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

2. 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 10 -29 e cm ACME [Science (2014)] d e [e cm] 10 -38 10 -28 10 -30 10 -32 10 -34 10 -36 10 -40 Extensions to the Std. Model Standard Model 10 -26 Test extensions to the Standard Model  Tests of particle physics at the 10 TeV level

3. Measure with electron spin resonance _ Measurement precision:

4. 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, 062108 (2006) Leanhardt et al, J. Mol. Spectrosc. 270, 1-25 (2011)

5. 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

6. 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

7. 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

8. 3  1 J=1, F=3/2 -1/2 1/23/2 m F =-3/2

9. 3  1 J=1, F=3/2 E lab -1/2 1/23/2 m F =-3/2

10. 3  1 J=1, F=3/2 BrBr E lab -1/2 1/23/2 m F =-3/2

11. -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))

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

13. t m F Depletion Hf F F +

14.  /2 pulse π/2 t Transfer Hf F F F F + +

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

16.  /2 pulse Hf F F F F + + π/2 t Transfer

17. m F Depletion π/2 t Transfer Hf F F +

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

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

20. -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 10 -27 e cm

21. Example sequence

22. eEDM measurements d e < 2.6 x 10 -28 e cm

23. 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

24. Outlook Current statistical sensitivity: 3 x 10 -28 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 10 -29 e cm

25. 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

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

28.  /2 pulse details II Erot t Depletion 1 23 4 1 2 3 4

29. fBD vs fB for stray gradients

30. 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

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

32. 3.2 mHz 2.8 x 10^-28 e- cm