Physics 129, Fall 2010; Prof. D. Budker

Transcription

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

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

3 Parity of atomic states Spatial inversion (P) : x xy, yz, z Or, in polar coordinates : r r, θ π θϕ, ϕ+ π z θ z x ϕ y x y 3

4 Parity of atomic states It might seem that P is an operation that may be reduced to rotations This is NOT the case Let s see what happens if we invert a coordinate frame : z θ x ' x ϕ y y ' Now apply a rotation around z x" z '' z ' y" Right-handed frame left handed P does NOT reduce to rotations! 4

5 Parity of atomic states An 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 5

6 Parity of atomic states In hydrogen, the electron is in centro-symmetric nuclear potential In more complex atoms, an electron sees a more complicated potential If we approximate the potential from nucleus and other electrons as centrosymmetric (and not parity violating), then : Wavefunctions in this form are automatically of certain parity : ψ nlm P 1 l ( ) ψ nlm This is because: 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: 1 ( ) l i i 6

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: l l l n ( ) 1( ) 2 ( ) W A R N I N G ( 1) L 7

8 Parity of atomic states A bit of formal treatment Hamiltonian is P-invariant (ignoring PNC) : P -1 HP=H spatial-inversion operator commutes with Hamiltonian : [P,H]=0 stationary states are simultaneous eigenstates of H and P What about eigenvalues (p; Pψ=pψ)? Note 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= 1 p=1 even parity; p=-1 odd parity 8

9 Intrinsic parity of particles Consider a reaction: a + b c + d Initial wavefunction: Final wavefunction: a b relative motion c d relative motion Initial parity: p( ( ) l a)p( b) 1 Final parity: p( c)p( d) ( ) l 1 ' Physics 129, Fall 2010, Prof. D. Budker;

10 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 - p( a)p( b) ( 1) l ( ) l p( c)p( d) 1 ' n + n d : J=1; relative ang. moment. of p and n (mostly) 0 p( d ) = p( p)p( n) The π is captured from an l=0 orbit, so we have: p( d)p( π ) = p( p)p( n)p( π ) = p( n)p( n) ( ) l 1 ' Physics 129, Fall 2010, Prof. D. Budker;

11 Intrinsic parity of particles ( ) l ' p( d)p( π ) = p( p)p( n)p( π ) = p( n)p( n) 1 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 p( π ) = p( n) Neutron parity is chosen positive p( π ) = 1 Gauge bosons,, Z, W +, W -, g negative parity Leptons: not much to talk about: disrespect of parity Physics 129, Fall 2010, Prof. D. Budker;

12 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 scalar not observed 1 2 (k 1 - k 2 ) pseudoscalar observed! Only possible if p(e + ) p(e - ) = -1 Physics 129, Fall 2010, Prof. D. Budker;

13 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 forbidden Week interactions do not respect C Physics 129, Fall 2010, Prof. D. Budker;

14 Parity-Violation: Particles Nuclei Atoms Molecules

15 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

16 z z y x What is parity? P x y z x Rotation around y y =y Left hand cannot be rotated into right hand!

17 Normal vs. axial vectors Under Spatial Inversion (P): V -V A A r, p, E, d = e r, L = r p, S, B Similarly for scalars (pseudo-scalars) Under Spatial Inversion (P): S S PS -PS Energy, any V V, A A any A V,

18 Continuous: Discrete vs. Continuous Transformations and Symmetries 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

19 The (broken) law of parity Because the laws of Nature should be the same in the real world and its mirror image, no pseudoscalar correlation should be observed in experiments, for example I p Does not apply to cork-screws!

20 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 us Physics 129, Fall 2010, Prof. D. Budker;

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

22 Prof. C. S. Wu ( ) The shatterer of the parity illusion (1956)

23 The Co-60 experiment

24 Parity and Quantum Mechanics ˆ 1 1 PHP = Hˆ PHP ˆ P = HP ˆ PHˆ = HP ˆ If Hamiltonian is P-invariant nondegenerate sate is eigenfunction of P PΨ = pψ Now, PP = I Ψ = PPΨ = P( pψ) = ppψ = p 2 Ψ p 2 = 1 p = ± 1 Atomic states are even or odd If parity is violated eigenstates are of mixed parity

25 Atomic Parity Violation (APV) e γ Z e Electromagnetic interaction (conserves parity) Weak interaction (violates parity) APV = PNC = Parity Non-Conservation

26 Atomic PNC: optical rotation PNC M1 E1 M1-E1 PNC interference

27 Optical Rotation Linear Polarization Medium Circular Components ψ

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 Prof. E. N. Fortson No reversals New approaches needed for progress 28

29 Atomic PNC: Stark interference PNC+E DC M1 E1 E1 Stark -E1 PNC interference Reversals!

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

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

32 Why the French? A A A A T O M T O M T O M E T O M E

33 The Boulder Cs PNC Experiment P-odd, T-even correlation: σ [E B] 5 reversals to distinguish PNC from systematics

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

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

36 What were we doing all this time? Bi, diatomic molecules, Sm (Novosibirsk) with L. M. Barkov and M. Zolotorev Tl (Berkeley) with E. D. Commins, D. DeMille, and M. Zolotorev Dy M. Zolotorev, D. DeMille, E. D. Commins, A.-T.Nguyen, A. Cingoz, N. Leefer Sm S. M. Rochester 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,

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

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) 38

39 Anapole Moment of a current distribution (e.g., a nucleus) ( ) ( ) ( ) ( ) = = = = = = + + = = r d r j r a R a R A r d r j r c m R R m R A r d r j cr R A r r R r R R r R r d r R r j c A R k k l k k k 3 2 (2) 3 3 (1) 3 (0) 3 ) ( ); ( ) ( 2 1 ; 0 ) ( ) ( 1 π δ T-conserving; P-violating Ya. B. Zel dovich

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

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

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

43 The Yb PV Experiment Electric and magnetic fields define handedness Rotational Invariant: ε B E ε B ( )( ) 43

44 PV effects on rates Transition rates E-field modulation E E dc + R R ± 1 E = β E cosωt = β E 2 sin 2 2 cos θ + 2Eβξcosθ sin θ 2 θ Eβξcosθ sin θ interference m = -1 m = 0 R +1 m = +1 3 D 1 R 0 R -1 1 S 0 Compute ratio r = ( R R 1) R0 for 1st and 2nd harm. signal st nd Ratio difference yields PV asymmetry: r( 1 ) r(2 ) = ± 2( ξ β E ) dc

45 Typical Stark-induced signal Signal Amplitude [V] Signal Amplitude [V] st harmonic signal fit PNC line shape (x100) d harmonic signal fit DC bias 43 V/cm f [MHz] 174 Yb resonance split by B 70 G; E=3 kv/cm PV asymmetry: ~ / E/(kV/cm) Asymmetric lineshape AC Stark effect 45

46 Atoms in electric field: the Stark effect or LoSurdo phenomenon Johannes Stark ( ) Nazi Fascist 46

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=±π/4 47

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 48

49 Yb PV Amplitude: Results Theoretical prediction Mean value 68% confidence band ζ/β (mv/cm) Run number ζ/β=39(4) stat. (5) syst. mv/cm ζ =8.7± ea 0 Accuracy is affected by HV-amplifier noise, fluctuations of stray fields, and laser drifts to be improved

50 Progress in Yb APV 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 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, (2009)]

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

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

53 The parity violation experiment in Dy evolved into 53

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

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

56 Next steps... Succeeded in laser cooling of atomic beam Operate new apparatus optimized for the α-dot experiment Measure frequency to ~1 mhz Dy APV will be back! α α 18 ~ 10 / yr

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