New Measurement of the Electron Magnetic Moment and the Fine Structure Constant
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Transcript of New Measurement of the Electron Magnetic Moment and the Fine Structure Constant
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Gabrielse
New Measurement of the Electron Magnetic Momentand the Fine Structure Constant
Gerald GabrielseLeverett Professor of Physics
Harvard University
Almost finished student: David HannekeEarlier contributions: Brian Odom, Brian D’Urso, Steve Peil, Dafna Enzer, Kamal Abdullah
Ching-hua Tseng Joseph Tan
N$F 0.1 m
220 years6.5 theses
2006 DAMOP ThesisPrize Winner
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Gabrielse
Why Does it take Twenty Years and 6.5 Theses?
• One-electron quantum cyclotron• Resolve lowest cyclotron states as well as spin• Quantum jump spectroscopy of spin and cyclotron motions• Cavity-controlled spontaneous emission• Radiation field controlled by cylindrical trap cavity• Cooling away of blackbody photons• Synchronized electrons identify cavity radiation modes• Trap without nuclear paramagnetism• One-particle self-excited oscillator
Explanation 1: Van Dyck, Schwinberg, Dehemelt did a good job in 1987! Phys. Rev. Lett. 59, 26 (1987)
Explanation 2a: We do experiments much too slowly
Explanation 2b: Takes time to develop new ideas and methods needed to measure with 7.6 parts in 1013 uncertainty
firs
t mea
sure
men
t wit
h th
ese
new
met
hods
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Gabrielse
The New Measurement of Electron g
U. Michigan
beam of electrons
spins precesswith respect to cyclotron motion
U. Washington
one electron
observe spinflip
thermalcyclotronmotion
Harvard
one electron
quantum cyclotronmotion
resolve lowestquantum levels
cavity-controlledradiation field(cylindrical trap)
100 mK
self-excitedoscillator
inhibit spontan.emission
cavity shiftsCrane, Rich, …Dehmelt, Van Dyck
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Gabrielse
Magnetic Moments, Motivation and Results
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Gabrielse
Magnetic Moments
e.g. What is g for identical charge and mass distributions?
2( )2 2 2 2
e ev L e e LIA L
mv m mv
B
B
Lg
magneticmoment
angular momentum
Bohr magneton2
e
m
1g
v ,e m
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Gabrielse
Magnetic Moments
B
Sg
magneticmoment
angular momentum
Bohr magneton2
e
m
1g
2g
2.002 319 304 ...g
identical charge and mass distribution
spin for Dirac point particle
simplest Dirac spin, plus QED
(if electron g is different electron has substructure)
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Gabrielse
Why Measure the Electron Magnetic Moment?
1. Electron g - basic property of simplest of elementary particles
2. Determine fine structure constant – from measured g and QED (May be even more important when we change mass standards)
3. Test QED – requires independent
4. Test CPT – compare g for electron and positron best lepton test
5. Look for new physics beyond the standard model
• Is g given by Dirac + QED? If not electron substructure (new physics)
• Muon g search needs electron g measurement
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Gabrielse
New Measurement of Electron Magnetic Moment
B
Sg
magneticmoment
spin
Bohr magneton2
e
m
13
/ 2 1.001159 652 180 85
0.000 000 000 000 76 7.6 10
g
• First improved measurement since 1987• Nearly six times smaller uncertainty• 1.7 standard deviation shift• Likely more accuracy coming• 1000 times smaller uncertainty than muon g
B. Odom, D. Hanneke, B. D’Urso and G. Gabrielse,Phys. Rev. Lett. 97, 030801 (2006).
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Gabrielse
Dirac + QED Relates Measured g and Measured 42 3
2 3 41 .2
..1 C C C Cg
a
QED CalculationMeasure
weak/strong
Sensitivity to other physics (weak, strong, new) is low
1. Use measured g and QED to extract fine structure constant
2. Wait for another accurate measurement of Test QED
Kinoshita, Nio,Remiddi, Laporta, etc.
Diracpointparticle
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GabrielseBasking in the Reflected Glow of Theorists
KinoshitaRemiddi G.G
2004
1
2
2
3
4
3
4
4
5
.
1
.
2
.
C
C
C
C
a
g
C
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Gabrielse
42 3
2 3 41 .2
..1 C C C Cg
a
experimentaluncertainty
theoretical uncertainties
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Gabrielse
New Determination of the Fine Structure Constant2
0
1
4
e
c
• Strength of the electromagnetic interaction• Important component of our system of fundamental constants• Increased importance for new mass standard
1
10
137.035 999 710
0.000 000 096 7.0 10
• First lower uncertainty since 1987• Ten times more accurate than atom-recoil methods
G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, B. Odom,
Phys. Rev. Lett. 97}, 030802 (2006).
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Gabrielse
42
2 3 20 0
2
22
1
2 122
1 12
1 1
4 (4 ) 2
2
22
( )
4( )
e
e
pCs recoil
Cs p e Cs D
recoil Cs C
D C e
e m ceR
hc h c
R h
c m
MM fR h hc
c M M m M f
f M MR c
f M m
Next Most Accurate Way to Determine use Cs example)
• Now this method is 10 times less accurate• We hope that will improve in the future test QED
Combination of measured Rydberg, mass ratios, and atom recoil
(Rb measurement is similar except get h/M[Rb] a bit differently)
Chu, …
Haensch, …Tanner, …
Pritchard, …
Haensch, …
Werthe, Quint, … (also Van Dyck)
Bir
aben
, …
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GabrielseEarlier MeasurementsRequire Larger Uncertainty Scale
ten timeslarger scaleto see largeruncertainties
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Gabrielse
Test of QED
Most stringent test of QED: Comparing the measured electron g to the g calculated from QED using an independent
1215 10g
• The uncertainty does not comes from g and QED• All uncertainty comes from [Rb] and [Cs]• With a better independent could do a ten times better test
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GabrielseFrom Freeman Dyson – One Inventor of QED
Dear Jerry,
... I love your way of doing experiments, and I am happy to congratulate you for this latest triumph. Thank you for sending the two papers.
Your statement, that QED is tested far more stringently than its inventors could ever have envisioned, is correct. As one of the inventors, I remember that we thought of QED in 1949 as a temporary and jerry-built structure, with mathematical inconsistencies and renormalized infinities swept under the rug. We did not expect it to last more than ten years before some more solidly built theory would replace it. We expected and hoped that some new experiments would reveal discrepancies that would point the way to a better theory. And now, 57 years have gone by and that ramshackle structure still stands. The theorists … have kept pace with your experiments, pushing their calculations to higher accuracy than we ever imagined. And you still did not find the discrepancy that we hoped for. To me it remains perpetually amazing that Nature dances to the tune that we scribbled so carelessly 57 years ago. And it is amazing that you can measure her dance to one part per trillion and find her still following our beat.
With congratulations and good wishes for more such beautiful experiments, yours ever, Freeman.
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Gabrielse
Direct Test for Physics Beyond the Standard Model
2* 130 // 2
mm GeV c
g
Does the electron have internal structure? Brodsky, Drell, 1980
2* 600 // 2
mm GeV c
g
limited by the uncertainty in independent values
if our g uncertaintywas the only limit
* 10.3m TeV LEP contact interaction limitNot bad for an experiment done at 100 mK, but LEP does better
:)2 (2 SM Hadronic Weak NewPhyD sicQE sa g gg
Is g given by Dirac + QED? If not electron substructure
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Gabrielse
Muon Test for Physics Beyond the Standard ModelNeeds Measured Electron g
:)2 (2 SM Hadronic Weak NewPhyD sicQE sa g gg
expected to be bigger than for electronby ~40,000
less accurately measuredthan we measure electron gby a factor of 1000
big contributionmust be subtracted out
need need test the QED calculationof this large contribution
Muon search for new physics needs the measurement of the electron g and
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GabrielseCan We Check the 3 Muon Disagreementbetween Measurement and “Calculation”?
:)2 (2 SM Hadronic Weak NewPhyD sicQE sa g gg
m/me)2 ~ 40,000 muon more sensitive to “new physics” ÷1,000 how much more accurately we measure ÷ 3 3 effect is now seen
If we can improve the electron g uncertainty by an additional factor of 13 should be able to see the 3 effect (or not)
(also need improved calculations, of course)
Not impossible to imagine, but may be impossible in practice
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Gabrielse
How Does One Measure the Electron gto 7.6 parts in 1013?
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Gabrielse
How to Get an Uncertainty of 7.6 parts in 1013
• One-electron quantum cyclotron• Resolve lowest cyclotron as well as spin states• Quantum jump spectroscopy of cyclotron and spin motions• Cavity-controlled spontaneous emission• Radiation field controlled by cylindrical trap cavity• Cooling away of blackbody photons• Synchronized electrons probe cavity radiation modes• Elimination of nuclear paramagnetism• One-particle self-excited oscillator fi
rst m
easu
rem
ent w
ith
thes
e ne
w m
etho
ds
Give introduction to some of the new and novel methods
Make a “Fully Quantum Atom” for the electron
Challenge: An elementary particle has no internal states to probe or laser-cool
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Gabrielse
Basic Idea of the Measurement
Quantum jump spectroscopyof lowest cyclotron and spin levelsof an electron in a magnetic field
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Gabrielse
150 GHzc
Tesla6B
One Electron in a Magnetic Field
n = 0
n = 1n = 2n = 3
n = 4
0.1m
2
0.1m
2
7.2 kelvinch
Need lowtemperature
cyclotron motionT << 7.2 K
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GabrielseFirst Penning Trap Below 4 K 70 mK
Need lowtemperature
cyclotron motionT << 7.2 K
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Gabrielse
David Hanneke G.G.
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Gabrielse
Electron Cyclotron Motion Comes Into Thermal Equilibrium
hotcavity blackbody
photons
electron
spontaneousemission
T = 100 mK << 7.2 K ground state always Prob = 0.99999…
cold
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Gabrielse
Electron in Cyclotron Ground State
0.23
0.11
0.03
9 x 10-39
On a short time scale in one Fock state or anotherAveraged over hours in a thermal state
average numberof blackbody
photons in the cavity
QND Measurement of Cyclotron Energy vs. Time
S. Peil and G. Gabrielse, Phys. Rev. Lett. 83, 1287 (1999).
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Gabrielse
Spin Two Cyclotron Ladders of Energy Levels
1
2c
eB
m
n = 0n = 1
n = 2n = 3
n = 4
n = 0
n = 1n = 2n = 3
n = 4
ms = -1/2 ms = 1/2
c
c
cc
c
c
cc
2s c
g
Cyclotron frequency:
Spin frequency:
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Gabrielse
Basic Idea of the Fully-Quantum Measurement
1
2c
eB
m
n = 0n = 1
n = 2n = 3
n = 4
n = 0
n = 1n = 2n = 3
n = 4
ms = -1/2 ms = 1/2
c
c
cc
c
c
cc
2s c
g
Cyclotron frequency:
Spin frequency:
12
c
c
s s
c
g
Measure a ratio of frequencies: B in free
space310
• almost nothing can be measured better than a frequency• the magnetic field cancels out (self-magnetometer)
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Gabrielse
Special Relativity Shift the Energy Levels
2 c
eB
m n = 0
n = 1
n = 2n = 3
n = 4
n = 0
n = 1n = 2n = 3
n = 4
ms = -1/2 ms = 1/2
3 / 2c / 2c
5 / 2c 7 / 2c
5 / 2c 3 / 2c
7 / 2c 9 / 2c
2s c
g
Cyclotron frequency:
Spin frequency:
92
10c
c
h
mc
Not a huge relativistic shift, but important at our accuracy
Solution: Simply correct for if we fully resolve the levels
(superposition of cyclotron levels would be a big problem)
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Gabrielse
Cylindrical Penning Trap2 2 22V z x y
• Electrostatic quadrupole potential good near trap center• Control the radiation field inhibit spontaneous emission by 200x
(Invented for this purpose: G.G. and F. C. MacKintosh; Int. J. Mass Spec. Ion Proc. 57, 1 (1984)
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Gabrielse
One Electron in a Penning Trap
• very small accelerator• designer atom
12 kHz
153 GHz
200 MHz
Electrostaticquadrupolepotential
Magnetic field
cool detect
need tomeasurefor g/2
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Gabrielse
Frequencies Shift
B in Free SpacePerfect Electrostatic
Quadrupole Trap
Imperfect Trap• tilted B• harmonic
distortions to V
2s c
g
'c c c
'z c
m z z
m
c
eB
m
2s c
g 2s c
g
Problem: not a measurable eigenfrequency in animperfect Penning trap
Solution: Brown-Gabrielse invariance theorem2 2 2( ) ( ) ( )c c z m
2s
c
g
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Gabrielse
Spectroscopy in an Imperfect Trap
• one electron in a Penning trap• lowest cyclotron and spin states
2
2
( )
2
( )2
1( )32
2 2
s c s c c a
c c c
za
c
z
cc
v vg
g
f
To deduce g measure only three eigenfrequencies of the imperfect trap
expansion for c z mv
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Gabrielse
Detecting and Damping Axial Motion
Axial motion200 MHz
oftrapped electron
V(t)
feedback
measure voltage
self-excited oscillator
I2Rdamping
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Gabrielse
QND Detectionof One-Quantum Transitions
12( )cyclotron cfreq E hf n
n=1
n=0
n=0cyclotrongroundstate
n=0cyclotrongroundstate
n=1cyclotronexcitedstate
one-
elec
tron
sel
f-ex
cite
d os
cill
ator
time
2 22
2 22
1
2 zB B m zz B zH
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Gabrielse
Quantum Non-demolition Measurement
B
QND
H = Hcyclotron + Haxial + Hcoupling
[ Hcyclotron, Hcoupling ] = 0
QND: Subsequent time evolutionof cyclotron motion is notaltered by additionalQND measurements
QNDcondition
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GabrielseObserve Tiny Shifts of the Frequencyof a One-Electron Self-Excited Oscillator
one quantumcyclotronexcitation
spin flip
Unmistakable changes in the axial frequencysignal one quantum changes in cyclotron excitation and spin
B"Single-Particle Self-excited Oscillator" B. D'Urso, R. Van Handel, B. Odom and G. Gabrielse Phys. Rev. Lett. 94, 113002 (2005).
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Gabrielse
Emboldened by the Great Signal-to-Noise
Make a one proton (antiproton) self-excited oscillator try to detect a proton (and antiproton) spin flip
measure proton spin frequency we already accurately measure antiproton cyclotron frequencies get antiproton g value
• Hard: nuclear magneton is 500 times smaller• Experiment underway Harvard also Mainz and GSI (without SEO) (build upon bound electron g values)
(Improve by factor of a million or more)
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Gabrielse
Need Averaging Time to Observe a One-quantum Transition
Cavity-Inhibited Spontaneous EmissionApplication of Cavity QED
decay time (s)
0 10 20 30 40 50 60
nu
mb
er
of
n=
1 t
o n
=0 d
ecays
0
10
20
30
= 16 s
excite, measure time in excited state
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Gabrielse
Cavity-Inhibited Spontaneous Emission
Free Space
B = 5.3 T
WithinTrap Cavity
frequency
ms75
1
1
16 sec
c
cavitymodes
InhibitedBy 210!
B = 5.3 T
PurcellKleppnerGabrielse and Dehmelt
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Gabrielse
frequency - c (ppb)
0 100 200 300
# o
f cyclo
tro
n e
xcit
ati
on
s“In the Dark” Excitation Narrower Lines
1. Turn FET amplifier off
2. Apply a microwave drive pulse of ~150 GH
(i.e. measure “in the dark”)
3. Turn FET amplifier on and check for axial frequency shift
4. Plot a histograms of excitations vs. frequency
Good amp heat sinking, amp off during excitation
Tz = 0.32 K
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Gabrielse
Big Challenge: Magnetic Field Stability
12 c c
s ag
n = 0n = 1n = 2n = 3
n = 0n = 1n = 2
ms = -1/2ms = 1/2
But: problem when Bdrifts during the measurement
Magnetic field cancels out
Magnetic field take~ month to stabilize
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Gabrielse
Self-Shielding Solenoid Helps a Lot
Flux conservation Field conservationReduces field fluctuations by about a factor > 150
“Self-shielding Superconducting Solenoid Systems”,G. Gabrielse and J. Tan, J. Appl. Phys. 63, 5143 (1988)
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GabrielseEliminate Nuclear Paramagnetism
Deadly nuclear magnetism of copper and other “friendly” materials
Had to build new trap out of silver New vacuum enclosure out of titanium
~ 1 year setback
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Gabrielse
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Gabrielse
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Gabrielse
Quantum Jump Spectroscopy
• one electron in a Penning trap• lowest cyclotron and spin states
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Gabrielse
Measurement Cycle
12 c c
s ag
n = 0n = 1n = 2n = 3
n = 0n = 1n = 2
ms = -1/2ms = 1/2
1. Prepare n=0, m=1/2 measure anomaly transition2. Prepare n=0, m=1/2 measure cyclotron transition
3. Measure relative magnetic field
3 hours
0.75 hour
Repeat during magnetically quiet times
simplified
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Gabrielse
Precision:Sub-ppb line splitting (i.e. sub-ppb precision of a g-2 measurement) is now “easy” after years of work
It all comes together:• Low temperature, and high frequency make narrow line shapes• A highly stable field allows us to map these lines
Measured Line Shapes for g-value Measurement
cyclotron anomaly
n = 0n = 1n = 2n = 3
n = 0n = 1n = 2
ms = -1/2ms = 1/2
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Gabrielse
Cavity Shifts of the Cyclotron Frequency
12 c c
s ag
n = 0n = 1n = 2n = 3
n = 0n = 1n = 2
ms = -1/2ms = 1/2
Within a Trap Cavity
frequency
1
16 sec
c
cavitymodes
spontaneous emissioninhibited by 210
B = 5.3 T
cyclotron frequencyis shifted by interactionwith cavity modes
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Gabrielse
Cavity modes and Magnetic Moment Error
Operating between modes of cylindrical trap where shift from two cavity modes cancels approximately
first measured cavity shift of g
use synchronization of electrons to get cavity modes
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Gabrielse
Summary of Uncertainties for g (in ppt = 10-12)
Test ofcavityshift
understandingMeasurement
of g-value
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Gabrielse
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Gabrielse
Attempt Started to Measure g for Proton and Antiproton
• Improve proton g by more than 10• Improve antiproton g by more than 106
• Compare g for antiproton and proton – test CPT
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Gabrielse
( )pe
e
p pp e
e p e
gg H
g g H
H mg g
H m
CODATA 2002: gp=5.585 694 701(56) (10 ppb)
Current Proton g Last Measured in 1972
electron g-factor, measured to < 0.001 ppb (Harvard)
proton-electron mass ratio, measured to < 1 ppb (Mainz)
bound magnetic moment ratio, measured to 10 ppb (MIT: P.F. Winkler, D. Kleppner, T. Myint, F.G. Walther, Phys. Rev. A 5, 83-114 (1972) )
bound / free corrections,calculated to < 1 ppb (Breit, Lamb, Lieb, Grotch, Faustov, Close, Osborn, Hegstrom, Persson, others)
2 4 2 2
6
2 2
6
1 1 1 11
3 12 4 2
1 17.7053 10
3 41 11
3 6 1
1 17.7328 10
e e
e p
p pe
p p p
g H mZ Z Z Z
g m
g H amZ Z
g m a
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Gabrielse
History of Measurements of Proton g
(from bound measurements of p/e, with current values of ge, me/mp and theory)
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Gabrielse
Antiproton g-factor
Antiproton g-factor is known to less than a part per thousand
18601.5pg
We hope to do roughly one million times better.
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Gabrielse
Apparatus Built, Not Yet Tried
make spin flip
6 mm inner diameter
detect spin flip
Nick Guise
iron
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Gabrielse
Summary and Conclusion
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Gabrielse
How Does One Measure g to 7.6 Parts in 1013?
Summary
• One-electron quantum cyclotron• Resolve lowest cyclotron as well as spin states• Quantum jump spectroscopy of lowest quantum states• Cavity-controlled spontaneous emission• Radiation field controlled by cylindrical trap cavity• Cooling away of blackbody photons• Synchronized electrons probe cavity radiation modes• Trap without nuclear paramagnetism• One-particle self-excited oscillator fi
rst m
easu
rem
ent w
ith
thes
e ne
w m
etho
ds
Use New Methods
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Gabrielse
New Measurement of Electron Magnetic Moment
B
Sg
magneticmoment
spin
Bohr magneton2
e
m
13
/ 2 1.001159 652 180 85
0.000 000 000 000 76 7.6 10
g
• First improved measurement since 1987• Nearly six times smaller uncertainty• 1.7 standard deviation shift• Likely more accuracy coming• 1000 times smaller uncertainty than muon g
B. Odom, D. Hanneke, B. D’Urso and G. Gabrielse,Phys. Rev. Lett. 97, 030801 (2006).
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Gabrielse
New Determination of the Fine Structure Constant2
0
1
4
e
c
• Strength of the electromagnetic interaction• Important component of our system of fundamental constants• Increased importance for new mass standard
1
10
137.035 999 710
0.000 000 096 7.0 10
• First lower uncertainty since 1987• Ten times more accurate than atom-recoil methods
G. Gabrielse, D. Hanneke, T. Kinoshita, M. Nio, B. Odom,
Phys. Rev. Lett. 97}, 030802 (2006).
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Gabrielse
We Intend to do Better
• Use self-excited antiproton oscillator to measure the antiproton magnetic moment million-fold improvement?
• Compare positron and electron g-values to make best test of CPT for leptons
• Measure the proton-to-electron mass ration directly
Stay Tuned – The new methods have just been made to work all together
• With time we can utilize them better• Some new ideas are being tried (e.g. cavity-sideband cooling)• Lowering uncertainty by factor of 13 check muon result (hard)
Spin-off Experiments
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Gabrielse
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Gabrielse
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GabrielseFor Fun: Coherent State
0
0.1 m
1
Coherent state with 1n
'/ 2
0,
!c
in in tn
n
nee e n
n
a
Fock statesdo not oscillate
0.1 m
Eigenfunction of the lowering operator:
n=0 n = 1
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Gabrielse
200 MHz Detection of Axial Oscillation
• Turn off during sensitive times in experiment• Mismatched, current-starved HEMPT• High Q resonant feedthrough into 100 mK, 5 x 10-17 Torr vacuum enclosure
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Gabrielse
First One-Particle Self-Excited Oscillator
Feedback eliminates damping
Oscillation amplitude must be kept fixedMethod 1: comparator
Method 2: DSP (digital signal processor)
"Single-Particle Self-excited Oscillator" B. D'Urso, R. Van Handel, B. Odom and G. Gabrielse Phys. Rev. Lett. 94, 113002 (2005).
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Gabrielse
Use Digital Signal Processor DSP
• Real time fourier transforms• Use to adjust gain so oscillation stays the same
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Gabrielse
Detecting the Cyclotron State
cyclotronfrequency
C = 150 GHz too high todetect directly
axialfrequency
Z = 200 MHz relativelyeasy to detect
Couple the axial frequency Z to the cyclotron energy.
Small measurable shift in Z
indicates a change in cyclotron energy.B 2
z 0 2B B B z
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Gabrielse
Couple Axial Motion and Cyclotron Motion
2 22 ˆ[( / 2) ]B B z z z
change in changes effective z
Add a “magnetic bottle” to uniform B
n=0n=1n=2n=3
B2 22
2
1
2 zm zH B z
spin flipis also a change in
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Gabrielse
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Gabrielse
What About Measurements After 1987?
There was one – Dehmelt and Van Dyck used a lossy trap to see if cavity-shifts were problem for 1987 result
Not used by CODATA because • there was a non-statistical distribution of measurements that was not understood• the authors said that this result should be regarded as a confirmation of the assigned cavity shift uncertainty
Before we released our measurement, Van Dyck expressed the same point of view to me