Possible measurement of electron EDM in atoms with spatially alternating electric field

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

2. upper limit at present 　|de| < 1.6×10-27ecm Berkeley group 205Tl ground state 6 2 P1/2 (F=1) Tl: enhancement factor –585　(Z=81) PRL88,071805(2002) PRA50,2960(1994) electronEDM Electric Dipole Moment P-odd T-odd

3. Atomic EDM 2 types of atomic EDM 　 　paramagnetic atom ← electron EDM 　diamagnetic atom ← nuclearSchiff moment ← quark chromo-EDM and θQCD e EDM Enhancement factor: dA/de ～ O(Z3α2) 　inner core region : relativistic motion 　 a strong mixing between opposite-parity states PRA50,2960(1994)

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

5. Accumulation of EDM spin precessionin 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. Sideward component exact matching v alternating π-flips one-way π-flips Bπ E mismatching GOOD BAD Derivative to the EDM precession Small velocity-dependence of the sensitivityto 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)

7. Advantages to use 220Fr The heaviest alkali atom, Z=87 Large enhancement from e EDM dFr/de~ 1×103 F=1/2 hyperfine structure valence electron 7s1/2 + nuclear spin I=1 spin precession Sufficiently long lifetime 　　　　　　　τ=39.2 sec (T1/2 =27.2sec) RIBF(RIKEN) production rate > 5×106/sec

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

9. Atomic excitation 7s1/2 F=1/2 states mF = +1/2 : stable 　 mF = -1/2 : unstable →　fluorescence FranciumD1 line: transition between 7s1/2 and 7p1/2 states (λ= 817nm) Optical Pumping D2: 718nm D1: 817nm Rn-like closed shell + 1 valence electron D2 line: used for atomic cooling transition between 7s1/2 and 7p3/2 states (λ= 718nm)

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

11. thermal Li-beam source Ext.Cav. Diode Laser system 6Li co-magnetometer Stable alkali with nuclear spin I=1 　　thermal atomic beam: available similar configuration of angular momentum Atomic magnetic moment: close to 220Fr relative difference: O(10-3) Negligible EDM dLi/dFr~ 4×10-6 trajectorycombination onto220Fr-path

12. Planned setup

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

14. Momentum transfer with photon successive scatterings of ~104 photons cycling transition for deceleration D2 line (2s1/2→ 2p3/2) 671.0nm (446.8THz, 1.848eV) (F, F’) = (3/2, 5/2) circular polarization Radiative lifetime (2p3/2) 26.9ns Momentum : 1.87×104eV/c Doppler shift : 1.49GHz Compensating field : 0.1065T (for v=1000m/s) Although hyperfine transitions, (F, F’) = (3/2, ＊) are irresolvable, circular polarization allows only (3/2, 5/2) for successive transitions.

15. 220Fr 7.57MHz, 5.44m/s 2.67mW/cm2 maximum deceleration (s0→∞) power-broadened line width 220Fr 6.01×104m/s2 field, gradient and laser power 220Fr 5.952×10-4 T2/ m This condition should NOT be satisfiedat the exit. 6Li Deceleration Rate Light absorption and scattering rate

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

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

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 6Lico-magnetometer beam design and construction

20. 220Fr 7s1/2 (F=1/2) Maximum EDM spin rotation 224,226Fr: same spin, but small production rates PRA50,2960(1994) Francium the heaviest alkali atom accelerator prduction required Largest enehancement（~1000） • Alkali • Low excitation enerygy • Small saturation intensity ～3mW/cm2 • Polarization or atomic cooling 6Li : spin analogue negligible EDM

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

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

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

24. Thallium figure PRL88,071805(2002)