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
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
“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
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