1. The University of Oklahoma Funding sources for preliminary research: National Research Council (US) NATO SfP (for field measurement.) OU Office of the Vice President for Research Current Funding (as of June 1, 2006) National Science Foundation Neil Shafer-Ray, The University of Oklahoma Measuring the Electron’s Electric Dipole Moment using zero-g-factor paramagnetic molecules 3rd International Symposium on LEPTON MOMENTS Centerville, Cape Cod, MA Wednesday June 21 2006, 10:30am

2. The University of Oklahoma Stated Goal of my NSF sponsored research: (1)To probe for an e-edm at a competitive (10 -28 e cm) level. (2) To provide support for a ~10 -32 e cm measurement by the Brookhaven-based e-edm collaboration

3. The University of Oklahoma g-factors of the electron

4. The University of Oklahoma g-factors of the electron g =2.0023193043718(14) Gabrielse, this meeting g edm =0.00000000000000000(5) Commins, PRL, 2004 For the electron:

5. The University of Oklahoma g-factors of the electron For paramagnetic molecules YbF, HgF, PbF, PbO, For an ideal e-edm system, we want term 2 to be much bigger than term 1. For ground-state PbF, one can work with See Shafer-Ray, PRA, 2006 Kozlov, Labzowsky, J Phys B, 1995 1) boring 2) exciting

6. The University of Oklahoma g-factors of the electron For paramagnetic molecules YbF, HgF, PbF, PbO, For an ideal e-edm system, we want term 2 to be much bigger than term 1. 1) boring 2) exciting For ground-state PbF, one can work with See Shafer-Ray, PRA, 2006 Kozlov, Labzowsky, J Phys B, 1995 3) trouble

7. The University of Oklahoma Pb F S z = 1/2 S  =(1/2) 1/2 L z =  =1 L  =1 Both spin and orbital angular momentum interact strongly with nuclear axis. |  +S z |= ½. Spin-orbit interaction favors L  opposite to S . Simple vector picture of g z for X 1 2  1/2 PbF: Molecular frame. Kozlov et al, J Phys B, 1987

8. The University of Oklahoma Simple vector picture of g z for X 1 2  1/2 PbF: Lab frame Pb F G || =0.034 G  = -0.326

9. The University of Oklahoma Pb F G || =0.034 G  = -0.326 Simple vector picture of g z for X 1 2  1/2 PbF: Lab frame

10. The University of OklahomaPbF G || =0.034 G  = -0.326 Simple vector picture of g z for X 1 2  1/2 PbF: Lab frame E

11. The University of Oklahoma g factor of PbF F=1, |M F |=1, high-field seeking ground state: g-factor can be tuned to zero!

12. The University of Oklahoma Incoherent combination of |1,1>, |1,0> and |1,-1> states P(  ) = probability of finding the system In the state M=F when quantization axis is in the direction of . Shafer-Ray, Orr-Ewing, Zare, JPC, 1995 E LASER RADIATION |1,1> + |1,-1> Graphical Description angular momentum distribution

13. The University of Oklahoma EFFECT OF MAGNETIC FIELDS OR AN e-EDM ON THE DISTRIBUTION OF ANGULAR MOMENTUM |1,1> + Exp[i  U t /  ] |1,-1> B

14. The University of Oklahoma Problem 1: The Geometric Phase Effect As a molecule moves in a region for which E is not fixed, a topological rotation of the angular momentum alignment occurs.

15. The University of Oklahoma To really take advantage of g≈0, we would like an experiment that occurs at B=0 in a very homogeneous E field. Here is one vision of such an experiment... Problem 2: Many errors are tied to the product g B applied. For these errors, there is no advantage to g small if g B applied remains large. Problem 1: The Geometric Phase Effect

16. The University of Oklahoma PbF molecular beam source optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - Schematic of PbF g=0 measurement LIF or REMPI detection region (probe M=0 state)

17. The University of Oklahoma PbF molecular beam source optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - Schematic of PbF g=0 measurement LIF or REMPI detection region (probe M=0 state)

18. The University of Oklahoma First things first: Production and detection of PbF Pb / F 2 flow reactor: Operational Temperature 1200K

19. The University of Oklahoma (0,0) band 5.0 4.0 0.0 -2.0 -3.0 3.0 2.0 1.0 energy (eV) X 2  1/2 A 2  1/2 B 2  1/2 PbF + 3.05.07.0 R(Bohr) 1+1 X 1 2  1/2 →B 2  1/2 REMPI of PbF OU data, 2005

20. The University of Oklahoma Observation of an ionization threshold for PbF

21. The University of Oklahoma R(Bohr) 5.0 4.0 0.0 -2.0 -3.0 3.0 2.0 1.0 energy (eV) ? 2  1/2 PbF + 3.05.07.0 State selective ionization of PbF + via 1+1+1 doubly-resonant multi-photon ionization. X 2  1/2 A 2  1/2

22. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state) X 1 2  1/2 (F=1) A 2  1/2 (F=1) |M|=1 M=0

23. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state) X 1 2  1/2 (F=1) A 2  1/2 (F=1) |M|=1 M=0

24. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state) M=0 400MHz |M|=1

25. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state) M=0 400MHz |M|=1

26. The University of Oklahoma Requirements for large Rabi population amplitude in Raman pumping from a state A to a state B (1)  of lasers on resonance.   A B C (2) At least 1 state C that couples to both A and B. (3) A finely tuned ratio of A-C to B-C coupling.

27. The University of Oklahoma P M=0 P |M|=1 M=0 |M|=1 X 1 2   A 2   E DC   k = B RF,effective ^ ^^ P M=0 P |M|=1  = 0  =  /2

28. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state)

29. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state)

30. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state) PROBE+

31. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state) PROBE+

32. The University of Oklahoma optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state) PROBE+

33. The University of Oklahoma PROBE- optical polarization (create M=0 state) high-field region Raman-RF pump probe + probe - LIF or REMPI detection region (probe M=0 state)

34. The University of Oklahoma R(Bohr) 5.0 4.0 0.0 -2.0 -3.0 3.0 2.0 1.0 energy (eV) ? 2  1/2 PbF + 3.05.07.0 X 2  1/2 A 2  1/2 X 2  3/2 I. Excite X 2  1/2 to X 2  3/2 II A. Excite to A 2  1/2 and observe blue photons. II B. Excite to ? 2  1/2 and observe PbF + ions correlated to e -. OR Detection of PbF

35. The University of Oklahoma Technical Note RF1 RF2  RF1 fixed to a frequency standard.  RF2 =  RF1 +  tan(  ) S S zero crossing independent of ±M phase

36. The University of Oklahoma Conclusions We have found a system for which the effect of background magnetic fields may be suppressed by seven orders of magnitude. We have developed a source of PbF as well as sensitive state selective REMPI of the molecule. We are designing a beam machine to take advantage of this new system.

37. The University of Oklahoma THANKS TO: Chris McRaven, Sivakumar Poopalasingam, Milinde Rupasinghe Graduate Students: Chris Crowe, Dustin Combs, Chris Bares Undergraduate Students: Professor Emeritus: George Kalbfleisch

38. The University of Oklahoma The University of Oklahoma Neil Shafer-Ray Eric Abraham George Kalbfleisch Kim Milton John Furneaux Chung Kao Petersburg Nuclear Physics Institute Victor Ezhov Mikhail Kozlov University of Latvia Marcis Auzinsch BNL Greg Hall Trevor Sears Andrew Sandorfi Lino Miceli Mark Baker Craig Thorn Mike Lowry Xiangdong Wang U Cal Berkeley Dmitry Budker Derek Kimball And thanks to the e-EDM COLLABORATION

39. The University of Oklahoma First e-edm Collaboration Meeting, February 2005 Brookhaven National Laboratory