the university of oklahoma measuring the electron’s electric dipole moment using zero-g-factor...
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The University of Oklahoma
Measuring the Electron’s Electric Dipole Moment usingMeasuring the Electron’s Electric Dipole Moment usingzero-g-factor paramagnetic moleculeszero-g-factor paramagnetic molecules
APS March Meeting, 2006APS March Meeting, 2006
Funding sources for preliminary research:
National Research Council (US)
NATO SfP (for field measurement.)
OU Office of the Vice Presidentfor Research
Neil Shafer-Ray, The University of Oklahoma
Current funding:
National Science Foundation
DOE EPSCoR Laboratory-StatePartnership
The University of Oklahoma
I am very sorry that I was not able to deliver this talk. My grandmother has passed away a few hours ago and I must return to the United States.
Sunday, October 8, 11:30pmNeil Shafer-Ray
To all,
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CP (time reversal) violation
K-zero-long decay
http://www.bnl.gov/bnlweb/history/nobel/nobel_80.asp
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A completely different place to look for CP violationA completely different place to look for CP violationis in the interaction of fundamental particles with external is in the interaction of fundamental particles with external
fields.fields.
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The study of the magnetic moment of the electronThe study of the magnetic moment of the electronis an integral part of some of the mostis an integral part of some of the most
compelling experiments of the last 100 years.compelling experiments of the last 100 years.
GHz/ 39962458.1)( BB SBgU
Stern and Gerlach 1922"space quantization"g=1 to 10% (assumed integral spin)Nobel Prize 1943
II Rabi 1938Magnetic Resonanceresonant line widths <10kHzNobel Prize 1944 MAINSTAY of MODERN CHEMISTRY
Norman RamseySeparated Oscillator Beam Resonanceresonant line witdths <100HzNobel Prize 1989 STANDARD OF TIME
Hans G. Dehmeltion trapping, spectroscopy of a single
trapped electron.Nobel Prize 1989
2.002319304361716Gerald GabrielseQuantum nondistructive measurement
of the quantum structure ofa single electron in a magnetic trap
STANDARD OF MASS?
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An EDM proportional to spin would also give CPAn EDM proportional to spin would also give CP
g = 2.0023193043617(16)Gabrielse,PRL 2006
gedm = 0.00000000000000000(5)Commins, PRL, 2004
GHz/ 39962458.1
)(
B
edmB SEgSBgU
cme1093080.1 11
The University of Oklahoma
Su
per
Sym
.S
td. M
od
.
(Hoo
geve
en 1
990)
(Arn
owitt
200
1)
- Commins & coworkers, Tl, PRL, 2002
- Hinds & coworkers, YbF, DAMOP, 2005
An EDM proportional to spin would also give CPAn EDM proportional to spin would also give CP
The University of Oklahoma
I. Introduction
What is the OU group up to?
How was the current experimental limit on the magnitude of the e-EDM obtained?
OutlineOutlineOutline
What are some of the current experiments beingcarried out to measure the e-edm
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To search for an e-EDM we will look for
U=U+M –U-M
in a strong E field.
Symmetry leads to a ±M degeneracy of any molecule or atom that is not broken by an electric field along the quantization axis.
The existence of an electron electric dipole moment would break this symmetry.
How the current limit on electron EDM is knownHow the current limit on electron EDM is known
Precision structurecalculations arenot necessary.
Major Difficulty:A backgroundmagnetic field mimics an EDM.
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The Commins Experiment withThe Commins Experiment with22PP1/2 1/2 (F=1, M=(F=1, M=±1) ±1) TlTl
.)( zzsysedmzz
syszB FEgFBgU
For an atom or molecule in a strong electric field,
)( SEgSBgU edmB
For an isolated electron,
edmsysedm gg for light atoms/molecules (Schiff's theorem.)
0sysedmg for diamagnetic atoms
edmsysedm gg for relativistic (heavy atoms/molecules.)
We want to use heavy paramagnetic atoms or molecues.
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z
Bz
eTl Bh
Eh
d
h
U )34.0()77.0)(585(2
The Commins Experiment withThe Commins Experiment with22PP1/2 1/2 (F=1, M=(F=1, M=±1) ±1) TlTl
pG
B
cmvolt
E
cme
dmHz
h
U zzeTl
24/1010022.0
527
enhancement factor geometric factors
The University of Oklahoma
Tl(2P1/2 F=1), incoherent combination of|1,1>, |1,0> and |1,-1> states
P() = probabilityof finding the systemIn the state M=F whenquantization axis isin the direction of .
E
LASER RADIATION
Tl(2P1/2 F=1), |1,1> + |1,-1>
Graphical Description of the Commins e-EDM ExperimentGraphical Description of the Commins e-EDM Experiment
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EFFECT OF MAGNETIC FIELDS ONTHE DISTRIBUTION OF ANGULAR MOMENTUM
Tl(2P1/2 F=1),
|1,1> + Exp[i U t /] |1,-1>
B
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Bx
A small constant field Bx along an axis perpendicular to Bhas little effect.
B
EFFECT OF MAGNETIC FIELDS ONTHE DISTRIBUTION OF ANGULAR MOMENTUM
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B
A small field Bx along an axis perpendicular to Bthat rotates with the distribution may have a dramatic effect.
EFFECT OF MAGNETIC FIELDS ONTHE DISTRIBUTION OF ANGULAR MOMENTUM
Brot
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EFFECT OF A MAGNETIC FIELD ONOF ANGULAR MOMENTUM ORIENTATION
B
A small field Bx along an axis perpendicular to Bthat rotates with the distribution may have a dramatic effect.
The Ramsey beam resonance technique takes advantage of this dependenceof the Rabi rotation on the phase of the rotating field.
B
The Commins experimentCommins et al, PRL 88, 71805, 2002
U/ =RF
LASER LASER
The Commins experimentCommins et al, PRL 88, 71805, 2002
U/ RF
B
LASERLASER
The University of Oklahoma
600400200 0 200 400 600Hz
0.2
0.4
0.6
0.8
1
P 1
f
Expected Ramsey resonance signal forT = (2kT/m)1/2 / 2L = 140 Hz
(m=100 amu , T=500K, and interaction length L= 1000mm)
FL
UO
RE
SC
EN
CE
(L
IGH
T S
EE
N)
MISMATCH BETWEEN and RF
B E
The Commins experimentCommins et al, PRL 88, 71805, 2002
LASER
U/ =RF(+)
LASER
LASER
B
U/ =RF(-)
E
The Commins experimentCommins et al, PRL 88, 71805, 2002
LASER
The University of Oklahoma
600400200 0 200 400 600Hz
0.2
0.4
0.6
0.8
1
P 1
f
E||BE(-||)B
SHIFT GIVES EDM
SHIFT SHOWN TO BE ~ 10-7 OF THE WIDTH!!!
GREAT STATISTICS!
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limiting systematic error
B
E
2/' cEvB
sin)100(of splitting
/sin2|'||'| 2
Hz
cvEBBBB downup
sin ≈10-6
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Measurement of the e-EDM using paramagnetic moleculesMeasurement of the e-EDM using paramagnetic molecules
0.024Tl(2P1/2 F=1)
System(state)
E-field(kV/cm)
split @10-27e cm
(mHz)
B @10-27e cm
(nG)
0.02100
tcoherence
(ms)
3
YbF(X2,F=1)
10. 13 5 3
dlimit
(10-27e cm)
1.3
-Hind
s
Commins
1) Effective electric field is the internal field of the molecule.2) Idea by Saunders (Atomic Phys, 14 1975,71).3) Calculation of shift by N.S. Mosyagin, M.G. Kozlov, A.V. Titov,
(J Phys B, 31, L763)
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Effect of the large tensorsplit (energy dependence on |M|)
B
E
v
Only the projection of B on the E axiscontributes to the energy between ±M levels:
0)()( ''
,,
downzupzBBBB zz
2/' cEvB
away! goes systematic / 2cEv
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Effect of the large tensorsplit (energy dependence on |M|)
B
downE
Only the projection of B on the E axiscontributes to the energy between ±M levels: upE
6
,,
10
sin)1(of splitting
sin2
Gauss
BHz
BBB downzupz
A much less severe problemthen the vxE/c2 effect.
The University of Oklahoma
Easy to lose in statistics what one gains in intrinsic sensitivity.
Beam Expected Flux Speed Distribution
Tl(F=1,|M|=1) 8 × 1015/str/sec
YbF(J=1/2, F=1,|M|=1)6 × 1010/str/sec
0 400 800 v(m/s)
(from oven)
(from supersonicexpansion)
0 400 800 v(m/s)
Differences between an atomic beam and a beam of Differences between an atomic beam and a beam of paramagnetic moleculesparamagnetic molecules
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0.024Tl(2P1/2 F=1)
System(state)
E-field(kV/cm)
shift @10-27e cm
(mHz)
B @10-27e cm
(nG)
0.02100
tcoherence
(ms)
3
YbF(X2,F=1)
10. 13 5
PbO(a3,F=1)
.01 2.9 1
3
0.1
dlimit
(10-27e cm)
1.3
30(1?)
-
-
Hinds
Cs(2P1/2 F=3)
0.000254 0.00016 15 60Hunter
(DeMille)
Commins
-PbF(X21/2, F=1)
60-100 12 500 to 107 103 to 3(Shafer-
Ray)
(Weiss)
(Gould)
HfF+
(31)(Cornell) ~10 ~200 ~103~1 volt RF
ion trap
2x103
~103 -
-0.0050.0040.0050.004
100??
(Hinds)
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Cs Atomic Fountain (Provided by Harvey Gould)Cs Atomic Fountain (Provided by Harvey Gould)
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The OU PbF edm experiment
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g factor of PbF F=1, |Mg factor of PbF F=1, |MFF|=1, high-field-seeking ground state:|=1, high-field-seeking ground state:
g-factor can be tuned to zero!
11.0)3/2(21 Gg
017.0)( ||21 Gg
Shafer-Ray, PRA,73, 34102
The University of Oklahoma
PbF molecular beam source
optical polarization(create M=0 state) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
Schematic of PbF g=0 measurementSchematic of PbF g=0 measurement
LIF or REMPI detection region
(probe M=0 state)
The University of Oklahoma
PbF molecular beam source
optical polarization(create M=0 state) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
Schematic of PbF g=0 measurementSchematic of PbF g=0 measurement
LIF or REMPI detection region
(probe M=0 state)
The University of Oklahoma
First things first: Production and detection of PbFFirst things first: Production and detection of PbF
Pb / F2 flow reactor: Operational Temperature 1200K
Pb +MgF2 reactor: Operational Temperature 1200K
Pb +PbF2 reactor: Operational Temperature 1200K
The University of Oklahoma
PbF molecular beam source
optical polarization(create M=0 state) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
Schematic of PbF g=0 measurementSchematic of PbF g=0 measurement
REMPI detection region
(probe M=0 state)
The University of Oklahoma
Current Apparatus for Exploring PbF SpectroscopyCurrent Apparatus for Exploring PbF Spectroscopy
Nd:YAG 10ns, 10Hz
tunable dye laser0.1 cm-1 resolutiontunable dye laser
0.1 cm-1 resolution
PbF Source Chamberionization chamber
detection chamber
Not an ideal detection scheme:PbF molecules stay in probe region ~5s
Time between laser shots: 100msDuty cycle: 1/(20,000)
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PbF Source Chamberionization chamber
det
ect
ion
cha
mb
er
PbF
PbF
+
Current Apparatus for Exploring PbF SpectroscopyCurrent Apparatus for Exploring PbF Spectroscopy
The University of Oklahoma
PbF Source Chamberionization chamber
det
ect
ion
cha
mb
er
PbF
PbF
+
Current Apparatus for Exploring PbF SpectroscopyCurrent Apparatus for Exploring PbF Spectroscopy
The University of Oklahoma
(0,0) band
5.0
4.0
0.0
-2.0
-1.0
-3.0
3.0
2.0
1.0
ener
gy (
eV)
X21/2
A21/2
B21/2
PbF+
3.0 5.0 7.0R(Bohr)
1+1 X1+1 X11221/21/2 →→BB221/21/2 REMPI of PbF REMPI of PbF
OU data, 2005
McRaven, Poopalasingam, Shafer-Ray,Chemical Physics Letters, In Progress.
355-397nm
280 nm
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Observation of an ionization threshold for PbFObservation of an ionization threshold for PbF
McRaven, Poopalasingam, Shafer-Ray,Chemical Physics Letters, In Progress.
I.P. 7.55eV
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R(Bohr)
5.0
4.0
0.0
-2.0
-1.0
-3.0
3.0
2.0
1.0
ener
gy (
eV)
E' 43/2?
PbF+
3.0 5.0 7.0
State selective ionization of PbF+ via 1+1+1 doubly-resonant multi-photonionization.
X21/2
A21/2
(A→E') / nm442.4 440.8
(X
→A
) / n
m
436.612
436.320
WE HAVE DISCOVERED A NEW ELECTRONIC
STATE OF PbF(tentative assignment: E'43/2)
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f (A→E') / cm-1
226
12.1 f (A→E') / cm-1
226
12.1
226
41.8
226
41.8
f (X
→A
) /
cm-1
22889.9
22900.6
SIMULATION EXPERIMENT
Double Resonant Ionization of PbF
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R2-R21
JX1 1/2 3/2 5/2 7/2
3/2
P1-R21
R2-Q1
1/2 3/2 5/2
9/2
R2-P21
3/2 5/2
A→E' photon energy (cm-1)
We have used our0.1cm-1 lasers to
almost isolatethe J=1/2 state!
(Impossible with 1 resonant step.)
We now have a bluediode laser and will start scanningwith 10 MHz resolutionin the next few weeks
We have yet torotationally cool.(Bigger pumps
await promised DOEmoney. Program in
limbo untilCongress approves
the Energy and Waterappropriations bill.)
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Saturation of X->A transition in high J, X->A->E' ionization (probe laser power at 0.12 fluence J/cm^2 )
0.00E+00
5.00E-03
1.00E-02
1.50E-02
2.00E-02
2.50E-02
3.00E-02
3.50E-02
4.00E-02
0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0
pump energy (fluence-mJ/cm 2̂)
signa
l inten
sity (
mV)
X→A Saturation Curve(A→E' fluence at 0.12 J/cm2)
Sig
nal
In
ten
sity
(a.
u.)
0
5
fluence of X→A laser radiaion (mJ/cm2)
~40mJ/cm2 of 0.1cm-1 light to saturateX→A
ionization step at 437nm. A-state lifetime 3S
X→A transition may be saturatuatedwith ~15mW/mm2 diode laser radiation
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Saturation of E'->A transition in high J, X->A->E' ionization (pump laser power a 42.6 fluence mJ/cm2 )
0.00E+00
5.00E-02
1.00E-01
1.50E-01
2.00E-01
2.50E-01
3.00E-01
0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0
Probe energy(fluence J/cm2)
Sign
al int
ensit
y(m
v)A→E' Saturation Curve
(X→A fluence at 43 mJ/cm2)
fluence of A→E' laser radiaion (J/cm2)
Sig
nal
In
ten
sity
(a.
u.)
0
5
radiation drivingboth A→E' andE'→PbF+
ionization stepsaturated
A→E' step saturated
12J/cm2 to saturateA→E'→PbF+
ionization step at441nm.
E' lifetime <5ns
can not be ionized with cw laser radiation
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TIMING FOR OPTIMIZED PbF DETECTION
0 2usec
437nm X→A diode laser radiation.
6usec
10mW/mm2 cw
442nm A→E'→PbF+ pulse laser radiation 10 mJ/mm2, 10-100ns
208PbF ion signal
100-1000Hz
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2mm (x 0.1mm)
lase
r ra
dia
tion
PbF beam
re
p ra
te 1
0 H
z
Current set up.
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100 mm (x 0.1mm)
re
p ra
te 1
000
Hz
50,000 to50010
000,1 to10
/1
/10
2
1002
2
Hz
HzHz
cmmJ
cmmJ
mm
mm
PbF beam
Improvement over current spectra:
OPTIMIZED DETECTION OF PbF
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optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
X1 21/2 (F=1)
A 21/2 (F=1)
|M|=1
|M|=1M=0
M=0
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optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
X1 21/2 (F=1)
A 21/2 (F=1)
|M|=1
|M|=1M=0
M=0
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optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
M=0400MHz|M|=1
The University of Oklahoma
optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
M=0400MHz|M|=1
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Requirements for large Rabi populationamplitude in Raman pumping
from a state A to a state B
(1) of lasers on resonance.
A B
C
(2) At least 1 state C that couples to both A and B.
(3) A finely tuned ratio of A-C to B-C coupling.
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0 20 40 60 80 100 120 140ts0
0.2
0.4
0.6
0.8
1
P
Simulation of RF Raman .02
PM=0
P|M|=1
M=0 |M|=1X1 2
A 2
EDC
k = BRF,effective
^
^ ^
0 20 40 60 80 100 120 140ts0
0.2
0.4
0.6
0.8
1
P
Simulation of RF Raman .20
PM=0
P|M|=1
= 0= /2
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optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
The University of Oklahoma
optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
The University of Oklahoma
optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
PROBE+
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optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
PROBE+
The University of Oklahoma
optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
PROBE+
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PROBE-
QQpgBedm ..
optic
al p
olar
izatio
n
(cre
ate
M=0
sta
te) high-field region
Raman
-RF p
ump
prob
e +
prob
e -
LIF or REMPI detection region
(probe M=0 state)
reverse sign with changing E.^
small, E even^
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Using Ramsey fringes to lock the electric field: Using Ramsey fringes to lock the electric field:
/2
0
4214/2
02
)()sin(
))sin1(sin(cos)(
dttSignaltS
NdttSignalQ
4 2 0 2 4EEovoltcm1
0.5
0
0.5
1
RF1
RF2
RF1 fixed to a frequency standard.
RF2=RF1+
40 20 0 20 40EEovoltcm1
0.5
0
0.5
1
Q
S
S
zero crossing independent of ±M phase
The University of Oklahoma
A totally different idea: Guided PbF molecules in a Coaxial cable A totally different idea: Guided PbF molecules in a Coaxial cable
Ra
ma
n-R
F
LIF
imag
ing
dete
ctor
polarizatiing laser radiation
Raman-RF
LIF image
EDM
1 to 100 meters
Disadvantages: Must use LIF detection g=0.017 (not zero)Advantage: long (~1second) coherence time
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Conclusions
• We have found a system for which the effect of background magnetic fields may be suppressed by seven orders of magnitude.
• We have developed a source of PbF as well as sensitive state selective REMPI of the molecule.
• We are designing a beam machine to take advantage of this new system.
The University of Oklahoma
THANKS TO:
Chris McRaven , Sivakumar Poopalasingam,Milinda Rupasinghe
Graduate Students:
Chris Crowe, Dustin Combs, Chris BaresUndergraduate Students:
Professor George Kalbfleisch:
March 14, 1931 - September 12 2006
The University of Oklahoma
The University of OklahomaNeil Shafer-Ray Kim MiltonJohn Furneaux
Petersburg
Nuclear Physics
Institute
Victor Ezhov
Mikhail Kozlov
University of Latvia
Marcis Auzinsch
BNL Chemistry
Greg Hall
Trevor Sears
U Cal Berkeley
Dmitry Budker
And thanks to the e-EDM COLLABORATION