fully quantum measurement of the electron magnetic momentfschney/seminar.ss09/padeffke.pdfthermal...
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Fully Quantum Measurement of the Electron Magnetic
Moment
prepared by Maren Padeffke
(presented by N. Herrmann)
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Outline
Motivation and HistoryExperimental MethodsResultsConclusionSources
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Motivation and History
Why measure the Electron Magnetic MomentTheoretical Prediction of the g ValueHistory of g Value Measurements
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Why measure the Electron Magnetic Moment
Electron g – basic property of simplest of elementary particles
Determine fine structure constant α– QED predicts a relationship between g and α
Test QED– Comparing the measured electron g to the g
calculated from QED using an independent α
TMeV
cme
sg
eB
B
1110)43(788381749.52
−⋅==
=h
rr
μ
μμ
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Theoretical Prediction of the g Value
e.g. What is g for identical charge and mass distributions?
2( )2 2 2 2
e ev L e e LIA Lmv m m
v
ρμ πρπρ ρ
= = = = =⎛ ⎞⎜ ⎟⎝ ⎠
h
h
Bμ
BLgμ μ=r
r
h
magneticmoment
angular momentum
Bohr magneton
2emh
1g =
ρ
v ,e m
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Feynman diagrams
(added by NH)
Dirac particle: g=2
Each vertex contributes √α
QED corrections
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Dirac+QED Relates Measured g
• C1= 0.5• C2= -0.328... (7 Feynman diagrams) analytical
• C3= 1.181... (72 Feynman diagrams) analytical
• C4~ -1.71 (involving 891 four-loop Feynman diagrams) numerical
42 3
2 3 41 .2
..1 C C C Cg aα α α απ ππ
δπ
⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠
= + + + + +⎛ ⎞⎜ ⎟⎝ ⎠
Measure
Diracpointparticle QED Calculation
weak/strong
Sensitivity to other physics (weak, strong, new) is lowKinoshita, Nio,
Remiddi, Laporta, etc.
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42 3
2 3 41 .2
..1 C C C Cg aα α α απ ππ
δπ
⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠
= + + + + +⎛ ⎞⎜ ⎟⎝ ⎠
experimentaluncertainty
theoretical uncertainties
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Basking in the Reflected Glow of Theorists
KinoshitaRemiddi G.Gabrielse
2004
1
2
2
3
5
3
4
4
5
.
1
.
2
.
C
C
C
C
a
g
C
απ
απ
απ
α
δ
π
απ
⎛ ⎞⎜ ⎟⎝ ⎠
⎛ ⎞⎜ ⎟⎝ ⎠
⎛ ⎞⎜
⎛ ⎞⎜ ⎟⎝ ⎠
⎛ ⎞⎜
⎟⎝ ⎠
⎟⎝ ⎠
= +
+
+
+
+
+
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History of g Value Measurements
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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UW 1981
UW 1987
UW 1990
Harvard 2004
∆g/g x 1012
3040 20
10
0 -10
40 30 20
10
0 -10
(g/2 – 1.001 159 652 180.86) x 1012
History of the Measured Values
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Experimental Methods
• g Value Measurement Basics• Single Quantum Spectroscopy and Sub-Kelvin• Cyclotron Temperature• Sub-Kelvin Axial Temperature• Cylindrical Penning Trap• Magnetic Field Stability• Measurements
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g Value Measurement: Basics
12 kHz
153 GHz
200 MHz
Electrostaticquadrupolepotential Magnetic field
cool detect
need tomeasurefor g/2
• very small accelerator
• designer atom
Quantum jump spectroscopy of lowest cyclotron and spin levels of anelectron in a magnetic field
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• Quantized motions of a single electron in a• Penning Trap (without special relativity)
- g could be determined by measurement of cyclotron and spinfrequency: g/2 = ωs/ωc ≈1
- since g≠2, ωc and ωs are not equal non-zero anomaly shift ωa
- g-2 can be obtained directly from cyclotron and anomalyfrequencies: g/2- 1 = ωs/ωc ≈1x10−3
g-2 experimentsgain three orders ofmagnitude in precisionover g experiments
12c
eBm
νπ
=2s cgν ν=
g/2- 1 = (ωs−ωc)/ωc = ωa/ωc ≈1x10−3
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Experimental key feature
(added by NH)
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Single Quantum Spectroscopy and Sub-Kelvin Cyclotron Temperature
• cooling trap cavity to sub-Kelvin temperatures ensures that cyclotron oscillator is always in ground state (no blackbody radiation)
• relativistic frequency shift between two lowest quantum states is precisely known
0.23
0.11
0.03
9 x 10-39
Averagenumber
of blackbodyphotons in
the cavity
Note: 153 GHz -> T=hf/k=7.3K
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Sub-Kelvin Axial Temperature• Anomaly and cyclotron resonance acquire an inhomogeneous• broadening proportional to the temperature Tz of the
electron's• axial motion
– Occurs because a magnetic inhomogeneity is introduced to allow detection of spin and cyclotron transition
anomaly (left) and cyclotron (right) with Tz = 5 K (dashed) and Tz = 300 mK (solid)
• cooling Tz to sub-Kelvin narrows the cyclotron and anomaly line• widths
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Cylindrical Penning Trap
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David Hanneke G.Gabrielse
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Measurement procedure
Quantum jump spectroscopy
Probablility to change state as function of detuning of drive frequency
(NH)
PRL 97, 030801 (2006)
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Quantum nondemolitionmeasurement
(NH)
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Advantages of a Cylindrical Penning Trap
• well-understood electromagnetic cavity mode structures
• reducing the difficulties of machining the electrodes
• cavity modes of cylindrical traps are expected to have higher Q values and a lower spectral density than those of hyperbolic traps
– allows better detuning of cyclotron oscillator, which causes an inhibition of cyclotron spontaneous emission
• frequency-shift systematics can be better controlled
– these shifts in the cyclotron frequency were the leading sources of uncertainty in the 1987 University of Washington g value measurements
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Magnetic Field Stability• in practice, measuring the cyclotron and anomaly frequencies• takes several hours• temporal stability of magnetic field is very important
• trap center must not move significantly relative to the• homogeneous region of the trapping field
• magnetism of the trap material themselves must be stable
• pressure and temperature must be well-regulated
time (hours)
0 20 40 60
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Eliminate Nuclear Paramagnetism
• attempts to regulate the temperature and heat flows could not• make sufficient precise for line widths an order of magnitude • narrower• entire trap apparatus was rebuilt from materials with
smaller nuclear paramagnetism
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Measurements
• due to a coupling to the axial motion, the magnetron, cyclotron,
• and spin energy changes can be detected as shifts in the axial
• frequency
• the measurements from Harvard University were taken at• νc = 146.8 GHz and νc = 149.0 GHz with νz = 200 MHz
cyclotron anomaly
one quantumcyclotronexcitation
spin flip
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ResultsUncertainties
g -values
• First parenthesis statistic, second systematic uncertainty
• Non-parenthesized: corrections applied to obtain correct value for g,
• parenthesized: uncertainties
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From 2004 to 2008
g/2 = 1.001 159 652 180 86(57)g/2 = 1.001 159 652 180 85(76)g/2 = 1.001 159 652 180 73(28)
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How Does One Measure g to some Parts in 10-1213?
Conclusion
• 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
first
mea
sure
men
t with
th
ese
new
met
hods
Use New Methods
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Sources
hussel.harvard.edu/~gabrielse/gabrielse/papers/2004/OdomThesis.pdf
http://hussle.harvard.edu/~hanneke/CV/2007/Hanneke-HarvardPhD_Thesis.pdf
www.phys.uconn.edu/icap2008/invited/icap2008-gabrielse.pdf
vmsstreamer1.fnal.gov/VMS_Site_03/Lectures/Colloquium/presetatins/070124Gabrielse.ppt