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

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

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

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:

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

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

YbF energy levels

EDM measurement 𝜙 ϕ= (μB∓d e E eff )T ħ 𝐸 eff 𝐵 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

Measuring the electron EDM

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

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

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 473 493-496 (2011) D M Kara etal. New. J. Phys. 14 103051 (2012)

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

YbF fountain 0.5s coherence time instead of 0.5ms 6× 10 −31 e cm in 8hrs Tarbutt et al. New J. Phys. 15 053034 (2013)

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

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