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

electron EDM

PRA50,2960(1994)

upper limit at present

　 |de| < 1.6×10-27 ecm Berkeley group 205Tl ground state 6 2 P1/2 ( F=1)

Tl: enhancement factor –585 　 (Z=81)PRL88,071805(2002)

Electric Dipole Moment

P-odd T-odd

Atomic EDM

PRA50,2960(1994)

e EDM Enhancement factor: dA /de ～ O (Z3α2)　　　　　 　 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 θQCD

Direction of Electric Field in beam experiment

205Tl-exp. : E ⊥ v requirement: counter-propagating beams

Motional magnetism

v×E rotation

E // v preferable

voltage accumulation

E // v difficult to apply

Accumulation of EDM spin precessionin spatially alternating electric field

Accumulative EDM precessions in

Canceling Voltages

l o n g i t u d i n a l v i e w

F

π - f l i p

E D Mp r e c e s s i o n

F

v

E Bπ - f l i p

A t o m

H V

G N D

Spin rotates in each electrode by 180degrees with static magnetic field.

Longitudinal E-field

exact matching

mismatching

alternatingπ-flips

one-wayπ-flips

BADGOOD

v

EBπ

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)

-0.01

-0.005

0

0.005

0.01

0.015

0.02

0.9 0.95 1 1.05 1.1

B_add 1radB_add 0.1radB_add 0.01radB_add 0.001rad

y-component of the polarization

Elapsed time factor

0

0.2

0.4

0.6

0.8

1

1.2

0.9 0.95 1 1.05 1.1

deriv. B_add 1radderiv. B_add 0.1radderiv. B_add 0.01radderiv. B_add 0.001rad

derivative to the EDM precession

Elapesed time factor

Sideward component

Derivative to the EDM precession

Advantages to use 220Fr

F

μd

BE AA

ω

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

Neutralization areaDipole 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 requiringhigh nuclear polarization

production: slow neutral RI beam

applicable to Francium

Atomic excitation

m F

7 s 1 / 2

7 p 1 / 2

D 1 l i n e= 8 1 7 n mλ

F = 1 / 2

F = 3 / 2

F = 3 / 2

F = 1 / 2

2 2 0 F r

－ 1 / 2＋ 1 / 2

－ 1 / 2＋ 1 / 2＋ 3 / 2

－ 3 / 2

－ 1 / 2＋ 1 / 2

－ 1 / 2＋ 1 / 2＋ 3 / 2

－ 3 / 2

unpo

l.

σ＋

- 3 5 0 0 0

- 3 0 0 0 0

- 2 5 0 0 0

- 2 0 0 0 0

- 1 5 0 0 0

- 1 0 0 0 0

- 5 0 0 0

0

7 s

8 s

9 s

1 0 s

7 p 1 / 2

8 p 1 / 2

9 p 1 / 2

7 p 3 / 2

8 p 3 / 2

9 p 3 / 2

6 d 3 / 2

7 d 3 / 2

8 d 3 / 2

6 d 5 / 2

7 d 5 / 2

8 d 5 / 2

5 f

6 f

C a lc u la te d b y D z u b a P h y s .L e t t .A 9 5 ,2 3 0 (1 9 8 3 )e t a l .

F r a n c i u m

Ene

rgy

leve

l[cm

]-1

i o n i z a t i o n e n e r g y 4 . 0 7 e V( 2 n d s m a l l e s t o f a l l t h e a t o m s )

Francium D1 line: transition between 7s1/2 and 7p1/2 states (λ= 817nm)

Rn-like closed shell + 1 valence electron

Optical Pumping

mF = +1/2 : stable 　mF = -1/2 : unstable → 　 fluorescence

7s1/2 F=1/2 states

D1: 817nm

D2: 718nm

D2 line: used for atomic cooling transition between 7s1/2 and 7p3/2 states (λ= 718nm)

Slow Alkali Beams

saturation intensity 　 (Fr D2-line) 　 　

22

30

0 mW/cm 67.2 π12

ω

cI

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

6Li co-magnetometerStable 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

trajectory combination onto 220Fr-path

thermal Li-beam source

Ext.Cav. Diode Laser systemsystem

Planned setup

Deceleration of 6Li beam with Zeeman slower method

thermal 6Li atomic beamlow-velocity component: too tiny a portion….

7.0E-4

0.0E+0

1.0E-4

2.0E-4

3.0E-4

4.0E-4

5.0E-4

6.0E-4

30000 500 1000 1500 2000 2500

Velocity Distibution

300℃400℃500℃

Velocity[m/s]Deceleration is Required!

Head-on collisions with photons

a deceleration with a single laser

position

resonance with applied magnetic field

atoms entering with high velocity

atoms entering with low velocity

Basic concept of the deceleration

cancellation

Doppler shift ⇔ Zeeman shift

Momentum transfer with photon

cycling transition for deceleration D2 line (2s1/2→ 2p3/2) 671.0nm (446.8THz, 1.848eV)

(F, F’) = (3/2, 5/2) circular polarizationAlthough hyperfine transitions, (F, F’) = (3/2, ＊ ) are irresolvable,circular polarization allows only (3/2, 5/2) for successive transitions.

Momentum : 1.87×104eV/cDoppler shift : 1.49GHzCompensating field : 0.1065T (for v=1000m/s)

successive scatterings of ~104 photons

Radiative lifetime (2p3/2) 26.9ns

1 - p h o t o n m o m e n t u m1 . 8 4 8 e V / c0 . 0 9 9 m / s

l a s e rb e a m

F l u o r e s c e n c e( r a n d o m d i r e c t i o n )

F l u o r e s c e n tr e c o i l

L a s e r a b s o r p t i o n

r e c o i l o ni n d u c e d e m i s s i o n

6 L i a t o m

A t o m i cm o m e n t u m

6Li Deceleration RateLight absorption and scattering rate

20

0

]/)(2[1

2/

D

p s

s

22

30

0 mW/cm 56.2 π12

ω ,

limit) capture 3.97m/s (equiv. MHz92.5π2

shiftDoppler :

included)shift (Zeeman

resonance from detuninglaser :

cIIIs ss

D

01 FWHM sΓ power-broadened line width

0

1 107

2 107

3 107

4 107

480 490 500 510 520

sat. fact 1sat. fact 3sat. fact 10sat. fact 30

Ph

oton

Sca

tter

ing

Rat

e[s-1

]velocity [m/s]

Bz = 5.33 x 10-2 T

260max sm1084.1

2

Mca

maximum deceleration (s0→∞)

field, gradient and laser power 1

22

0

2

0

0

0max 1/mT 10085.2

1

dzdB

Bs

cs

sa

dz

dBB

B

This condition should NOT be satisfied at the exit.

220Fr 7.57MHz, 5.44m/s2.67mW/cm2

220Fr 6.01×104m/s2

220Fr 5.952×10-4 T2 / m

magnet

Profile coil: field gradientBias coil: uniform shift Extraction coils: sudden drop

6Li beamentrance

6Li beamexit

inhomogeneoussolenoids

MAX 0.12T

MAX 0.01T MAX 0.02T

Example of parameter setting

929m/s→ 200m/s 6 L i a t o m L a s e r

additional slowering as required

Summary

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

Francium the heaviest alkali atomaccelerator prduction requiredLargest enehancement （ ~1000 ）

PRA50,2960(1994)

Alkali•Low excitation enerygy•Small saturation intensity ～ 3mW/cm2

•Polarization or atomic cooling

220Fr 7s1/2 (F=1/2)

Maximum EDM spin rotation224,226Fr: same spin, but small production rates

6Li : spin analogue negligible EDM

Electron EDM (Electric Dipole Momemnt)

positronelectron

電荷分布の偏り

finite EDM P-odd T-odd interaction

“Spin Echo”-like Method tough against velocity mismatching

exact matching

mismatching

alternatingπ-flips

one-wayπ-flips

BADGOOD

Magnitude of the Spin-Flip field

Lande-factor

1,0,

3

2

)1(2

)1()1()1(

2)1(2

)1()1()1(1

21

ILFSJ

FF

IIJJFFgg

JJ

LLSSJJg

JF

J

MHz/gauss87.12

32

F

B

Rotation frequency in magnetic field

passage time in spin-flip field

s10250m/s

m10

v4-

2

atom

flipL

Magnitude of the Spin-Flip field

gauss1036.1s)102(MHz/gauss)87.1(2

1 3-4-

1eV⇔241.80THz10-19eV ⇔24μHz

Thallium figure

PRL88,071805(2002)