2. Physics 129, Fall 2010; Prof. D. Budker

3. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html Intrinsic parity of particles A brief history of parity: Concept found (no parity in everyday life): O. Laporte, 1924 Concept understood: Wigner, 1927 Concept becomes dogma Dogma fails: Lee, Yang, Wu, 1956-1957

4. 3 Parity of atomic states Spatial inversion (P) :Spatial inversion (P) : Or, in polar coordinates :Or, in polar coordinates :

5. 4 Parity of atomic states It might seem that P is an operation that may be reduced to rotationsIt might seem that P is an operation that may be reduced to rotations This is NOT the caseThis is NOT the case Let’s see what happens if we invert a coordinate frame :Let’s see what happens if we invert a coordinate frame : Now apply a  rotation around z’Now apply a  rotation around z’ Right-handed frame  left handed P does NOT reduce to rotations !P does NOT reduce to rotations !

6. 5 Parity of atomic states An amazing fact : atomic Hamiltonian is rotationally invariant but is NOT P-invariantAn amazing fact : atomic Hamiltonian is rotationally invariant but is NOT P-invariant We will discuss parity nonconservation effects in detail later on in the course…We will discuss parity nonconservation effects in detail later on in the course…

7. 6 Parity of atomic states Wavefunctions in this form are automatically of certain parity : In hydrogen, the electron is in centro-symmetric nuclear potentialIn hydrogen, the electron is in centro-symmetric nuclear potential In more complex atoms, an electron sees a more complicated potentialIn more complex atoms, an electron sees a more complicated potential If we approximate the potential from nucleus and other electrons as centro- symmetric (and not parity violating), then :If we approximate the potential from nucleus and other electrons as centro- symmetric (and not parity violating), then : Since multi-electron wavefunction is a (properly antisymmetrized) product of wavefunctions for each electron, parity of a multi-electron state is a product of parities for each electron:Since multi-electron wavefunction is a (properly antisymmetrized) product of wavefunctions for each electron, parity of a multi-electron state is a product of parities for each electron: This is because:

8. 7 Comments on multi-electron atoms Potential for individual electrons is NOT centrosymmetric Angular momenta and parity of individual electrons are not exact notions (configuration mixing, etc.) But for the system of all electrons, total angular momentum and parity are good ! Parity of a multi-electron state: W A R N I N G

9. 8 Parity of atomic states A bit of formal treatment… Hamiltonian is P-invariant (ignoring PNC) : P -1 HP=HHamiltonian is P-invariant (ignoring PNC) : P -1 HP=H  spatial-inversion operator commutes with Hamiltonian :  spatial-inversion operator commutes with Hamiltonian : [P,H]=0  stationary states are simultaneous eigenstates of H and P  stationary states are simultaneous eigenstates of H and P What about eigenvalues (p; Pψ=pψ) ?What about eigenvalues (p; Pψ=pψ) ? Note that doing spatial inversion twice brings us back to where we startedNote that doing spatial inversion twice brings us back to where we started P 2 ψ=P(P ψ)=P(pψ)=p(Pψ)=p 2 ψ. This has to equal ψ  p 2 =1  p=  1P 2 ψ=P(P ψ)=P(pψ)=p(Pψ)=p 2 ψ. This has to equal ψ  p 2 =1  p=  1 p=1 – even parity; p=-1 – odd parityp=1 – even parity; p=-1 – odd parity

10. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html Intrinsic parity of particles Consider a reaction: a + b  c + d Initial wavefunction: Initial parity: Final wavefunction: Final parity:

11. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html Intrinsic parity of particles  Parity of proton is defined: p(p) = +1  Parity of other particles is found from processes like a + b  c + d and parity conservation  Example: d + π -  n + n  d : J=1; relative ang. moment. of p and n (mostly) 0  The π – is captured from an l=0 orbit, so we have:

12. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html Intrinsic parity of particles  What can we say about l’ ?  Total angular momentum of the two neutrons: 1 (because the d spin is 1, and the π - spin is 0)  Total wavefunction is antisymmetric (fermions)  If spin singlet  l’ = 0, 2, …  cannot be! (because the total angular momentum is 1)  If spin triplet  l’ = 1  Neutron parity is chosen positive   Gauge bosons, , Z, W +, W -, g  negative parity  Leptons: not much to talk about: disrespect of parity

13. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html Intrinsic parity of antiparticles  Not arbitrary! Must be related to that of particles   0 is its own antiparticle  all pions have odd parity  All antibosons have the same parity as their bosons  For fermions it is the opposite: opposite parity for particles and antiparticles  How do we know?  Dirac and Experiment  Consider para-Ps decay: e + e - ( 1 S 0 )    Possible amplitudes:  1   2 scalarnot observed  1   2  (k 1 - k 2 )pseudoscalar observed!  Only possible if p( e + ) p( e - ) = -1

14. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html Charge conjugation (C)  A misnomer; better way to think about this: All particles  antiparticles  If a particle is an eigenstate of C (most are not), c=  1 (because c 2 = 1)  c(  ) = -1 (this is e/m field, after all)  0   +  allowed  0   +  +  forbidden  Week interactions do not respect C

15. Parity-Violation: Particles Nuclei Atoms Molecules

16. Outline 1. What is parity? Parity violation 2. Atomic parity violation (APV=PNC) a.Optical-rotation expts b.APV-Stark interference c.Brief (personal) history of APV 3.APV in Yb 4.APV in Dy 5.Conclusions

17. What is parity? x y z P x’ y’ z’ x’’ z’’ y’’=y’ Rotation around y’  Left hand cannot be rotated into right hand !

18. Normal vs. axial vectors Under Spatial Inversion (P): V  -Vr, p, E, d = e  r, … A  AL = r  p, S, B Similarly for scalars (pseudo-scalars) Under Spatial Inversion (P): S  SEnergy, any V  V’, A  A’ … PS  -PSany A  V, …

19. Discrete vs. Continuous Transformations and Symmetries Continuous: Translation → momentum conservation Translation in time → energy conservation Rotation → angular momentum conservation Discrete: Spatial Inversion (P) → P-invariance (parity) Charge Conjugation (C) → C-invariance Time reversal (T) → T-invariance CP CPT Permutation of identical particles → PSP, spin-statistics

20. The (broken) law of parity  Because the laws of Nature should be the same in the “real” world and its mirror image, no pseudo- scalar correlation should be observed in experiments, for example  Does not apply to cork-screws !

21. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html The  -  paradox (the demise of parity)  Two particles with same mass and same lifetime…  But opposite parity ???  In modern terminology:  + =  + = K + ( )  Resolution of the paradox: parity violation in weak interactions

22. The theorists who said: check it ! Prof. T. D. Lee Prof. C. N. Yang

23. Prof. C. S. Wu (1913-1997) The shatterer of the parity illusion (1956)…

24. The Co-60 experiment

25. Parity and Quantum Mechanics If Hamiltonian is P-invariant  nondegenerate sate is eigenfunction of P Atomic states are even or odd If parity is violated  eigenstates are of mixed parity

26. Z e e  Weak interaction (violates parity) Electromagnetic interaction (conserves parity) Atomic Parity Violation (APV) APV = PNC = Parity Non-Conservation

27. M1M1M1M1 E1E1E1E1 PNC M1-E1 PNC interference Atomic PNC: optical rotation

28. Optical Rotation  Medium Linear Polarization Circular Components

29. 28 PNC optical rotation: Tl Vetter, Meekhov, Lamoreaux, Fortson, PRL 74, 2658 (1995) Result: PNC to 1 % (exp); 3 % (theo) 500 data hrs averaged Many absorp. length → line wings Polarimetric sensitivity: ~10 -8 rad No reversals New approaches needed for progress Prof. E. N. Fortson

30. M1M1M1M1 E1E1E1E1 PNC+E DC E1 Stark -E1 PNC interference Reversals ! Reversals ! Atomic PNC: Stark interference

31. Atomic parity violation: the parents Profs. Marie-Anne and Claude Bouchiat

32. Atomic PV landmarks 1959 Ya. B. Zel’dovich: PNC (Neutr. Current)  Opt. Rotation in atoms 1974 M.-A. & C. Bouchiat heavy Z 3 enhancement  PV observable in heavy atoms 1978-9 Novosibirsk, Berkeley discovery of PV in OR(Bi) and Stark-interf.(Tl) …1995 Boulder, Oxford, Seattle, Paris Cs PV measured to 1-2% in Cs, Tl, Bi, Pb 1997 Boulder anapole moment 0.35% measurement, discovery of anapole moment

33. Why the French? ATOMATOM ATOMATOM ATOMEATOME ATOMATOM E

34. The Boulder Cs PNC Experiment P-odd, T-even correlation:  [E  B] 5 reversals to distinguish PNC from systematics 1982-1999

35. The Champions of Parity The Champions of Parity violation Prof. Carl E. Wieman

36. Atomic PV landmarks 1959 Ya. B. Zel’dovich: PNC (Neutr. Current)  Opt. Rotation in atoms 1974 M.-A. & C. Bouchiat heavy Z 3 enhancement  PV observable in heavy atoms 1978-9 Novosibirsk, Berkeley discovery of PV in OR(Bi) and Stark-interf.(Tl) …1995 Boulder, Oxford, Seattle, Paris Cs PV measured to 1-2% in Cs, Tl, Bi, Pb 1997 Boulder anapole moment 0.35% measurement, discovery of anapole moment 2009 Berkeley Large APV in Yb (personal landmark) 26 years

37. What were we doing all this time? 1983-1988 Bi, diatomic molecules, Sm (Novosibirsk) with L. M. Barkov and M. Zolotorev 1989-1994 Tl (Berkeley) with E. D. Commins, D. DeMille, and M. Zolotorev 1989- Dy M. Zolotorev, D. DeMille, E. D. Commins, A.-T.Nguyen, A. Cingoz, N. Leefer 1995-1997 Sm S. M. Rochester 1995- Yb S. J. Freedman, C. J. Bowers, G. Gwinner, J. E. Stalnaker, D. F. Kimball, V. V. Yashchuk, K. Tsigutkin, A. Family, D. Dounas-Frazer,…

38. Why did it take so long to detect PNC? Dr. A.-T. Nguyen says: it was deposited

39. 38 Parity Violation in Yb: motivation Atomic Physics: §Verification of large predicted atomic PV effect (x100 Cs; DeMille, Kozlov et al, Das et al) Nuclear Physics: §Nuclear spin-dependent PV – anapole moments (valence neutrons) §Isotopic ratios and neutron distributions (6 stable isotopes;  N=8)

40. Anapole Moment of a current distribution (e.g., a nucleus) T-conserving; P-violating Ya. B. Zel’dovich

41. 40 1959 Ya. B. Zel’dovich, V. G.Vaks AM first introduced 1980-84 V.V. Flambaum, I.B. Khriplovich & O.P. Sushkov Nuclear AM detectable in atoms Anapole Moments PNC within nucleus !  probe of weak meson couplings 1997 C. E. Wieman and co-workers Cs AM detected ! 1995 E.N.Fortson and co-workers Tl AM – small…

42. 41 Atomic Yb: energy levels and transitions PV amplitude:  10 -9 e·a 0 DeMille (1995) +5d6p |M1|  10 -4 μ B J.E. Stalnaker, et al, PRA 66(3), 31403 (2002) β  2·10 -8 ea 0 /(V/cm) C.J. Bowers et al, PRA 59(5), 3513 (1999); J.E. Stalnaker et al, PRA 73, 043416 (2006)

43. Stark-PV-interference technique (invented by the Bouchiats in 1970s)

44. 43 Electric and magnetic fields define handedness The Yb PV Experiment

45. m = -1 m = +1 m = 0 R0R0 R -1 R +1 1S01S0 3D13D1 Transition rates interference Compute ratio for 1st and 2nd harm. signal Ratio difference yields PV asymmetry: PV effects on rates E-field modulation

46. 45 Typical Stark-induced signal 174 Yb resonance split by B  70 G; E=3 kV/cm PV asymmetry: ~ 2·10 -4 / E/(kV/cm) Asymmetric lineshape ← AC Stark effect DC bias 43 V/cm

47. 46 Atoms in electric field: the Stark effect or LoSurdo phenomenon Johannes Stark (1874-1957) Nazi Fascist

48. 47 Reversals and pseudo-reversals E-field reversal (14 ms: 70-Hz modulation) Lineshape scan ( 200 ms/point x 100 pts/lineshape = 40 s ) B-field reversal (every few minutes) Polarization angle (occasionally) E-field magnitude B-field magnitude Angle magnitude For θ=  /4→

49. 48 Systematics control strategy APV is mimicked by combinations of two or more imperfections Enhance one imperfection; measure the other Adapted from the Berkeley eEDM expt. of Prof. Commins et al

50. Yb PV Amplitude: Results Accuracy is affected by HV-amplifier noise, fluctuations of stray fields, and laser drifts → to be improved  =39(4) stat. (5) syst. mV/cm  |  |=8.7±1.4×10 -10 ea 0

51. Near Future…  Verification of expected isotopic dependence  PV in odd isotopes: NSD PV, Anapole Moment  PV in a string of isotopes; neutron distributions, … Further Ahead (?)  Testing the Standard Model [Brown et al PHYSICAL REVIEW C 79, 035501 (2009)] Completed Work Lifetime Measurements General Spectroscopy (hyperfine shifts, isotope shifts) dc Stark Shift Measurements Stark-Induced Amplitude (β): 2 independent measurements M1 Measurement (Stark-M1 interference) ac Stark Shift Measurements Verification of APV enhancement Progress in Yb APV

52. 51 K. Tsigutkin A. Family D. Dounas-Frazer post-doc undergradgrad.student V. V. Yashchuk S. J. Freedman J. E. Stalnaker

53. Another atom: Dy §Ideal APV amplifier?  Fully degenerate opposite-parity levels  Large Z 3 (Z=66) §Also  Many stable isotopes: A=164-156  Large Z 3 (Z=66)  Two I=5/2 isotopes (anapole) 52

54. 53 parity violation experiment The parity violation experiment in Dy evolved into…

55. α Search for temporal variation of α in radio-frequency transitions of Dy Support:

56. Search for temporal variation of the fine-structure "constant" in radio-frequency transitions of Dy AB Ground State 0 20,000 Energy (cm -1 ) For  /  ~ 10 -15 /yr  d  /dt ~ 2 Hz/yr !! A B   ~ (3-2000) MHz d  /dt ~ 2  10 15 Hz  /  Dzuba, Flambaum, Kozlov, et al

57. Next steps... Succeeded in laser cooling of atomic beam Operate new apparatus optimized for the  -dot experiment Measure frequency to ~1 mHz Dy APV will be back!

58. Physics 129, Fall 2010, Prof. D. Budker; http://budker.berkeley.edu/Physics129_2010/Phys129.html