 + α / πα / πα / πα / π
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
gfree= 2 (1 + C1αααα/ππππ + C2(αααα/ππππ)2 + C3(αααα/ππππ)3 + C4(αααα/ππππ)4 + C5(αααα/ππππ)5 +....
1st order in αααα:
Schwinger termC1 = ½
QED contributions to the g-factor of the free electron
magnetic field
Ref.:J. Schwinger, Phys. Rev. 73, 416 (1948); Hanneke et al., PRL 100, 120801 (2008)
The theory of quantum electrodynamics is,I would say, the jewel of physics
- our proudest possession.R. Feynman
The theory of quantum electrodynamics is,I would say, the jewel of physics
- our proudest possession.R. Feynman
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
gfree= 2 (1 + C1αααα/ππππ + C2(αααα /ππππ)2 + C3(αααα /ππππ)3 + C4(αααα /ππππ)4 + C5(αααα /ππππ)5 +....
Free electron: QED contributions of 2nd and 3rd order
2nd order in αααα: C2 = - 0.328 478 966
7 graphs
3rd order in αααα: C3 = 1.176572 graphs
Ref.:B. Lautrup et al., Phys. Rep. 3, 193 (1972)
not shown:4th order in α:α:α:α:
C4 = -1.9108891 graphs
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Bm
e
e
e
c =ωBm
eg
e
e
L2
=ω
cyclotron frequency:cyclotron frequency:Larmor precession
frequency:
Larmor precession
frequency:
e
c
e
Leg
ω
ω⋅= 2
g-Factor of the free electron
B: magnetic field in
Penning trap
e
c
e
aeg
ω
ω⋅=− 22or ratheror rather (get 3 orders of magnitude
in accuracy by Nature)
(get 3 orders of magnitude
in accuracy by Nature)
q1
Folie 7
q1 quint_local; 18.05.2003
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Ref.:T. Beier, Physics Reports 339, 79 (2000)
QED and highly charged ions
self energy vacuum polarization vertex correction
basic processes in bound-state QED:
bound-state QED: quantum physics in strong fields
bound-state QED coupling parameter for U91+: Zα ≈ 0.67
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Ref.:U.D. Jentschura, P.J. Mohr, G. Soff, PRL 82, 53 (1999); T. Beier, Physics Reports 339, 79 (2000)
Bound-state QED: treatment non-perturbative in Zαααα
non-perturbativetreatment
no expansionin Zαααα
perturbative treatment: expansion in Zαααα
Non-perturbative bound-state QED was developed in the last 20 years by excellent theoreticians like:
Beier, Blundell, Breit, Czarnecki, Glazov, Jentschura, Johnson, Karshenboim, Lindgren, Lee, Milstein, Mohr, Pachucki, Persson, Plunien, Salomonson, Sapirstein,
Shabaev, Soff, Sunnergreen, Terekhov, Tupitsyn, Volotka, Yerokhin, and others.
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
SELFENERGY
VACUUMPOLARIZATION
gbound/gfree ≈≈≈≈ 1 - (Zαααα)2/3 + αααα(Zαααα)2/4ππππ + ....+ ....+ ....+ ....
bound-state QEDDirac theory
Bound-electron g-factor:Feynman graphs 1st order in α/πα/πα/πα/π
Ref.:T. Beier, Physics Reports 339, 79 (2000)
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Bound-electron g-factor:Feynman graphs 2nd order in α/πα/πα/πα/π
Ref.:T. Beier, Physics Reports 339, 79 (2000)
50505050 graphs
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Bound-electron g-factor
Ref.:D. Glazov
NUCLEAR CHARGE Z
CO
NT
RIB
UT
ION
TO
G-F
AC
TO
R
1-loop QED free electron
2-loop QED free electron
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
BM
Q
ion
ion
c =ωBm
eg
e
Je
L2
=ω
Ion cyclotron frequency:Ion cyclotron frequency:Larmor precession
frequency of the
bound electron:
Larmor precession
frequency of the
bound electron: B
g-Factor of the bound electron ina hydrogen-like ion(nucleus has no spin, e.g. 12C5+, 16O7+, 28Si13+, 40Ca19+)
e
Q
M
mg
ion
ion
e
ion
c
e
LJ ⋅⋅⋅=
ω
ω2
our
measurement
our
measurement
external input
parameter
external input
parameter
→ 'experimental
g-factor'
→ comparison
with theory
→ 'experimental
g-factor'
→ comparison
with theory
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
A single highly charged ion stored in a Penning trap
potential
z
axial confinement
ion
radial confinement
ring
endcap
endcap
U0
magnetic
B0
physical electric
(MODIFIED) CYCLOTRON MOTION
w+
MAGNETRON DRIFT
w-
AXIAL MOTION
wz
B
combined ion motion
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Precision trap (PT)
� Very homogeneous magnetic field
Analysis trap (AT)
� Magnetic bottle for spin detection
Creation trap (CT)
� In-trap ion creation of
highly-charged ions
~1
4 c
m7mm
Triple Penning Trap System
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Precision trap (PT)
� Very homogeneous magnetic field
Analysis trap (AT)
� Magnetic bottle for spin detection
Creation trap (CT)
� In-trap ion creation of
highly-charged ions
Triple Penning Trap System
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
HCI g-factor apparatus
SUPERCONDUCTINGSOLENOIDS
PENNING TRAP @ 4K
CRYOELECTRONICS
@ 4 K
SUPERCONDUCTING MAGNETWITH ROOM TEMPERATUR BORE
CRYOSTAT
MAGNETIC BOTTLE
SINGLE IONIN TRAP
PRECISION TRAP
TARGET
FEP
MICROWAVE INLET
MINI EBIS
`DOUBLE TRAP‘
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
g-Factor trap in Mainz(GSI/Heidelberg collaboration)
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
νz = 360 kHz
B
compensationelectrode
ring electrode
end cap
end cap
compensationelectrode
dEp/dt = Pcool = -I2R
resistive cooling
LRCU = I R
Electronic detection andresistive cooling of trapped ions
νc2 = ν-
2 + νz2 + ν+
2
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Mass-to-charge ratio [Volt]
Ele
ctr
. D
ete
cti
on
sig
nal
hydrogen-like ionshydrogen-like ions
Charge breeding of carbon and oxygen ionsin cryogenic EBIS (electron-beam ion source)
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Isolating a single highly charged ion
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
High-resolution cyclotron frequency measurementof a single highly charged silicon ion
28Si13+
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
� Other modes can be coupled to
axial motion via rf-sideband coupling
-1500 -1000 -500 0 500 1000 1500
0
2
4
6
8
10
12
-2 -1 0 1 2
0
3
6
9
12
Sig
na
l (d
BV
rms)
Frequency / Hz -670900
-15 -10 -5 0 5 10 15
0
2
4
6
8
10
12
14
16
Sig
na
l (d
BV
rms)
Frequency / Hz -670900
� Axial frequency directly measured as
narrow “dip”
RLzrfv νννν ++−=+
zv
Eigenfrequency Measurement
)( zv
),( −+ vv
RνLνRLzrfv νννν −−+=−
300mHz
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Continuous Stern-Gerlach effect:Determination of spin direction
B2B1
z
1
2
2B
KE
Lz
m=D
2B
mz
z
w
mw =D
CLASSICALSTERN-GERLACH
CONTINUOUSSTERN-GERLACH
SEPARATION IN POSITION SPACE SEPARATION IN FREQUENCY SPACE
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Quantum jump spectroscopy:Spin-flip transitions in the analysis trap
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Anke
WagnerSven
SturmBirgit
Schabinger
The lab team(before spinflip)
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
The lab team (after spinflip)
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Measurement Cycle
704790 704820 704850 704880
-210
-200
-190
-180
Sig
nal (d
BV
)
Axial Frequency (kHz)
6 0 7 0 8 0 9 0 1 0 0
-0 .5
-0 .4
-0 .3
-0 .2
-0 .1
0 .0
0 .1
0 .2
0 .3
0 .4
0 .5
F
ractio
na
l a
xia
l fr
eq
uen
cy d
iffe
ren
ce
(H
z)
M e a s u re m e n t n u m b e r
AT PT
2. PT: Measurement of eigenfrequencies and
simultaneous irradiation with microwaves
1. AT: Detection of spin orientation: → spin up
0 1 0 2 0 3 0 4 0 5 0
-0 .5
-0 .4
-0 .3
-0 .2
-0 .1
0 .0
0 .1
0 .2
0 .3
0 .4
0 .5
Fra
ctio
na
l a
xia
l fr
equ
en
cy d
iffe
rence (
Hz)
M e a s u re m e n t n u m b e r
3. AT: Detection of spin orientation → spin down
+vzv cv
Lv
c
L
ν
ν=Γ
4. Spin flip in PT? → spin has flipped!
−v(offline)
Precision measurement of bound electron g-factor in hydrogen-like silicon
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Bound electron magnetic moment measurementon hydrogen-like silicon 28Si13+
Sp
infl
ip p
rob
abil
ity (
%)
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
gJ(12C5+) = 2.001 041 590 18 (3) theoretical value
gJ(12C5+) = 2.001 041 596 4 (10)(44) our measurement
gJ(12C5+) = 2.001 041 590 18 (3) theoretical value
gJ(12C5+) = 2.001 041 596 4 (10)(44) our measurement
Comparison of theory and experiment:g-Factor of the bound electron in
H-like carbon 12C5+, oxygen 16O7+ and silicon 28Si13+
Lit.:
T. Beier et al., PRL 88, 011603 (2002)
V. Shabaev et al., PRL 88, 091801 (2002)
V. Yerokhin et al., PRL 89, 143001 (2002)
K. Pachucki, V. Yerokhin et al., PRA 72, 022108 (2005)
S. Sturm et al., PRL 107, 023002 (2011)
gJ(16O7+) = 2.000 047 020 32 (11) theoretical value
gJ(16O7+) = 2.000 047 025 4 (15)(44) our measurement
gJ(16O7+) = 2.000 047 020 32 (11) theoretical value
gJ(16O7+) = 2.000 047 025 4 (15)(44) our measurement
gJ(28S13+) = 1.995 348 958 0 (17) theoretical value
gJ(28S13+) = 1.995 348 958 7 (5)(3)(8) our measurement
gJ(28S13+) = 1.995 348 958 0 (17) theoretical value
gJ(28S13+) = 1.995 348 958 7 (5)(3)(8) our measurement
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
BM
Q
ion
ion
c =ωBm
eg
e
Je
L2
=ω
Ion cyclotron frequency:Ion cyclotron frequency:Larmor precession
frequency of the
bound electron:
Larmor precession
frequency of the
bound electron: B
Q
eg
M
me
L
ion
cJ
ion
e⋅⋅=
ω
ω
2
Electron mass
our
measure-
ment
our
measure-
ment
→ determination
of electron mass
→ determination
of electron mass
theory as
input
parameter
theory as
input
parameter
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
� Several Г-resonances at different
cyclotron energies to check systematics
→ extrapolation to zero energy
Experimental Result
0
10
20
30
40
50
1.00.0-1.0 0.5
(Γ/Γι
0-1) / 10
-9
Fra
ction
al sp
inflip
ra
te /
%
FWHM: 7·10-10
-0.5
0,00 0,05 0,10 0,15 0,20 0,25
0,0
0,2
0,4
0,6
0,8
1,0
1,2
Γ/Γ
0 -
1 / 1
0-9
U2
exc (V
2)
Г0 = 4 736. 210 500 89 (11)(7)(stat.) (syst.)
� Probing Zeeman transition at different Γ’s
several 100 times:
→ Г-resonance
� Γ0’ is extracted from fit
� Resonance width and thus statistical error
limited by magnetic field fluctuations
� Dominant systematics:
� image charge shift: -282(14) ppt
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Result
me=0,000 548 579 909 067 (14)(9)(2) u(stat)(syst)(theo)
δme/me=3·10-11
Г0 = 4 736. 210 500 89 (11)(7)(stat.) (syst.)
gtheo = 2. 001 041 590 176 (6)
0
1
2 Γ=
ion
theoione
q
egmm
TheoryExperiment
[S. Sturm et al., Nature 506, 467-470 (2014)]
2013
2010
2007
2004
2001
1998
1995
-6 -4 -2 0 2 4 6
Farnham
Hori
this work
Verdú
me/m
this work
e-1 (parts per billion)
Year
CODATAHäffner
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Result
me=0,000 548 579 909 067 (14)(9)(2) u(stat)(syst)(theo)
δme/me=3·10-11
Г0 = 4 736. 210 500 89 (11)(7)(stat.) (syst.)
gtheo = 2. 001 041 590 176 (6)
0
1
2 Γ=
ion
theoione
q
egmm
TheoryExperiment
[S. Sturm et al., Nature 506, 467-470 (2014)]
2013
2010
2007
2004
2001
1998
1995
-6 -4 -2 0 2 4 6
Farnham
Hori
this work
Verdú
me/m
this work
e-1 (parts per billion)
Yea
r
CODATAHäffner
2013
2010
2007
2004
2001
1998
1995
-6 -4 -2 0 2 4 6
Farnham
Hori
this work
Verdú
me/m
this work
e-1 (parts per billion)
Yea
r
CODATAHäffner
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Who has forgotten the walnut?Who has forgotten the walnut?
500000 tons500000.000015 tons
Relative Precision: 3·10-11
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Profit of an improved electron mass me
Important ingredient in fine-structure constant measurement:
Rbe
Rb
e
recoilM
h
m
M
c
R
cm
hR ∞∞ ==222α
Rb
recoilM
kv
h=
5 ppt,
CODATA (T. Hänsch) 2010
115 ppt,
E. Myers 2010
1241 ppt,
F. Biraben 2011
30 ppt, our value
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
Measurements of the electron mass over the years
Mq
em
electron
c
ion
ce
ν
ν=
Bm
e
e
electron
cπ
ν2
=
Ion
B
e-
BM
qion
cπ
ν2
=
1970 1980 1990 2000 201010
-10
10-9
10-8
10-7
10-6
10-5
rela
tive
un
ce
rta
inty
of m
e
year
CODATA Indirect measurement via µB/µΝ
Gärtner: vc via particle loss (first direct)
Gräff: vc via ToF
Van Dyck: vc via image currents (first non-destructive)
Wineland: vc via laser fluorescence + vL + gtheo
(first bound electron)
Gabrielse: vc via image currents
Farnham: vc via image currents (first single ion)
Häffner: vc/vL of 12
C5+
+ gtheo
Verdú: vc/vL of 16
O7+
+ gtheo
Hori: antiprotonic helium
common
mass spectrometry
International Accelerator Facility for
Beams of Ions and Antiprotons at Darmstadt
Fundamental Constants Meeting, Eltville, Germany, February 2015, Wolfgang Quint
• “Abteilung für gespeicherte und gekühlte Ionen” at MPIK, Heidelberg
• Atomic Physics Division at GSI Helmholtzzentrum, Darmstadt
• QUANTUM group at the Institut für Physik, Mainz
• International Max Planck Research School – Quantum Dynamics
Special thanks to
Experiment: Jiamin Hou, Sven Sturm, Anke Wagner,
Günter Werth, Klaus Blaum
Theory: Jacek Zatorski, Zoltán Harman, Christoph H. Keitel