1. Cavity-Enhanced Parity-Nonconserving Optical Rotation in Hg, Xe, I (and Cs) T. Peter Rakitzis Department of Physics, University of Crete, & Institute of Electronic Structure and Laser (IESL) Foundation for Research and Technology – Hellas (FORTH)

2. Atomic Physics Searches for “New Physics” 1(a). Anomalous magnetic moment of the muon 3.6  discrepancy between experiment and theory (b) Muonic hydrogen (p +   ) experiments  proton radius puzzle (proton radius appears to be 4% smaller than in all other experiments) 2. Searches for Electron Dipole Moments (EDM) of electrons and of other particles 3. Time-varying fundamental constants 4. Atomic Parity Non-Conservation (PNC).

3. Parity Violation Parity Violating (Weak force)

5. Only this happens

6. Atomic PNC Parity transformation: [H atomic, P]=0 => Atomic stationary states are eigenstates of Parity Z-boson exchange spoils parity conservation (between electrons and quarks in nucleus) Electromagnetic Electroweak H0  H0H0  H0 HW  HWHW  HW HWHW

7. P = +1 Parity P (r  ‒ r) P = -1 P = +1 + + + + + + ‒ ‒ ‒ ‒

8. e e Without PNC o EE What is Atomic PNC? Atomic energy levels have definite parity, even (e) or odd (o) E&M does not violate parity Ground state Excited states H=H 0 S S P

9. S +   P S +   P WITH PNC P +   S EE What is Atomic PNC? Ground state Excited states PNC term in the Hamiltonian mixes states of DIFFERENT Parity, but with same total angular momentum (mixes S and P)  ~   EE Z3Z3 (in favorable cases, high Z, small  ) H=H 0 + H W mixing Goal to measure this small mixing

10. Considering only the E-M terms in the Hamiltonian, atomic states possess well-defined parity (even or odd). E1 Electric Dipole transition Connects states of OPPOSITE Parity M1 Magnetic Dipole transition Connects states of the SAME Parity o (e) e (o) o (e) o  e e  o o  o e  e M1 transition amplitude typically about 10 000 times smaller than E1 Parity selection rules of dipole transitions B E Atomic parity violation

11. 6s 7s All other one-photon transitions are forbidden (except a very small M1 from hyperfine n-mixing) Stark-Interference Method in Cesium ( 2 S 1/2 ) E1(PV) Too small to measure directly (either by fluorescence or absorption) The highly-forbidden 6s-7s transition

12. E1(  ) 6s 7s An external DC E field mixes s and p states ( 2 S 1/2 +  2 P J ) ( 2 S 1/2 +  2 P J )  E1(PV) |E1(  )  E1(PV)| 2 = E1(  ) 2  2E1(  ) E1(PV) + E1(PV) 2 6p Sign of interference term can be changed by reversing the  field polarity Stark-Interference Method in Cesium neglibible 7p  E = 3230 cm -1

13. Stark-Interference Method in Cesium |E1(  )  E1(PNC)| 2  E1(  ) 2 [1 + 2 E1(PNC)/E1(  )]  10 -6 Sign changed by inverting E-field and B-field polarities, and sign of detected m-state (by changing laser frequency). Signal changes by only about 1 in a million, yet Wieman measured this to 0.35% precision! Sensitive to new particles with Ε > 1 ΤeV

14. Stark-Interference Method in Cesium |E1(  )  E1(PNC)| 2  E1(  ) 2 [1  2 E1(PNC)/E1(  )]  10 -6 Sign changed by inverting E-field and B-field polarities, and sign of detected m-state (by changing laser frequency). Signal changes by only about 1 in a million, yet Wieman measured this to 0.35% precision! Sensitive to new particles with Ε > 1 ΤeV

15. Signal Reversals E   E B   B M   M (3 such reversals) |E1(  )  E1(PNC)| 2  E1(  ) 2 [1  2 E1(PNC)/E1(  )] Reversals good to ~10 -4 (uncertainty) PNC Signal ~10 -6 One reversal not enough 2 Reversals good to ~10 -8 (uncertainty) Two reversals are enough 5 Reversals allowed redundancy for finding systematic errors

16. Optical Rotation Method in Thallium M1E1(PV) 6P 1/2 6P 3/2 A  = |M1  iE1(PV)| 2 = M1 2  2Im[M1 E1(PV)] + E1(PV) 2  phase difference between right and left circularly polarized light B E

17. Circular Dichroism  A + – A –  = A + + A – = 2 Im[E1(PV)/M1 ] From dispersion relations (Kramers-Kronig):  = (n + – n – )/(n-1)  PNC = (  L  (n + – n – ) = (  L  (n-1) Im[E1(PV)/M1 ]  PNC ~  L  Im[E1(PV)/M1 ] Atom densitypath length Optical Rotation

18. 6 x 10 -7 rad Optical Rotation in Thallium with 6 x 10 -9 rad (1%) sensitivity PRL 74, 2654-62 (1995) OxfordSeattle Curves proportional to refractive index Optical Rotation Method in Thallium

19. It took several minutes to replace the vapor cell with the empty cell Thallium Crossed polarizers Problems: Small signals Birefringent backgrounds No Signal reversals Very slow background subtraction Oven at 1000° C Since light with (+) and (-) helicities have different absorption probabilities, they will also have different refractive indices, n + and n , and will, therefore, rotate linearly polarized light

20. Signal + Background Background Signal Weakness of technique: Poor, 15 minute subtraction procedure

21. Background Instabilities over 1 hour Note: PNC signal ~ 1  rad

22. 1) Stark Interference Cs, 0.35% Science 275, 1759 (1997) 2) Optical Rotation Tl 1% PRL 74, 2654 (1995) Best atomic PNC measurements Improve this one!

23. Why measure atomic PNC?

24. A PV  H W  Q W  m Z SignalMass of Z boson need precise atomic theory, or isotope ratio measurements where atomic theory cancels Compared to m Z from CERN Found new physics beyond standard model AGREE (within error) DISAGREE Constrain bounds for new physics Currently, agreement (Cs) to within 0.5% Constrains mass of Z′ bosons, m Z′  1.3 TeV.

25. Nuclear Spin Independent Nuclear Spin Dependent (I   0) (Higher order term; contribution about 100 times smaller) Experimentally distinguishable

26. M1E1(PV) o +  e Anapole moment Anapole moment appears as a difference in the E1(PV) amplitudes between the hyperfine transitions Hyperfine structure

27. JILA ′97 Difference in PNC measured different hyperfine components (4-3 and 3-4) show presence of Anapole moment Average is spin-independent PNC Stark-Interference Method in Cesium Standard Model prediction (with atomic structure)

28. Constraints on PNC meson-nucleon couplings PRC 65, 045502 (2002) Poor agreement Between Cs and Tl Either nuclear theory and/or some experiments are wrong. More experiments needed Cs Tl

29. PNC isotope ratios

30. Atomic PNC measurments needed for: 1) Search for new physics beyond Standard Model. (search for various Z′ bosons, including Dark-Matter candidates) 2) Strong test of nuclear theory via nuclear-spin-dependent PNC measurements 3) Measurement of neutron distribution of nuclei (“neutron skin”) through PNC isotope ratios. Summary

31. In progress: PNC experiments on Fr and Ra + High Z (large PNC effect), Radioactive half lives ~20 minutes. Ongoing experiments (~1000 trapped atoms) the past ~15 years, at large collider facilities TRIUMPH (Vancouver) and KVI (Groningen) Experiments at colliders, and are no longer table top  Yb PNC signal at Berkeley (18+ years)  PNC in state-selected diatomic molecules (anapole moments)

32. Our Goal: The improvement of the optical rotation technique, by investigating cavity-enhancement methods, to see if we can make a PNC experiment that is:  “Simple” and tabletop  Can produce results quickly (significantly less than 20 years…)  Allows reproducibility quickly by other groups Received an ERC grant to do this…

33. Cavity Enhancement seems an obvious idea… Birefringent Medium N  E. Zavattini et al., “Experimental Observation of Optical Rotation Generated in Vacuum by a Magnetic Field”, Phys. Rev. Lett. 96, 110406 (2006). N  44 000  Birefringence Sensitivity  5 x 10 -13 rad/m Increase path length by N roundtrips … and it works very well for linear birefringence HOWEVER, for cavity-amplification of Chiral Optical Rotation, there are many problems

34. Chiral Optical Rotation cancels in Linear Cavity Circularly Birefringent Medium   Chiral optical rotation of light polarization cancels exactly with the return trip. To work, this symmetry must be broken…  Total rotation = 0

35. Cavity resonance split by B field and Chiral sample C C Solution: Bowtie cavity with counterpropagating laser beams Magnetic field with magneto-optic window

36. Advantages of Cavity Signal enhanced by N > 1000. Birefringent backgrounds suppressed. Two signal reversals (B  ‒ B, M  ‒ M) Allows absolute chirality measurements without need to remove sample.  Many applications

37. Applications: Atomic PNC Measure atomic PNC in systems that couldn’t be done before Analytical chemistry Measurement of chirality of microsamples Use with microfluidic devices Circular dichroism (biomolecule structure, e.g. protein folding) Improve time resolution Much smaller sample concentrations necessary

38. High-finesse optical cavity Experiment is being built, construction should be finished in 2-3 months.

39. We Propose Cavity-Enhanced Optical Rotation in Xe, Hg, Iodine, (Cs) Atoms Room Temperature, instead of 1000 °C 200 °C cell, or 2-D MOT (High Z + Volatile) Experiments Successful In progress Our proposals

41. High-Density Iodine Atoms from I 2 photodissociation 532 nm, 50W/cm 2 532 nm photodissociation Iodine cell Recombination

42. Optical Rotation around 1315nm in Iodine Advantages: Predicted signals (2-30 Tl) Birefringent background suppression 2 Fast Signal reversals Fast background subtraction All at room temperature L. Bougas et al. PRL 108, 210801 (2012) (Editor’s choice) Proposals: G. Katsoprinakis et al. PRA 87, 040101(R) (2013)

43. Simulated Iodine PNC signal with hyperfine resolution Differences between predictions from Cs and Tl gives 5% differences in iodine PNC signals 1% precision needed

44. PNC Optical Rotation transitions in metastable Xe and Hg

45. High-density (10 12 cm -3 ) metastable Xe or Hg in a discharge lamp Lykourgos Bougas (PhD student)

46. Simulated optical rotation signals 10 19 cm -3 column density Optical rotation (  rad) Detuning (GHz) Metastable Hg 609 nm 10 18 cm -3 column density Metastable Xe 988 nm Measureable signals for expected conditions (not as large as for Iodine)

47. Advantages of atomic PNC in Xe, Hg, I, (Cs): (1) Odd-neutron nuclei ( 199 Hg, 201 Hg, 129 Xe, 131 Xe) Sensitivity for 199 Hg is 6 times more than Yb (Berkeley). (2) Iodine (and Cs) have odd-proton nuclei (3) PNC measurements on isotope chains is important Xe and Hg have 15 commercially available stable isotopes Iodine has several commercially available radioactive isotopes (4) Cs has this best atomic theory of all high-Z atoms Covers all the advantages of all other PNC experiments We are investigating whether this new direction will yield an inexpensive and “easy” atomic PNC experiments, which can be reproduced relatively quickly by other groups.

48. Acknowledgements (Crete) Lykourgos Bougas Dr. George Katsoprinakis Dr. Wolf von Klitzing V. Flambaum (UNSW) V. Dzuba (UNSW) J. Sapirstein (Notre Dame) Funding ERC Starting grant ERC Proof-of-Concept grant G.M.E. Herakleitos