EDM Measurements
using Polar Molecules
B. E. Sauer
Imperial College London
J. J. Hudson, M. R. Tarbutt, Paul Condylis, E. A. Hinds
Support from:
EPSRC, PPARC, the EU
Two motivations to measure EDMs
EDM violates T symmetry
Deeply connected to CP violation and the
matter-antimatter asymmetry of the universe
EDM is effectively zero in standard model
but
big enough to measure in non-standard models
direct test of physics beyond the standard model
CP from particles to atoms (main connections)
field theory
CP model
Higgs
SUSY
Left/Right
electron/quark
level
nucleon
level
nuclear
level
dpara
de
dq
atom/molecule
level
dn
dcq
Strong
CP
NNNN
GG
%
Schiff
moment
ddia
Predicted values for the electron edm de (e.cm)
Status of theory and experiment of
electron EDM
10-22
10-24
10-26
10-28
MSSM
φ~1
Multi
Left Higgs
Right
MSSM
φ ~ α/π
Thallium experiment (2002)
de < 1.6 x 10-27 e.cm
10-30
10-32
10-34
Limited by stray and
motional magnetic fields
10-36
New approach required
Standard Model
Using Dirac theory, the
first order edm energy is 〈H1〉 = 〈Ψ0|-de β Σ⋅Ε| Ψ0 〉 .
〈 |
As a matrix equation this becomes
〈H1〉 =
f0
0
g0
0 2de σ·E
| 〉
f0
0
g0
only acts on relativistic part of
the wavefunction
^ 2, so
|g 0〉 is only appreciable at small r, where E ≈ Zr/r
〈H1〉
≈
〈g0|2de
^
Zr
σ⋅
|g0〉.
r2
expanding the wavefunction | Ψ0〉 in angular eigenstates:
|Ψ0〉 = as|s〉 + ap1/2|p〉 + ⋅⋅⋅
which to leading order gives
〈Η
1〉
≈ 8asap1/2
Z(Zα)2
de 〈σ⋅⋅λ〉
^
Z from electric field near nucleus
(Zα)2 from the small (relativistic) wavefunction
^
λ is the axis defined by the s-p mixing
In atoms, asap1/2 ~ Eext, and for Z=70
〈Η 1〉atom ~ de 100 Eext.
(Sandars, 1965)
In heavy polar molecules . . .
• the wavefunction is already mixed along the
internuclear axis λ: as ap ~ 0.1
• a very modest external field can polarize λ along σ
〈Η 1〉molecule ~ de 10 (in atomic units of field!)
Effective field (GV/cm)
BaF
10
YbF
26
PbO*
30
PbF
-29
HgF
100
Polarization of YbF
Field η E (GV/cm)
20
15
10
5
0
0
10
20
30
Applied field E (kV/cm)
for Tl atoms η is “only” ~ -600
E= 130kV/cm → ηE = 0.08GV/cm
The basic idea of the experiment
amplification
ηde σ
E
Interaction energy
-de ηE•σ
odd under P and T
system containing electron
electric field
The lowest two levels of YbF in an electric field E
X2Σ+ (N = 0,v = 0)
+deηE
| -1 〉
| +1 〉
F=1
-deηE
|0〉
F=0
Goal: to measure the splitting 2deηE
Interferometer to measure 2deηE
| +1 〉
| -1 〉
|0〉
E |+1 〉 B
|0 〉 ?
|0 〉
| -1 〉
Pump
Split
A-X Q(0) F=1
170 MHz π pulse
Recombine
Probe
170 MHz π pulse
A-X Q(0) F=0
Phase difference = 2 (µ
µBB+deηE)T/h
Part of the optical setup
Interferometer results
Fluorescence signal
• Scan a small magnetic field, measure the |0〉 signal.
Phase difference = 2(µBB+deηEext)T/h
Measuring the edm
Detector count rate
-E
− 4deηET/h
E
δφ = 4deηET/h
-B0 B0
Applied magnetic field
Histogram of measured de/σ
σ
Phys. Rev. Lett. 89, 023003
(2002)
Mean value: (-0.2±3.2)×
×10-26 e.cm
90 mHz
pure shot noise
Extremely robust against systematic errors from Bstray
Magnetic systematics?
No coupling µ • v × E to motional magnetic field
electron spin is coupled to internuclear axis
µ
and internuclear axis is coupled to E
F-
E
Yb+
∴< µ × E > = 0
no motional systematic error
YbF is practically immune to B⊥:
∆ = 6.7 MHz @ 8.3kV/cm
|F=1〉
|F=0〉
Extra splitting is suppressed by the factor
µB2 Bz B⊥
∆2
, 10-10!
Not unique to molecules, e.g. Xe*
Why isn’t the result better?
bandhead at 552.1 nm
1
3
5
7
9
11
174P(8)
13
15
17
GHz
174P(9)
174Q(1)
174Q(0)
4
19
5
GHz
6
174Q(0)
172P(8)
176P(9)
0.2
0.4
GHz
0.6
0.8
Signal to Noise ratio
S
= deηEext T/h
N
I0 t 1/2
IB + I0/2
Cold molecules might help with:
• Io more molecules in ground rotational state
• IB less background from overlapping transitions
• T coherence time could be much longer for
trapped molecules (1s vs. 1ms)
Supersonic YbF beam
delay generator
scan
YAG laser
1064 or 532 nm
20 mJ in 10 ns
dye laser
550 nm
10 bar Ar
solenoid valve
PMT
target
skimmer
Cooling the rotational temperature
176
P(9)
172
P(8)
Fluorescence Signal
T=1500K
174
Q(0)
T=10K
T=5K
0.2
0.3
0.4
0.5
0.6
Laser frequency offset (GHz)
0.7
0.8
Cold slow molecules
Our approach:
• supersonic expansion gives low rotational
temperature, narrow velocity distribution
• Xe carrier gas gives slow center-of-mass energy
for Stark decelerator
• laser ablation is well suited to YbF, BaF etc.
trap
τ ~ 1s
E
B
supersonic source
decelerator
pump
split
recombine
interferometer
probe
Proposed decelerator for YbF
300 m/s
-
-
-
-
-
-
+
+
+
+
+
+
YbF
Potential
Energy
off
off
Potential Energy
with switched
fields
off
off
off
100 stages of 150 kV/cm
can bring the YbF to rest
Prototype YbF decelerator
metastable CO signal
Test result using CO
Short alternating gradient
decelerator built by
Rijnhuizen/Berlin group of
G. Meijer and R. Bethlem
1.5
1.75
2.0
1.25
time of flight (ms)
2.5
Signal:noise figures
2002
result
supersonic
beam
cold
cloud
background
150kHz
640kHz
40kHz
fringe height
1.5 kHz
160 kHz
10 kHz
coherence time
1.5 ms
1 ms
1s
de in 1 day 3 10-26 e cm 6 10-28 e cm 3 10-30 e cm
long time = narrow fringes
Current status of EDMs
d(muon) < 7×
×10-19
neutron:
electron:
d e.cm
10-20
Electromagnetic
10-22
d(proton) < 6 × 10-23
YbF expt
10-24
Multi
Higgs
10-28
10-29
d(neutron) < 6 × 10-26
SUSY
φ∼1
Left-Right
d(electron) < 1.6 × 10-27
φ ∼ α/π
1960 1970 1980 1990 2000 2010 2020 2030
cold
molecules