Atomic Parity Violation in Ytterbium

1. Atomic Parity Violation in Ytterbium K. Tsigutkin, D. Dounas-Frazer, A. Family, and D. Budker http://budker.berkeley.edu

2. PV Amplitude: Current results z/b=39(4)stat.(5)syst. mV/cm  |z|=8.7±1.4×10-10 ea0 Accuracy is affected by HV amplifier noise, fluctuations of stray fields, and laser drifts → to be improved

3. Sources of parity violation in atoms Z0-exchange between e and nucleus  P-violating, T-conserving product of axial and vector currents is by a factor of 10 larger than leading to a dominance of the time-like nuclear spin-independent interaction (Ae,VN) A contribution to APV due to Z0 exchange between electrons is suppressed by a factor ~1000 for heavy atoms.

4. Nuclear Spin-Independent (NSI) electron-nucleon interaction NSI Hamiltonian in non-relativistic limit assuming equal proton and neutron densities r(r) in the nucleus: The nuclear weak charge QW to lowest order in the electroweak interaction is The nuclear weak charge is protected from strong-interaction effects by conservation of the nuclear vector current. Thus, APV measurements allows for extracting weak couplings of the quarks and for searching for a new physics beyond SM • NSI interaction gives the largest PNC effect compared to other mechanisms • PV interaction is a pseudo-scalar  mixes only electron states of same angular momentum

5. NSI interaction and particle physics implications APV utilizes low-energy system and gives an access to the weak mixing angle, Sin2(W), at low-momentum transfer. • J.L. Rosner, PRD 1999 • V.A. Dzuba, V.V. Flambaum, and O.P. Sushkov, PRA 1997 • J. Erler and P. Langacker, Ph.Lett. B 1999

6. Isotope ratios and neutron distribution The atomic theory errors can be excluded by taking ratios of APV measurements along an isotopic chain. While the atomic structure cancels in the isotope ratios, there is an enhanced sensitivity to the neutron distribution rn(r). f(r) is the variation of the electron wave functions inside the nucleus normalized to f(0)=1. R is sensitive to the difference in the neutron distributions.

7. ~Z3 scaling of APV effects Considering the electron wave functions in nonrelativistic limit and point-like nucleus the NSI Hamiltonian becomes: Since it is a local and a scalar operator it mixes only s and p1/2 states. • Z due to scaling of the probability of the valence electron to be at the nucleus • Z from the operator p, which near the nucleus(unscreened by electrons)  Z. • |QW|N~Z. Strong enhancement of the APV effects in heavy atoms

8. Signature of the weak interaction in atoms hNSI mixes s1/2 and p1/2 states of valence electron  APV of dipole-forbidden transition. If APC is also induced, the amplitudes interfere. Interference E1-PV interference term is odd in E E-field Stark-effect E1 PC-amplitude  E Reversing E-field changes transition rate Transition rate  APVAStark

9. Atomic structure of Yb Proposed by D. DeMille, PRL 1995 By observing the 6s21S0 – 6s6p 3P1 556 nm decay the pumping rate of the 6s21S0 – 6s5d3D1 408 nm transition is determined. The population of 6s6p 3P0 metastable level is probed by pumping the 6s6p 3P0 - 6s7s 3S1 649 nm transition.

10. Yb isotopes and abundances Seven stable isotopes, two have non-zero spin C.J. Bowers et al, PRA 1999

11. Rotational invariant and geometry of the Yb experiment Reversals: B – even E – odd q qp/2 – odd |b| = 2.24(25)10-8 e a0/(V/cm) – Stark transition polarizability (Measured by J.Stalnaker at al, PRA 2006) |z| = 1.08(24)10-9 (QW/104) e a0– Nuclear spin-independent PV amplitude (Calculations by Porsev et al, JETP Lett 1995; B. Das, PRA 1997 )

12. PV effect on line shapes:even isotopes PV-Stark interference terms 174Yb Rate modulation under the E-field reversal yields:

13. Experimental setup Light collection efficiency: Interaction region: ~0.2% (556 nm) Detection region: ~25% Yb density in the beam ~1010 cm-3 E-field up to 15 kV/cm, spatial homogeneity 99% Reversible B-field up to 100 G, homogeneity 99%

14. Optical system and control electronics Light powers: Ar+: 12W Ti:Sapp (816 nm): 1W Doubler (408 nm): 50 mW PBC: Asymmetric design, 22 cm Finesse 17000 Power 10 W Locking: Pound-Drever-Hall technique

15. m = +1 m = 0 m = -1 3D1 R+1 R0 R-1 1S0 Fast (70 Hz) E-modulation schemeto avoid low-frequency noise and drift issues Transitionrates E-field modulation PV-asymmetry:

16. Fast E-modulation scheme: Profiles 174Yb Effective integration time: 10 s p-p Shot noise limited SNR in respect to PV signal ~2 (for 1 s integration time)  0.1% accuracy in 70 hours E0=5 kV/cm Edc=40 V/cm q=p/4 • Lineshape scan: ~20 s • E-field reversal: 14 ms (70 Hz) • B-field reversal: 20 minutes • Polarization angle: 10 minutes • E-field magnitude • B-field magnitude • Angle magnitude DC bias 43 V/cm

17. PV Amplitude: Current results z/b=39(4)stat.(5)syst. mV/cm  |z|=8.7±1.4×10-10 ea0 Accuracy is affected by HV amplifier noise, fluctuations of stray fields, and laser drifts → to be improved

18. Fast E-modulation scheme: Systematics Assume stray electric and magnetic fields (non-reversing dc) and small ellipticity of laser light: PV asymmetry and systematics give four unknowns: Reversals of B-field and polarization (±p/4) yield four equations Solve for PV asymmetry, stray fields, and noise

19. Problems • Photo-induced PBC mirror deterioration in vacuum • Technical noise (above shot-noise) • Stray electric fields (~ V/cm) • Laser stability

20. Power-buildup cavity design and characterization C. J. Hood, H. J. Kimble, J. Ye. PRA 64, 2001 Ringdown spectroscopy

21. Power-buildup cavity design and characterization: mirrors Mirror set used during the latest APV measurements: Finesse of 17000 with ATF mirrors Photodegradation: a factor of 3 increase of S+A losses in 2 runs (~8 hours of exposure with ~10 W of circulating power)

22. Summary • 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 shifts measured • Verification of PV enhancement And then… • PV in a string of even isotopes; neutron distributions • PV in odd isotopes: NSD PV, Anapole Moments …

23. Sources of NSD interaction Hyperfine correction to the weak neutral current Weak neutral current Anapole moment kA-Anapole moment k2-Neutral currents kQW-Radiative corrections

24. Anapole moment In the nonrelativistic approximation PNC interaction of the valence nucleon with the nuclear core has the form: n(r) is core density and ga is dimensionless effective weak coupling constant for valence nucleon. • As a result, the spin  acquires projection on the momentum p and forms spin helix • Spin helix leads to the toroidal current. This current is proportional to the magnetic moment of the nucleon and to the cross section of the core. Khriplovich & Flambaum neutron: mn=-1.2; gn=-1 proton: mp=3.8; gp=5 Anapole moment is bigger for nuclei with unpaired proton

25. h0 Nuclear physics implication: weak meson coupling constants There are 7 independent weak couplings for p-, r-, and w-mesons known as DDH constants. Proton and neutron couplings, ga, can be expressed in terms of 2 combinations of these constants: At present the values of the coupling constants are far from being reliably established. The projected measurement of the anapole moment in 173Yb should provide an important constraint.

26. PV effect on line shapes:odd isotopes zNSD10-12 ea0 for odd Yb isotopes z=10-9ea0 z` must be measured with 0.1% accuracy