1. Measuring the Electron EDM Using Ytterbium Fluoride (YbF) Molecules
“measuring the shape of the electron”
Joe Smallman

2. The electron electric dipole moment (EDM)
Displacement of centre of charge from centre of mass 𝐸 − −
𝑑 𝑒 − − − − −
𝑈=− 𝑑 𝑒 ∙ 𝐸
𝑑 𝑒 ǁ 𝜎

3. Electron EDM estimates
David A. Aguilar
Harvard-Smithsonian Center for Astrophysics 
not enough CP violation
|dethallium|< 1.6 x 10-27e.cm

4. How small is that? Assume: − 𝑑 𝑒 ∙ 𝐸 ≈0.25 𝑚𝐻𝑧
𝑑 𝑒 ≈ 10 −27 𝑒.𝑐𝑚=2× 10 −19 𝑒. 𝑎 0 =5× 10 −19 𝐷
𝐸≈1𝐺𝑉/𝑐𝑚
≡− 𝜇 𝐵 ∙𝐵 for ≈17𝑓𝑇 magnetic field
≈ 10 −10 𝑐𝑚 −1
≈ 10 −18 𝑒𝑉
− 𝑑 𝑒 ∙ 𝐸 ≈0.25 𝑚𝐻𝑧
EDM interaction:

5. How atoms and molecules can help
Amplify the electron EDM interaction!
− 𝑑 𝑒 ∙ 𝐸
complicated special relativity
− 𝑑 𝑒 ∙ 𝐸 eff
𝑑 𝑒
𝐸 eff = 𝐸 eff max η 𝐸 app 𝑧 𝑛
𝐸 app 𝑧
structure
dependent
factor ~ 𝑍 3
polarisation
factor
𝑛 ∙ 𝑧

6. YbF electric field enhancement
𝐸 eff =14.5 GV/cm for 𝐸 app =10 kV/cm
Enhancement of !
Needs ‘only’ nano-Gauss level of B-field control

7. YbF energy levels

8. EDM measurement 𝜙 ϕ= (μB∓d e E eff )T ħ 𝐸 eff𝐵 𝜙
𝐸 eff 𝐹
Torque:
d 𝐹 dt = 𝑑 e × 𝐸 𝐞𝐟𝐟 +( 𝜇 × 𝐵 )
∆𝜙<7 μrad
ϕ= (μB∓d e E eff )T ħ or
∆𝑈<2 mHz

9. Measuring the electron EDM

10. Interference fringes
𝑆= cos 2 ϕ
ϕ= (μB∓d e E eff )T ħ

11. Lots of other parameter modulations
E-field direction
B-field direction
B-field magnitude
rf pulse frequency (independently)
rf pulse amplitude (independently)
rf pulse phase difference
laser frequency
demonstrated in
last slide

12. Result d e = −2.4± 5.7 stat ± 1.7 syst × 10 −28 e.cm
2011 dataset: 6194 measurements (6min/measurement)
d e = −2.4± 5.7 stat ± 1.7 syst × 10 −28 e.cm
d e <1× 10 −27 e.cm with 90% confidence
J J Hudson et al. Nature (2011)
D M Kara etal. New. J. Phys (2012)

13. Upgrades since 2011 3rd layer of magnetic shielding
Less magnetic field noise
Longer inner magnetic shield
Reduce end effects
Separate rf transmission line from HV plates
Reduce end effects, higher applied E-field, less leakage
Shorten rf pulses
Reduce systematics associated with rf detuning
old scheme
new scheme

14. YbF fountain 0.5s coherence time instead of 0.5ms
6× 10 −31 e cm in 8hrs
Tarbutt et al. New J. Phys (2013)

15. The YbF eEDM team Joe Smallman Ben Sauer Mike Tarbutt Ed Hinds
Jack Devlin
Jony Hudson

16. EDM measurement Measure the EDM induced splitting + 𝑑 𝑒 𝐸 eff
mF=-1
nuclear spin
electron spin
mF=0
mF=+1
+ 𝑑 𝑒 𝐸 eff
- 𝑑 𝑒 𝐸 eff
large tensor Stark shift