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![Page 1: Measurement of the electron’s electric dipole moment Mike Tarbutt Centre for Cold Matter, Imperial College London. Ripples in the Cosmos, Durham, 22 nd.](https://reader035.fdocuments.us/reader035/viewer/2022062716/56649de95503460f94ae3afa/html5/thumbnails/1.jpg)
Measurement of the electron’s electric dipole moment
Mike Tarbutt
Centre for Cold Matter, Imperial College London.
Ripples in the Cosmos, Durham, 22nd July 2013
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+- Spin
Edm+-Spin
Edm
The electron’s electric dipole moment (EDM, de)
T
T CPimplies
Insufficient CP
Either de = 0, or T
10-24
10-22
10-26
10-28
10-30
10-32
10-34
10-36
Multi Higgs
Left -Right
MSSM
Other SUSY
Standard ModelPr
edic
ted
valu
es f
or th
e el
ectr
on e
dm d
e (e.
cm)
![Page 3: Measurement of the electron’s electric dipole moment Mike Tarbutt Centre for Cold Matter, Imperial College London. Ripples in the Cosmos, Durham, 22 nd.](https://reader035.fdocuments.us/reader035/viewer/2022062716/56649de95503460f94ae3afa/html5/thumbnails/3.jpg)
Measuring the EDM – spin precessionB & E
EParticle precessing in
a magnetic fieldParticle precessing in parallel magnetic and
electric fields
Particle precessing in anti-parallel magnetic
and electric fields
Measure change in precession rate when electric field direction is reversedWe use the valence electron in the YbF molecule
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We use a beam of YbF molecules
Eff
ecti
ve f
ield
, E
eff (
GV
/cm
)
Interaction energy = - de .Eeff
Eeff = F P
Structure dependent, ~ 10 (Z/80)3 GV/cm
Polarization factor
![Page 5: Measurement of the electron’s electric dipole moment Mike Tarbutt Centre for Cold Matter, Imperial College London. Ripples in the Cosmos, Durham, 22 nd.](https://reader035.fdocuments.us/reader035/viewer/2022062716/56649de95503460f94ae3afa/html5/thumbnails/5.jpg)
Pulsed YbF molecular beam
hf = 2mB
2nd rf pulse
1st rf pulse
± 2 de EeffE
±B
analyze spin direction
Simplified measurement scheme
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Result (2011)
de = (-2.4 ± 5.7stat ± 1.5syst) × 10-28 e.cm
| de | < 10.5 × 10-28 e.cm (90% confidence level)
6194 measurements of the EDM, each derived from 4096 beam pulses Each measurement takes 6 minutes
Nature 473, 493 (2011)
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Implications
10-24
10-22
10-26
10-28
10-30
10-32
10-34
10-36
Multi Higgs Left -
Right
MSSM
Other
SUSY
Standard Model
Pred
icte
d va
lues
for
the
elec
tron
edm
de (
e.cm
)
Mass of new particle
CP-violating phase
For Ms= 200 GeV and qCP ≈1
=> de ≈ 10-24 e.cm
Excluded region
Ms > 4 TeV ? qCP < 10-3 ?
e e
gselectron
gaugino
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Some other electron EDM experiments
• ThO at Harvard \ Yale - new result anticipated with very high sensitivity
• WC at Michigan – in development
With molecules:
• HfF+ at JILA – trapped ion with rotating E & B fields, very long coherence times, being developed
With ions:
• Gadolinium Garnets at LANL and Amherst – lots of electrons, but difficult to control systematic effects
With solids:
• Trapped ultracold Cs at Penn State and U. Texas, being developed
• Trapped ultracold Fr at Tohoku / Osaka, being developed
With atoms:
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d(m) 2×10-19
d(n) 3×10-26
d(p) 6×10-23
d(e) 1×10-27
10-20
10-22
10-24
s [d
] (e
.cm
)1960 1970 1980 1990 2000 2010 2020 2030
10-28
electron:neutron:
10-26
Year
Particle EDMs - historic and present limits
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M. Le Dall and A. Ritz, Hyperfine Interactions 214, 87 (2013)
CMSSM constraints from EDM measurements
tan b = 3, MSUSY=500GeV
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Future experiments with YbF molecules
Upgrades to existing experiment – x10 improvement (in progress)
x1000 improvement
Molecular fountain of ultracold YbF molecules (under development)
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Thanks...
Ed Hinds
Dhiren Kara
Ben SauerJony Hudson
Jack Devlin Joe Smallman
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The YbF EDM experiment – schematic
J. J. Hudson, D. M. Kara, I. J. Smallman, B. E. Sauer, M. R. Tarbutt & E. A. Hinds, Nature 473, 493 (2011)
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Atom / MoleculeElectricField
E
Using atoms & molecules to measure de
Interaction energy = - de .Eeff
Eeff = F P
Structure dependent, ~ 10 (Z/80)3 GV/cm
Polarization factor
For more details, see E. A. Hinds, Physica Scripta T70, 34 (1997)
For a free electron in an applied field E, expect an interaction energy -de.EN.B. Analogous to interaction of magnetic dipole moment with a magnetic field, -m . B
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Ground state YbF
-de Eeff
de Eeff
X 2S+ (n = 0, N = 0)
-1 +10F = 1
F = 0
170 MHz
MF
ElectricField
E
We measure the splitting 2deEeff between the MF = +1 and MF = -1 levels
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Measurement scheme – a spin interferometer
Pulsed YbF beam
PumpA-X Q(0) F=1
ProbeA-X Q(0) F=0
PMT
3K beam
F=1
F=0
rf pulse
B HV+
HV-
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Counts
BEE
Measuring the edm with the interferometer
Signal α cos2 [f/2] = cos2 [(mB B – de Eeff ) T / ћ]
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Modulate everything
±E±B
±B
±rf2f±rf1f
±rf2a±rf1a
±laser f±rf
spin interferometer
Signal
9 switches:
512 possible correlations
The EDM is the signal correlated with the sign of E.B We study all the other 511 correlations in detail
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F = 0
F = 1
rf
E
Sta
rk-s
hift
ed
hype
rfin
e in
terv
al
F = 0
F = 1
rf
E
Sta
rk-s
hift
ed
hype
rfin
e in
terv
al
rf detuning
phase shift: ~100 nrad/Hz
Imperfect E-reversal
Changes detuning via Stark shift
Phase correlated with E-direction
Correction to EDM: (5.5 ± 1.5) × 10-28 e.cm
Correcting a systematic error
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Effect Systematic uncertainty (10-28 e.cm)
Electric field asymmetry 1.1
Electric potential asymmetry 0.1
Residual RF1 correlation 1.0
Geometric phase 0.03
Leakage currents 0.2
Shield magnetization 0.25
Motional magnetic field 0.0005
Systematic uncertainties
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How to do better
The statistical uncertainty scales as: 1N
1T
1E
Total number of participating molecules
Coherence time
Electric field
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Cryogenic source of YbF
Produce YbF molecules by ablation of Yb/AlF3 target into a cold helium buffer gas Helium is pumped away using charcoal cryo-sorbs Produces intense, cold, slow-moving beams
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Cold, slow beam of YbF molecules
Rotational temperature: 4 ± 1 K Translational temperature: 4 ± 1 K
Speed vs helium flow
Mol
ecul
es /
ster
adia
n / p
ulse
Flow rate / sccm
Flux vs helium flow
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Magnetic guide
Permanent magnets in octupole geometry, depth of 0.6 T Separates YbF molecules from helium beam Guides 6.5% of the distribution exiting the source
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Laser cooling
Laser cooling is the key step!!
LaserLaser
Ground state
Excited state
AbsorptionSpontaneous emission
v’’= 0
v’= 0
v’’=1
v’’=2X2(N=1)
A2½
552 nm
584 nm568 nm
92.8%6.9%
0.3%
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Simulations for YbF in an optical molasses
6 beams each containing 12 frequencies from 3 separate lasers
– 750 mW total
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Sensitivity of an EDM fountain experiment
Quantity Value How determined?
Molecules in cell 1013 Measured by us
Extraction efficiency 0.5 % Measured by Doyle group
Fraction in relevant rotational state 24 % Boltzmann distribution
Fraction accepted by guide 6.5 % Magnetic guide simulation
Fraction cooled in molasses 0.76 % Molasses simulation
Rotational state transfer efficiency 100 % Pi-pulse
Fraction though fountain 7.5 % Free-expansion at 185mK
Detection efficiency 100 % Fluorescence on closed transition
Coherence time 0.25 s By design
Repetition rate 2 Hz By design
EDM sensitivity in 8 hours 6 x 10-31 e.cm Statistical sensitivity