Report

Atomic Parity Violation in Ytterbium K. Tsigutkin, D. Dounas-Frazer, A. Family, and D. Budker http://budker.berkeley.edu PV Amplitude: Current results 150 Theoretical prediction Mean value 68% confidence band z/b (mV/cm) 100 50 0 -50 0 2 4 6 8 10 12 14 16 18 20 Run number 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 Sources of parity violation in atoms Z0-exchange between e and nucleus P-violating, T-conserving product of axial and vector currents G hˆ 2 C1n e Z0 C 1N e 5e N N C2 N e e N 5 N N is by a factor of 10 larger than C , C leading to a dominance of the time-like nuclear spin-independent interaction (Ae,VN) 1p 2N A contribution to APV due to Z0 exchange between electrons is suppressed by a factor ~1000 for heavy atoms. Nuclear Spin-Independent (NSI) electron-nucleon interaction NSI Hamiltonian in non-relativistic limit assuming equal proton and neutron densities (r) in the nucleus: G ˆ hW 2 2 QW 5 ( r ) The nuclear weak charge QW to lowest order in the electroweak interaction is QW N Z (1 4 sin W ) N 2 sin W 2 MW 1 M Z 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 2 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 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 n(r). APV atomic (QW QW ) nuc nuc QW f(r) is the variation of the electron wave functions inside the nucleus normalized to f(0)=1. N (qn 1) Z (1 4 sin W )( q p 1) 2 qn n ( r ) f ( r )d r , q p p ( r ) f ( r )d r 3 3 R APV ( N ') APV ( N ) QW ( N ') QW ( N ) 1 qn qn qn qn R is sensitive to the difference in the neutron distributions. ~Z3 scaling of APV effects Considering the electron wave functions in nonrelativistic limit and pointlike nucleus the NSI Hamiltonian becomes: hˆW G 4 2me σ p 3 (r) (r) σ p 3 Since it is a local and a scalar operator it mixes only s and p1/2 states. 2 p1/ 2 hˆW s Z QW • 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 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. R APC APV 2 APC 2 APC APV o( APV ) 2 2 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 APVAStark Atomic structure of Yb Proposed by D. DeMille, PRL 1995 By observing the 6s2 1S0 – 6s6p 3P1 556 nm decay the pumping rate of the 6s2 1S0 – 6s5d 3D1 408 nm transition is determined. The population of 6s6p 3P0 metastable level is probed by pumping the 6s6p 3P0 6s7s 3S1 649 nm transition. Yb isotopes and abundances Seven stable isotopes, two have non-zero spin C.J. Bowers et al, PRA 1999 Rotational invariant and geometry of the Yb experiment εB ε EB AStark i b ( 1) q q E ε Reversals: B – even E – odd p/2 – odd j , m,1, m m j , m -q A PV i ( 1) ε -q j , m,1, m m j , m ; q m m q q |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 ) PV effect on line shapes: even isotopes E (E,0,0) ε (0,sinθ , cos θ) R b E 0 R 1 2 2 b 2 E2 sin θ 2E b sin θ cos θ 2 cos θ E b sin θ cos θ 2 2 174Yb PV-Stark interference terms Rate modulation under the E-field reversal yields: RE RE 2 RE RE bE 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% 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 Fast (70 Hz) E-modulation scheme to avoid low-frequency noise and drift issues R0 b E sin 2 E b cos sin 2 Transition rates R1 1 2 2 b 2 E 2 cos 2 E b cos sin 2 E-field modulation E Edc E0 cos t m = +1 m=0 m = -1 3D 1 R+1 R0 R-1 1S 0 1st PV-asymmetry: K Α 1 2 nd A 1 1st 1st A 1 2 nd A 1 2 A0 2 nd A0 16 b E0 Fast E-modulation scheme: Profiles 174Yb Effective integration time: 10 s p-p E0=5 kV/cm Edc=40 V/cm =p/4 Shot noise limited SNR in respect to PV signal ~2 (for 1 s integration time) 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 PV Amplitude: Current results 150 Theoretical prediction Mean value 68% confidence band z/b (mV/cm) 100 50 0 -50 0 2 4 6 8 10 12 14 16 18 20 Run number 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 Fast E-modulation scheme: Systematics Assume stray electric and magnetic fields (non-reversing dc) and small ellipticity of laser light: b bx , by , bz e ex , e y , ez 0, e iP sin , cos PV asymmetry and systematics give four unknowns: K 16 16bx e y b E0 Bz E0 16bx ez higher order Bz E0 Reversals of B-field and polarization (±p/4) yield four equations Solve for PV asymmetry, stray fields, and noise Problems • Photo-induced PBC mirror deterioration in vacuum • Technical noise (above shot-noise) • Stray electric fields (~ V/cm) • Laser stability Power-buildup cavity design and characterization F 2p T1 T 2 L1 L 2 F T1T 2 Pin 2p Ptrans 2 C. J. Hood, H. J. Kimble, J. Ye. PRA 64, 2001 0.20 Ringdown spectroscopy PBC transmission [V] =2.16 s F=9253 0.15 0.10 =1.74 s F=7454 0.05 =1.33 s F=5698 0.00 -10 -5 0 Time [s] 5 10 Power-buildup cavity design and characterization: mirrors REO set1 l=408 nm REO set2 l=408 nm ATF l=408 nm Boulder expt. l=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 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) 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 … Sources of NSD interaction G ˆ hNSD 0 γI (r ) 2 I Weak neutral current Anapole moment K I 1 K ( 1) A 2 Q ; A 1.15 10 3 A2 / 3 g ; A N Z ; w I 1 / 2 l ( I 1 / 2) Hyperfine correction to the weak neutral current 2 1/ 2 K I 1 C2 A-Anapole moment 2-Neutral currents QW-Radiative corrections Anapole moment In the nonrelativistic approximation PNC interaction of the valence nucleon with the nuclear core has the form: G g (σp) ˆ hA n( r ) n(r) is core density and g is 2 2 mp 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 A 1.15 103 A2 / 3 g neutron: n=-1.2; gn=-1 proton: p=3.8; gp=5 Anapole moment is bigger for nuclei with unpaired proton Nuclear physics implication: weak meson coupling constants There are 7 independent weak couplings for p-, -, and -mesons known as DDH constants. Proton and neutron couplings, g, can be expressed in terms of 2 combinations of these constants: 4 0 g p 8.0 10 70fp 19.5h 4 0 g n 8.0 10 47fp 18.9h fp fp 0.12h 0.18h 1 1 h h 0.7h 0 0 0 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. h0 1 PV effect on line shapes: odd isotopes E (E,0,0) ε (0,sinθ , cos θ) 2 R center β FF E 6 2 R side β FF E 2 2 (4sin θ cos θ) E β FF sin θ cos θ 2 2 2 cos θ E β FF sin θ cos θ 2 I J NSD zNSD10-12 ea0 for odd Yb isotopes z=10-9 ea0 z` must be measured with 0.1% accuracy