1 Objective Finish with PM measurements Discuss Friday’s filed measurements 1.
Fully Quantum Measurements of the Electron Magnetic Moment
Transcript of Fully Quantum Measurements of the Electron Magnetic Moment
Fully Quantum Measurements of the Electron Magnetic Moment
Brian Odom Research performed at Harvard University,
Gabrielse group Les Houches Physics with Trapped Charged Particles January 2012
New values for g and α
Funding: NSF
Newer values for g and α
Phys. Rev. Lett. 106, 080801 (2011)
The electron g-factor
Classical, non-relativistic Dirac equation as single- particle wave equation Quantum Electrodynamics (QED)
2.002 319 304g = ...
2g =
1g =
2e S
gm
µ
= −
B
Sgµ
µ≡
or, if you prefer …
g-factor from QED 2 3 4
1 2 3 41 ...2g C C C C non QEDα α α α
π π π π = + + + + + + −
Why measure the electron g-factor?
• Determination of α, using QED calculations
Why measure the electron g-factor?
• Determination of α, using QED calculations
• Precision test of QED
α-1137.03599 137.03600 137.03601
∆α / α (ppb)-100-50050100
muonium h.f. structure
electron g, UW 1987
quantum Hall effect
ac Josephson effect & γp,h
h / mn
h / mCs, optical trans- itions, mass ratios
electron g, Harvard 2006
h / mRb, mass ratios
Testing QED with measurements of α
?
Why measure the electron g-factor?
• Determination of α, using QED calculations
• Precision test of QED
• Probe for electron sub-structure (R < 10-18 m)
Why measure the electron g-factor?
• Determination of α, using QED calculations
• Precision test of QED
• Probe for electron sub-structure (R < 10-18 m)
• Precision test of Lorentz, CPT symmetry
Why measure the electron g-factor?
• Determination of α, using QED calculations
• Precision test of QED
• Probe for electron sub-structure (R < 10-18 m)
• Precision test of Lorentz, CPT symmetry
• Complement to the muon g-factor measurement
Why measure the electron g-factor?
• Determination of α, using QED calculations
• Precision test of QED
• Probe for electron sub-structure (R < 10-18 m)
• Precision test of Lorentz, CPT symmetry
• Complement to the muon g-factor measurement
• Prospects for improved proton to electron mass ratio
A single electron in a Penning trap
motion frequency hυ/kB damping axial 200 MHz 9.6 mK 1 Hz
cyclotron 149.0 GHz 7.2 K 0.02 Hz
spin 149.2 GHz 7.2 K 10-12 Hz
magnetron 130 kHz 6.4 µK 10-17 Hz
g-factor measurement
( )( ) ( )
2 1a z c 2
21 1c z c2 2
2=1
2 2g ω ω ω δ
ω δ ω ω δ− +
++ + +
g in free space:
g-2 in free space:
a
c
21 12 2g g ω
ω−= + = +
g-2 in a Penning trap:
[ Brown and Gabrielse. Rev. Mod. Phys. 58, 1 (1986) ] (3 orders of magnitude for free)
B s s
B B c
22Bg
Sω ωµ
µ µ ω
µµ
≡ = = =
Cylindrical Penning trap construction
Dilution refrigerator and magnet
A tabletop experiment … if you have a high ceiling
Experimental setup
B-fi
eld
shift
(ppb
)
-20
-10
0
10
20
time (hours)0 10 20 30 40 50 60
dew
ar te
mpe
ratu
re (C
)
19.0
19.5
20.0
20.5
21.0
21.5
B-fi
eld
shift
(ppb
)
-20
-10
0
10
20
time (hours)0 20 40 60
dew
ar te
mpe
ratu
re (C
)
19.0
19.5
20.0
20.5
21.0
21.5
B-field stability against room temperature
•Magnet with two broken shims •No temperature regulation
•Magnet with working shims •Shed temperature regulated
Friday, Saturday construction
< 1 ppb noise and drift at night
~ 0.1 K temperature regulation of dewar
The axial oscillator is coupled to a tuned-circuit amplifier
Response to a resonant rf-drive applied to an endcap
Detection of single electron axial motion
Feedback for self-excitation
B. D’Urso, R. Van Handel, B. Odom, D. Hanneke, and G. Gabrielse. Phys. Rev. Lett. 94, 113002 (2005)
Quantized cyclotron motion
Can we observe quantum jumps between the cyclotron states?
Cylindrical cavity suppresses decay
decay time (s)0 10 20 30 40 50 60
num
ber o
f n=1
to n
=0 d
ecay
s
0
10
20
30
time (s)0 100 200 300
axia
l fre
quen
cy s
hift
(Hz)
-3
0
3
6
9
12
15
τ = 16 s
• In free space, cyclotron lifetime = 0.08 s
• In our cylindrical traps, we have
achieved up to a 16 s lifetime
[ Peil and Gabrielse. Phys. Rev. Lett. 83, 1287 (1999) ]
Magnetic transitions are detected by a shift in the axial frequency
4
0
1
2
3
z
“Magnetic bottle” couples magnetic and axial oscillators
Detection of magnetic transitions
2z 0 2B B B z= + 2 21
E s c 22 k z zU Bµ ++=
Sub-Kelvin cyclotron temperature… Thermal Jumps
[ Peil and Gabrielse. Phys. Rev. Lett. 83, 1287 (1999) ]
• Permits single-quantum cyclotron spectroscopy
Sub-Kelvin cyclotron temperature… Thermal Jumps
[ Peil and Gabrielse. Phys. Rev. Lett. 83, 1287 (1999) ]
• Permits single-quantum cyclotron spectroscopy
Relativistic Corrections
• Eliminates relativistic error from ωc uncertainty
Single quantum cyclotron spectroscopy
time (s)0 100 200 300
axia
l fre
quen
cy s
hift
(Hz)
-3
0
3
6
9
12
15
Procedure: 1. Turn FET amplifier off 2. Apply a microwave drive pulse of ~150 GHz 3. Turn FET amplifier on, check for axial frequency shift 4. Plot a histograms of excitations vs. frequency
frequency - υc (ppb)0 100 200 300
# of
cyc
lotr
on e
xcita
tions
Single quantum cyclotron spectroscopy
time (s)0 100 200 300
axia
l fre
quen
cy s
hift
(Hz)
-3
0
3
6
9
12
15
Procedure: 1. Turn FET amplifier off 2. Apply a microwave drive pulse of ~150 GHz 3. Turn FET amplifier on, check for axial frequency shift 4. Plot a histograms of excitations vs. frequency
Poor amp heat sinking, amp off during excitation Tz = 16 K
frequency - υc (ppb)0 100 200 300
# of
cyc
lotr
on e
xcita
tions
Single quantum cyclotron spectroscopy
time (s)0 100 200 300
axia
l fre
quen
cy s
hift
(Hz)
-3
0
3
6
9
12
15
Procedure: 1. Turn FET amplifier off 2. Apply a microwave drive pulse of ~150 GHz 3. Turn FET amplifier on, check for axial frequency shift 4. Plot a histograms of excitations vs. frequency
Good amp heat sinking, amp on during excitation Tz = 3.7 K
frequency - υc (ppb)0 100 200 300
# of
cyc
lotr
on e
xcita
tions
Single quantum cyclotron spectroscopy
time (s)0 100 200 300
axia
l fre
quen
cy s
hift
(Hz)
-3
0
3
6
9
12
15
Procedure: 1. Turn FET amplifier off 2. Apply a microwave drive pulse of ~150 GHz 3. Turn FET amplifier on, 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
An unpleasant surprise:
Temperature-dependent B
•We observed a huge shift of B-field vs. trap temperature •Heat load changes are unavoidable as:
•Amplifier cycles on/off
•Anomaly drive is applied
•10 ppb / mK is far too much!
tem
pera
ture
(mK
)
707580859095
100105
time (hours)0 2 4 6 8 10
B fi
eld
shift
(ppb
)
-300-250-200-150-100
-500
Shift of -10 ppb / mK at 75 mK !!!
temperature (Kelvin)
0.0 0.5 1.0 1.5 2.0
mag
netic
fiel
d sh
ift (p
pb)
-100
0
100
200
300
400
500
600
700
temperature-1 (Kelvin-1)
0 5 10 15-100
0
100
200
300
400
500
600
700
•Nuclear paramagnetism makes standard Penning trap materials (copper, MACOR) incompatible with a stable B-field below 1 K
Curie-law paramagnetism…OF OUR TRAP!
40 ppb / K-1
New silver trap
Prototype silver tripod
temperature (Kelvin)
0.0 0.5 1.0 1.5 2.0
mag
netic
fiel
d sh
ift (p
pb)
-100
0
100
200
300
400
500
600
700
copper trapsilver trap
temperature-1 (Kelvin-1)
0 5 10 15-100
0
100
200
300
400
500
600
700
copper trapsilver trap
0.0 0.5 1.0 1.5 2.0
expa
nded
200
x
-10
0
10
20
30
•New silver trap decreases T-dependence of the field by ~ 400
•With the silver trap, sub-ppb field stability is easily achieved
Silver trap improvement
40 ppb / K-1
0.1 ppb / K-1
Finally—narrow line shapes
frequency - 170 410 496.7 Hz-0.5 0.0 0.5 1.0 1.5
spin
flip
frac
tion
0.00
0.05
0.10
0.15
0.20
2 ppb
frequency - 170 410 496.7 Hz-2 0 2 4 6 8 10
spin
flip
frac
tion
0.00
0.05
0.10
0.15
0.20
10 ppb
Comparison of line shapes
U. Wash. anomaly line
Harvard anomaly line
U. Wash. Harvard
Tz (K) 6 0.6 0.1 υz (MHz) 60 200 0.09 B2 (T/m2) 150 1500 10
H
UW
∆∆
H
UW0.1∆
∆ =
[ Van Dyck et al. Phys. Rev. Lett. 59, 26 (1987) ]
Scatter in g-factor measurements
uWave power (a.u.)0 20 40 60 80
176
178
180
182
184
186
Harvard 2006 UW 1987
UW 1991
uWave power (a.u.)0 20 40 60 80
176
178
180
182
184
186
Cavity mode structure
• Parametric response of large e- cloud maps cavity mode structure [ Tan and Gabrielse. App. Phys. Lett. 55, 2144 (1989) ]
Cavity mode structure
• Parametric response of large e- cloud maps cavity mode structure
• Modes coupling to centered single e- cloud are easily identified [ Tan and Gabrielse. App. Phys. Lett. 55, 2144 (1989) ]
TE 1n1 TM 1n1
First observation of cavity shift of g
Final Error Budget
Measurement summary
Harvard g-factor measurement: • Fully quantum measurement eliminates relativistic shift
( 1 ppt per quantum level )
• Low temperature allows quantum spectroscopy and narrows lines
• Cylindrical trap allows first quantitative treatment of cavity shift
Results : g / 2 = 1.001 159 652 180 85 (76) (0.76 ppt) α = 137.035 999 710 (90) (32) 137.035 999 710 (96) (0.70 ppb)
-1
Measurement summary
Harvard g-factor measurement: • Fully quantum measurement eliminates relativistic shift
( 1 ppt per quantum level )
• Low temperature allows quantum spectroscopy and narrows lines
• Cylindrical trap allows first quantitative treatment of cavity shift
g / 2 = 1.001 159 652 180 85 (76) (0.76 ppt) α = 137.035 999 710 (90) (32) 137.035 999 710 (96) (0.70 ppb)
-1
Results :
New values for g and α
g / 2 = 1.001 159 652 180 85 (76) (0.76 ppt) α = 137.035 999 710 (90) (32) 137.035 999 710 (96) (0.70 ppb)
g-factor from QED 2 3 4
1 2 3 41 ...2g C C C C non QEDα α α α
π π π π = + + + + + + −
Harvard 2008 measurement
Harvard 2008 measurement
Harvard 2008 measurement
α, a wrinkle and a new measurement
Phys. Rev. Lett. 106, 080801 (2011)
QED…Still standing 57 years later