Atomic Parity Violation in Ytterbium

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1 Atomic Parity Violation in Ytterbium K. Tsigutkin, D. Dounas-Frazer, A. Family, and D. Budker

Atomic PV: important landmarks! 1959 Ya. B. Zel dovich: APV (Neutr. Current) Opt. Rotation in atoms! 1974 M.-A. & C. Bouchiat Z 3 enhancement APV observable in heavy atoms!

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

4 Parity transformation x P : y! z x y z Parity transformation is a point reflection. det(p )=-1 Classification of classical variables: Rotational transformation Parity transformation Variables Scalars Vectors Scalars (P=1): Mass, Energy, Time Pseudoscalars (P=-1): Helicity Vectors (P=-1): Linear momentum, E-field, Force Pseudovectors (P=1): Angular momentum, B-field

5 Two frontiers in the search Collider experiments (pp, e + e -, etc) at higher energies (E >> M Z ) Indirect searches at lower energies (E < M Z ) but high precision High energy physics Particle, nuclear & atomic physics

6 Sources of parity violation in atoms Z 0 -exchange between e and nucleus P-violating, T-conserving product of axial and vector currents ĥ = G 2 N "C # 1N eγ µ γ 5 e Nγ µ N +C 2N eγ µ e Nγ µ γ 5 N$ % Z 0 e C1n is by a factor of 10 larger than C1p, C2N leading to a dominance of the time-like nuclear spin-independent interaction (A e,v N ) A contribution to APV due to Z 0 exchange between electrons is suppressed by a factor ~1000 for heavy atoms.

7 Nuclear Spin-Independent (NSI) electron-nucleon interaction NSI Hamiltonian in non-relativistic limit assuming equal proton and neutron densities ρ(r) in the nucleus: ˆ G h () W = QWγρ 5 r 2 2 The nuclear weak charge Q W to the lowest order in the electroweak interaction is Q W = N + Z(1 4sin 2 θ W ) N M = 2 W sin θw 1 Z M 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 2 NSI interaction gives the largest PV effect compared to other mechanisms PV interaction is a pseudo-scalar mixes only electron states of same angular momentum

NSI interaction and particle physics implications APV utilizes low-energy system and gives an access to the weak mixing angle, Sin 2 (θ W ), at low-momentum transfer. S. G.

8 NSI interaction and particle physics implications APV utilizes low-energy system and gives an access to the weak mixing angle, Sin 2 (θ W ), at low-momentum transfer. S. G. Porsev, K. Beloy, and A. Derevianko, PRL 2009 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

9 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 ρ n (r). nuc A = ξ ( Q + Q ) PV atomic W W Q N q Z q nuc 2 W = ( n 1) + (1 4sin θw)( p 1) q = ρ () r f()d r r, q = ρ () r f()d r r 3 3 n n p p PV n n n f(r) is the variation of the electron wave functions inside the nucleus normalized to f(0)=1. APV ( N') QW ( N') R 1 +Δ A ( N) Q ( N) Δq q qʹ W [ q ] n R is sensitive to the difference in the neutron distributions.

10 Amplitude interference: the trick for observing weak interaction in atoms h NSI mixes s 1/2 and p 1/2 states of valence electron A PV of dipole-forbidden transition. If A PC is also induced, the amplitudes interfere PC PV PC PC PV PV R A + A A + 2 A A + o( A ) Interference E-field Stark-effect E1 PC-amplitude E E1-PV interference term is odd in E Reversing E-field changes transition rate Transition rate A PV A Stark

11 Observing APV in Yb Proposed by D. DeMille, PRL 1995 Pumping rates of the 408-nm transition are detected by measuring the population of the 3 P 0 state, where 65% of the atoms excited to the 3 D 1 state decay spontaneously. The population of 6s6p 3 P 0 metastable level is probed by pumping the 6s6p 3 P 0-6s7s 3 S nm transition.

12 PV effect: line-shape signature! E = E ˆx! ε = ε (sinθ ŷ +cosθ ẑ) R 0 = 4ε 2 (β 2 E 2 sin 2 θ + 2E βς sinθ cosθ) R ±1 = 2ε 2 (β 2 E 2 cos 2 θ 2E βς sinθ cosθ) 174 Yb PV-Stark Interference

13 Experimental setup Light collection efficiency: Interaction region: ~0.2% (556 nm) Detection region: ~25% Yb density in the beam ~10 10 cm -3 E-field up to 15 kv/cm, spatial homogeneity 99% Reversible B-field up to 100 G, homogeneity 99%

Schematic of the optical system PBC: Asymmetric design Finesse 17000 Power 20 W Locking:

14 Schematic of the optical system PBC: Asymmetric design Finesse Power 20 W Locking: Pound-Drever-Hall technique Light powers: Ar + : 12W; Ti:Sapp (816 nm): 1W; Doubler (408 nm): 50 mw

cos(2 ωt) [0] [1] [2] M M M M m = -1 m = 0 m = +1 3 D 1 R +1 R 0 R -1 1 S 0

15 Fast (70 Hz) E-modulation scheme to avoid low-frequency noise and drift issues E-field modulation E E dc + E 0 cos(ωt) Transition rates R = R + R cos( ωt) + R cos(2 ωt) [0] [1] [2] M M M M m = -1 m = 0 m = +1 3 D 1 R +1 R 0 R -1 1 S 0 PV-asymmetry: 16 K R R 2 R ς = + = R R R E [1] [1] [1] [2] [2] [2] β 0

16 Fast E-modulation scheme: Profiles 174 Yb E 0 =5 kv/cm E dc =40 V/cm Effective integration time: 10 s p-p Shot noise limited SNR with respect θ=π/4 to PV signal ~ 2/ τ ( s ) 0.1% accuracy in 70 hours Lineshape scan: 20 s DC bias 43 V/cm E-field reversal: 14 ms (70 Hz) B-field reversal: 20 minutes Polarization angle: 10 minutes E-field magnitude B-field magnitude Angle magnitude

17 PV Amplitude: Current results Theoretical prediction Mean value 68% confidence band ζ/β (mv/cm) Run number ζ/β=39(4) stat. (3) 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

Stark-Induced Amplitude (β): 2 independent measurements! M1 Measurement (Stark-M1 interference)!

18 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

19 Statistical noise

20 Fast E-modulation scheme: Systematics E- and B-field imperfection: E= E+! E!!E=( E! 0 ˆx+!e y ŷ+!e z ẑ) cos(ωt) E! =(E dc ˆx+e y ŷ+e z ẑ) B= B+! B!!B=( b! x ˆx+ b! y ŷ+bẑ) B! =( b! x ˆx+ b! y ŷ+ b! z ẑ) Light polarization now includes a small ellipticity:! ε = ε (ŷsinθ + ẑ e iφ cosθ) Residual M1 transition: A (M1) M = Μ1 ( 1) M ( δ k!! ε ) -M Normalized-rate modulation amplitudes include additional terms: R R [1] M [2] M = r + r + r + r (Stark) (PV) (M1) ( φ) M M M M

21 M1- and φ-contribution 16 K R R 2 R ς = + = R R R E [1] [1] [1] [2] [2] [2] β 0

22 Stark contribution

23 Stark contribution measurements e y! # "!e z 2! E 0 + b x B $ & % + e z!e y 2! E 0 = 2.6 (1.6) stat (1.5) syst mv/cm

24 Error budget ς β = 39 (4) (3) mv/cm stat syst

25 Problems Photo-induced PBC mirror degradation in vacuum Fields imperfection Laser stability

26 Power-buildup cavity design and characterization: schematic

Power-buildup cavity design and characterization F = T P ε P trans in 1 + T 1 2 = T T 2π + L 2 1 + F 2π C. J. Hood, H. J. Kimble, J. Ye.

27 Power-buildup cavity design and characterization F = T P ε P trans in 1 + T 1 2 = T T 2π + L F 2π C. J. Hood, H. J. Kimble, J. Ye. PRA 64, L 2 2 PBC transmission [V] τ=2.16 µs F=9253 τ=1.74 µs F=7454 Ringdown spectroscopy 0.00 τ=1.33 µs F= Time [µs]

28 Power-buildup cavity design and characterization: mirrors REO set1 REO set2 ATF Boulder expt. λ=408 nm λ=408 nm λ=408 nm λ=540 nm Transmission 320 ppm 45; 23 ppm 150 ppm 40; 13 S+A losses 120 ppm 213; 83 ppm 30 ppm <1 ppm Mirror set used during the latest APV measurements: Finesse of 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)

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

30 Sources of NSD interaction Anapole moment ĥ NSD = G 2 κ I γ 0 γi ρ(! r) Weak neutral current Hyperfine correction to the weak neutral current K κ = κ A + κ 2 I + 1 I + 1/ 2 l K = ( 1) ( I + κ Q w ; + 1/ 2) κ κ A / 2 K = C I + 1 A 2α 2/3 µ g α α ; A = N + Z; κ A -Anapole moment κ 2 -Neutral currents κ QW -Radiative corrections

31 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 g α is dimensionless effective weak coupling constant for valence nucleon. ĥ A G g α 2 2 (σp) m p n(! r) As a result, the spin σ 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 3 2/3 κ A A µ α g α neutron: µ n =-1.2; g n =-1 proton: µ p =3.8; g p =5 Anapole moment is bigger for nuclei with unpaired proton

32 Nuclear physics implication: weak meson coupling constants There are 7 independent weak couplings for π-, ρ-, and ω-mesons known as DDH constants. Proton and neutron couplings, g α, can be expressed in terms of 2 combinations of these constants: g g p n = f 19.5h 4 0 π = f 18.9h 4 0 π f f 0.12h 0.18h π π ρ ω h h + 0.7h ρ ω h 0 At present the values of the coupling constants are far from being reliably established. The projected measurement of the anapole moment in 173 Yb should provide an important constraint.

33 PV effect on line shapes: odd isotopes! E = (E,0,0)! ε = (0,sinθ,cosθ) R center = β 2 E 2 F F! 6 R side = β 2 E 2 F F! 2 (4sin 2 θ + cos 2 θ) + E β F F! ς! sinθ cosθ cos 2 θ E β F F! ς! sinθ cosθ ς! = ς + I! J! ς NSD ζ NSD ea 0 for odd Yb isotopes ζ=10-9 ea 0 ζ` must be measured with 0.1% accuracy

Prospects for Atomic Parity Violation Experiments

Prospects for Atomic Parity Violation Experiments Konstantin Tsigutkin and Dima Budker http://socrates.berkeley.edu/~budker socrates.berkeley.edu/~budker/ Outline A brief story of parity violation in atoms