Precision spectroscopy of trapped HfF + with a coherence time of 1 second Kevin Cossel JILA eEDM collaboration

An eEDM violates P and T-reversal symmetry The eEDM has very small Standard Model theory background so is a good test of new physics |d e | < 9 x e cm ACME [Science (2014)] d e [e cm] Extensions to the Std. Model Standard Model Test extensions to the Standard Model  Tests of particle physics at the 10 TeV level

Measure with electron spin resonance _ Measurement precision:

Trapped molecular ions Long coherence time Large effective electric field Use low-lying 3  1 level Use many ions for better statistics Thermal (1-10 K) cloud reduces systematics due to many ions Meyer, Bohn, Deskevich, PRA 73, (2006) Leanhardt et al, J. Mol. Spectrosc. 270, 1-25 (2011)

Experimental setup ~10 cm End cap (+V) Linear Paul trap confines HfF + : RF micromotion at  rf = 2  (50 kHz) Secular trap motion at ~ 2  (4 kHz) Rotating bias field at  rot = 2  (250 kHz) Anti-Helmholtz coils

Experimental setup ~10 cm End cap (+V) Linear Paul trap confines HfF + : RF drive frequency of 50 kHz Secular trap frequency ~ 4 kHz Anti-Helmholtz coils Bias field rotates at 250 kHz

E (cm -1 ) 0 16,000 1+1+ 3131 3232 3333 1212 3131 1111 3  0+ 3  0- 3  0+ 3232 3333 v=0 v=1 J=1 J=2 F=3/2 F=1/2 HfF + energy levels

3  1 J=1, F=3/2 -1/2 1/23/2 m F =-3/2

3  1 J=1, F=3/2 E lab -1/2 1/23/2 m F =-3/2

3  1 J=1, F=3/2 BrBr E lab -1/2 1/23/2 m F =-3/2

-1/2 1/23/2 3  1 J=1, F=3/2 m F =-3/2 |d e |>0 3g u μB + 2d e E eff E eff ~ 24GV/cm 3g l μB - 2d e E eff BrBr E lab Zeeman co-magnetometer (DeMille AIP Conf Proc. 596, 72 (2001))

Experimental Sequence: Transfer Hf F F F F + + t Transfer

t m F Depletion Hf F F +

 /2 pulse π/2 t Transfer Hf F F F F + +

Free evolution π/2 t Transfer Hf F F F F + +   E = 3g u μB + 2d e E eff

 /2 pulse Hf F F F F + + π/2 t Transfer

m F Depletion π/2 t Transfer Hf F F +

Population Readout π/2 t Photodissociation Dump ions Transfer Hf F F +

Ramsey fringes Fractional population difference Free-evolution time (ms)  > 1 s

-B-B +B Upper Doublet Lower Doublet f BD = ¼ x [(f u (B) – f u (-B)) – (f l (B) – f l (-B))] = 2 d e E eff = 0.09(33) Hz d e < 8 x e cm

Example sequence

eEDM measurements d e < 2.6 x e cm

Systematic errors Other linear combinations: Also switch rotation direction No systematics observed in f BD : Added static B fields Shifted trap center Different E rot

Outlook Current statistical sensitivity: 3 x e cm in 100 hours Evaluating systematic errors Short-term improvements (4x better sensitivity): Longer coherence time Improve transfer and detection efficiency Long-term use ThF + Ground state 3  1 < 1 x e cm

Thank you! Matt Grau Will Cairncross Dan Gresh Yan Zhou Yiqi Ni Jun Ye Eric Cornell Huanqian Loh Kang-Kuen Ni Aaron Leanhardt Russ Stutz Laura Sinclair Tyler Coffey Tyler Yahn Bob Field John Bohn Ed Meyer Chris Greene Jia Wang St Petersberg

Rotating E and B field E-field defines quantization axis Excellent rejection of lab-frame residual B-field.

 /2 pulse details II Erot t Depletion

fBD vs fB for stray gradients

Ion-ion collisions Electric field from collision results in Berry’s phase High U kin (T)  single collisions cause decoherence Low T  phase diffusion To increase coherence time: Lower density Lower temperature Increase E rot

Berry’s phase Geometrical (Berry’s) phase due to rotating quantization axis  F

3.2 mHz 2.8 x 10^-28 e- cm