1. Possible measurement of electron EDM in atoms with spatially alternating electric field T. Haseyama RIKEN, Japan ( The Institute of Physical and Chemical Research ) Overview of the planned experiment Recent development on co-magnetometer beam

2. electron EDM PRA50,2960(1994) upper limit at present |d e | < 1.6×10 -27 ecm Berkeley group 205 Tl ground state 6 2 P 1/2 ( F=1) Tl: enhancement factor –585 (Z=81) PRL88,071805(2002) Electric Dipole Moment P-odd T-odd

3. Atomic EDM PRA50,2960(1994) e EDM Enhancement factor: d A /d e ～ O ( Z 3 α 2 ) inner core region : relativistic motion a strong mixing between opposite-parity states 2 types of atomic EDM paramagnetic atom ← electron EDM diamagnetic atom ← nuclear Schiff moment ← quark chromo-EDM and θ QCD

4. Direction of Electric Field in beam experiment 205 Tl-exp. : E ⊥ v requirement: counter-propagating beams Motional magnetism v×E rotation E // v preferable voltage accumulation E // v difficult to apply

5. Accumulation of EDM spin precession in spatially alternating electric field Accumulative EDM precessions in Canceling Voltages Spin rotates in each electrode by 180degrees with static magnetic field. Longitudinal E-field

6. exact matching mismatching alternating π-flips one-way π-flips BAD GOOD v E BπBπ Small velocity-dependence of the sensitivity to the EDM spin precession Rotation angle is velocity-dependent. EDM spin precession accumulates when the directions of the magnetic field are also alternating. elapsed time(relative) Sideward component Derivative to the EDM precession

7. Advantages to use 220 Fr The heaviest alkali atom, Z=87 Large enhancement from e EDM d Fr /d e ~ 1×10 3 F=1/2 hyperfine structure valence electron 7s 1/2 + nuclear spin I=1 spin precession Sufficiently long lifetime τ=39.2 sec (T 1/2 =27.2sec) RIBF (RIKEN) production rate > 5×10 6 /sec

8. Neutralization area Dipole Magnet, RF cavity RI Electrodes Glass nozzle Stopping chamber Detector (QMS) Yttrium Spin Selection (1st) Hexapole Magnet Spin Selection (2nd) Quadrupole Magnet RIABR （ Radio Isotope Atomic Beam Resonance ） for other experiments requiring high nuclear polarization production: slow neutral RI beam applicable to Francium

9. Atomic excitation Francium D1 line: transition between 7s 1/2 and 7p 1/2 states (λ= 817nm) Rn-like closed shell + 1 valence electron Optical Pumping m F = +1/2 : stable m F = -1/2 : unstable → fluorescence 7s 1/2 F=1/2 states D1: 817nm D2: 718nm D2 line: used for atomic cooling transition between 7s 1/2 and 7p 3/2 states (λ= 718nm)

10. Slow Alkali Beams saturation intensity (Fr D2-line) Na PRA55,605(1997) Na to reduce transverse momentum ２ -D Optical Molasses Doppler Limit 8.3cm/s or sub-Doppler cooling as required Longer time for EDM precession Zeeman technique

11. 6 Li co-magnetometer Stable alkali with nuclear spin I=1 thermal atomic beam: available similar configuration of angular momentum Atomic magnetic moment: close to 220 Fr relative difference: O(10 -3 ) Negligible EDM d Li /d Fr ~ 4×10 -6 trajectory combination onto 220 Fr-path thermal Li-beam source system Ext.Cav. Diode Laser system

12. Planned setup

13. Deceleration of 6 Li beam with Zeeman slower method thermal 6 Li atomic beam low-velocity component: too tiny a portion…. 300 ℃ 400 ℃ 500 ℃ Velocity[m/s] Deceleration is Required! Head-on collisions with photons a deceleration with a single laser cancellation Doppler shift ⇔ Zeeman shift

14. Momentum transfer with photon cycling transition for deceleration D2 line (2s 1/2 → 2p 3/2 ) 671.0nm (446.8THz, 1.848eV) (F, F’) = (3/2, 5/2) circular polarization Although hyperfine transitions, (F, F’) = (3/2, ＊ ) are irresolvable, circular polarization allows only (3/2, 5/2) for successive transitions. Momentum : 1.87 × 10 4 eV/c Doppler shift : 1.49GHz Compensating field : 0.1065T (for v=1000m/s) successive scatterings of ~10 4 photons Radiative lifetime (2p 3/2 ) 26.9ns

15. 6 Li Deceleration Rate Light absorption and scattering rate power-broadened line width maximum deceleration (s 0 →∞) field, gradient and laser power This condition should NOT be satisfied at the exit. 220 Fr 7.57MHz, 5.44m/s 2.67mW/cm 2 220 Fr 6.01 × 10 4 m/s 2 220 Fr 5.952 × 10 -4 T 2 / m

16. magnet Profile coil: field gradient Bias coil: uniform shift Extraction coils: sudden drop 6 Li beam entrance 6 Li beam exit inhomogeneous solenoids MAX 0.12T MAX 0.01TMAX 0.02T

17. Example of parameter setting 929m/s→ 200m/s additional slowering as required

18. Summary Electron EDM measurment w/ spatially alternating electric field Longitudinal electric field to reduce v × E systematics Spatially alternating longitudinal electric field avoids potential accumulation. π-flip at each boundary accumulation Effect of velocity spread is minimized by alternating π-flips. Fr atomic beam, RIABR, Zeeman slowering, … Deceleration of 6 Li co-magnetometer beam design and construction

20. Francium the heaviest alkali atom accelerator prduction required Largest enehancement （ ~1000 ） PRA50,2960(1994) Alkali Low excitation enerygy Small saturation intensity ～ 3mW/cm 2 Polarization or atomic cooling 220 Fr 7s 1/2 (F=1/2) Maximum EDM spin rotation 224,226 Fr: same spin, but small production rates 6 Li : spin analogue negligible EDM

21. Electron EDM (Electric Dipole Momemnt) positronelectron 電荷分布の偏り finite EDM P-odd T-odd interaction

22. “Spin Echo”-like Method tough against velocity mismatching exact matching mismatching alternating π-flips one-way π-flips BADGOOD

23. Magnitude of the Spin-Flip field Lande-factor Rotation frequency in magnetic field passage time in spin-flip field Magnitude of the Spin-Flip field 1eV ⇔ 241.80THz 10 -19 eV ⇔ 24μHz

24. Thallium figure PRL88,071805(2002)