Workshop on Fundamental Physics Using Atoms
7 - 9 August 2010, Osaka
Search for an electric dipole moment in 129Xe
atom using a nuclear spin oscillator
T. Inoue,1 T. Nanao,1 M. Tsuchiya,1 H. Hayashi,1 T. Furukawa,1 A. Yoshimi,2
M. Uchida,1 H. Ueno,2 Y. Matsuo,2 T. Fukuyama,3 and K. Asahi1
1
Tokyo Institute of Technology, Meguro-ku, Tokyo 152-8551, Japan
2 RIKEN, 2-1 Horosawa, Wako-shi, Saitama 351-0198, Japan
3 Ritsumeikan University, Nojihigashi, Kusatsu, Shiga 525-8577, Japan
OUTLINE:
1. Introduction
2. "Optically coupled" spin oscillator
3. Present status
4. Summary
1. Introduction
Electric Dipole Moment
(Permanent) Electric Dipole Moment
Electric Dipole Moment (EDM) d
s
+
++
-+

Eext = 0
+q
-+
+

+
a
=
d ≡ qa
-q -
or,
d

particle
or,
 (r )rd3r
i
L EDM   d   5 F
2
Electric dipole moment (EDM)
s
d
+ ++
- - -
s
+ ++
d
time reversal
spin :
s → -s
EDM :
d→d
- - -
d ≠ 0 ： Violation of T
⇒ Violation of CP (CPT theorem)
● The violation of CP is implemented in the
Standard Model (SM), but ...
● CP violation in SM (K-M mechanism) is
not sufficient to explain the matterantimatter asymmetry observed in the
universe.
Thus, ...
● An extra CP-violation is required.
Electric dipole moment (EDM)
s
d
+ ++
- - -
s
+ ++
d
time reversal
spin :
s → -s
EDM :
d→d
- - -
d ≠ 0 ： Violation of T
⇒ Violation of CP (CPT theorem)
Sites of EDM searches
• neutron
• paramagnetic atoms (Tl, Fr, Cs, ...)
• diamagnetic atoms (129Xe, 199Hg, Rn, Ra, ...)
• molecules
(TlF, YbF, PbO, ThO, ...)
• charged particles
(d, , ...)
dN
de
S
de
dN, d
⇒ Probing different facetｓ of anticipated new physics
Electric dipole moment (EDM)
s
+ ++
- - -
s
d
+ ++
d
time reversal
spin :
s → -s
EDM :
d→d
- - -
d ≠ 0 ： Violation of T
⇒ Violation of CP (CPT theorem)
M. Pospelov and A. Ritz,
Annals of Phys. 318, (2005) 119-169
EDM in
129Xe
atoms
•stable particle
•macroscopic number of particles
•EDM generated by a nuclear
Schiff moment
•P,T-violating NN interaction
Schiff moment
Tl, Fr, Cs…
129Xe, 199Hg,
Rn, Ra…
How does the EDM appear in a diamagnetic atom?
Point nucleus in an atom
Nucleus with a finite size
Nucleus
Electrostatic F(r)
due to a cloud of
atomic electrons
EDM d
q
q
=
+
d
=
q
EDM d
q
Dx = d/q
q
Atomic electrons do not
"know" whether the
nucleus has EDM.
Atomic electrons feel a nontrivial charge distribution
unside the nucleus.
Electron cloud
Nucleus
Electron cloud
Nucleus
datom ≠0
Nontrivial charge distribution in the nucleus generates an EDM in atom:
datom  2
0 Dˆ P P  eSchiff 0
E0  EP
P
,
where Dˆ  e Ri
i
Schiff  4 S   ( R)
S
1 
 2 5 2  3 

(
r
)
r
r  r d r
10  nucleus
3



Schiff moment
d(129Xe) = 3.8×105 fm2 ·S(129Xe)
d(199Hg) = 2.8×104 fm2 ·S(199Hg)
[Ginges & Flambaum, Phys. Rep. 397 (04) 63]
What generates a Schiff moment ?
--- (In language of nuclear physics)
CP-violating components of the NN interaction generate S.
●Case of
199Hg
S ( 199 Hg)  0.0010 g NN g(0)NN  0.074 g NN g(1)NN  0.018 g NN g(2)NN e fm3
with SkO' effective interaction,
[J.H. de Jesus and J. Engel, Ann. Phys. 318 (05) 119]

 d

d 
g(0)NN  d u  d d ,
g(1)NN
u
d
●Case of 129Xe
Flambaum, Khriplovich, Sushkov, 1985
Dzuba, Flambaum, Porsev, 2009
Yoshinaga's group, consideration fro shell model in progress.
Neutron EDM predicted values
d = 1027 e·cm
E = 10 kV/cm
D = 10 nHz
（ Dw  1°/day）
d(199Hg) < 3.1×10-29 ecm
Grifith et al., PRL 102 (2009) 101601
Standard Model
(dn = 10-(31-33) )
d(129Xe) < 4.1×10-27 ecm
Rosenberry and Chupp, PRL 86 (2001) 22
[Pendlebury and Hinds, NIM A 440 (00) 471]
Detection of an EDM
H  μ  B  d  E
Energy shift upon an E-field reversal
E // B
E // B
H   B  dE
H   B  dE
Shift in a precession frequency
 
Energy levels for a spin 1/2
(for a case of  > 0, d > 0)
m
B0
E0
m
⇒ signal of an EDM
D      
4dE
h
Desires long precession times => Spin maser
B0
E //  B
B0
E // B
h 
h 0
2 B  2dE
2 B  2dE
(E // B )   
(E //  B)
h
h
the difference
1
2
B0
E0
1
2
B

hν
B
E
s

E
s
Key issue for a high-sensitivity EDM
detection:
Free precession
Time
Transverse spin
Transverse spin
― Realization of a long precession time
‘Spin maser’ state
Time
[T.E. Chupp et al, Phys. Rev. Lett. 72 (94) 2363]
[M.A. Rosenberry and T.E. Chupp, Phys. Re. Lett. 86 (2001) 22]
Spin maser
●
129Xe
polarization vector P = I/I
● Static field B0 = (Bx, By, B0)
● P follows the Bloch equations:
1
P   B  P 
P
T1,2
B
relaxation term
or,
dPx
P
   Py B0  Pz By   x ,
dt
T2
dPy
dt
   Pz Bx  Px B0  
Py
T2
,
dPz
P
   Px By  Py Bx   z   P0  Pz  G.
dt
T1
Pumping term
[T.E. Chupp et al, Phys. Rev. Lett. 72 (94) 2363]
[M.A. Rosenberry and T.E. Chupp, Phys. Re. Lett. 86 (2001) 22]
Spin maser
● If a capacitor C is connected to form
a resonating circuit, the coil produces
a transverse B field, B(t),
Bx (t )  Py (t )
By (t )   Px (t )
B
dPx
P
   Py B0  Pz By   x ,
dt
T2
dPy
dt
   Pz Bx  Px B0  
Py
T2
,
dPz
P
   Px By  Py Bx   z   P0  Pz  G.
dt
T1
dPx
P
 w0 Py   Pz Px  x ,
dt
T2
dPy
dt
 w0 Px   Pz Py 
Py
T2
(1)
,
(2)
dPz
P
   Px Px  Py Py   z   P0  Pz  G.
dt
T1
(3)



B

P
 x  y 



 
B


Px 
 y



 w0   B0 




Taking (1) + i (2) and setting Px (t )  iPy (t )  eiwt P (t )

dP 
1
   Pz    i w  w0   P ,
d t 
T2 

2
dPz
P
  P  z   P0  Pz  G.
dt
T1
(4)
(3')
 dP

dPz

0
and

0
The steady state solutions 
.
dt
 dt

・Trivial solution:
・Non-trivial solution:
Peq  0, Pz eq 
P
eq

GT1
P0
GT1  1
1  1/ GT1 
G
1
eq
, with w =w0 .
 P0 
 , Pz 

 T2 
 T2
Spin oscillator
● Now we devise the transverse part of
the B field, B(t), to follow P
Bx (t )  Py (t )
By (t )   Px (t )
B(t)
B(t)
Spin detection
dPx
P
   Py B0  Pz By   x ,
dt
T2
dPy
dt
   Pz Bx  Px B0  
Py
T2
,
dPz
P
   Px By  Py Bx   z   P0  Pz  G.
dt
T1
Maser oscillation
transient
steady oscillation
Setup for the maser experiment
Si photodiode
・Bandwidth : 0 ～ 500 kHz
magnetic shield (4-layer)
・permalloy
B0
Solenoid coil (static field)
・B0 = 30.6 mG (I = 7.354 mA)
l/4 plate
Heater
T  70 C
spin precession signal
Pumping laser
・l = 794.76 nm
(Rb D1line)
・Dl = 3 nm
・Power ~ 11 W
PEM
129Xe
gas cell
18 mm
129Xe
: 230 torr
N2 : 100 torr
Rb : ~ 1 mg
Pyrex glass
SurfaSil coating
Probe laser
・DFB laser
・l = 794.76 nm
(Rb D1line)
・Dl = 8.4×10-6 nm
・Power : 15 mW
Spin polarization of 129Xe and Optical detection of nuclear precession
Spin polarization of 129Xe
Detection of precession of 129Xe
Transverse polarization transfer :
129Xe nuclei → Rb atoms (re-pol)
Optical pumping Rb atom
5P1/ 2
D1 line： 794.7 nm
ms  
1
2
ms  
1
2
Xe
Xe
129Xe
Rb
Rb
Xe
Circular polarization
(modulated by PEM)
Spin-echange in Rb-Xe
N2
129Xe
Detector
After
half-period precession
Rb
I
S
Xe
129Xe 129Xe
Rb
N2
Xe
B0
Probe laser beam :
single mode diode laser
(794.7nm)
5S1/ 2
Rb
Xe
Rb
Rb
Xe
Spin oscillator
“Optically coupled” spin maser
with a feedback field generated according to optical spin detection
Pumping and
relaxation effect
0
B0
①129Xe nuclear spin polarization
by optical pumping
Static magnetic field : B0  mG
Feedback system
Probe light
Feedback
torque
P(t)
Feedback coil
Feedback
circuit
② Optical detection of the spin
precession
Lock-in
detection
③Generation of a feedback field
precession signal
④Self-sustained spin precession
Photo
diode
P(t)
B(t)
Pumping light
Realization of maser oscillation at very low fields ( mG)
Suppression of drifts in the B0 field => Suppression of drifts in 
Magnetic Shield
Mirror
Heater
Fiber-coupled
Laser
Probe Laser
(DL-DFB)
PEM
Array-type
Laser
Glan Laser
prism
Ookayama Campus,
Tokyo Inst. of Technology,
Tokyo, Japan
Frequency determination
B0
Xe
Rb
Xe
 ref
VX
Lock-in
amplifier
35Hz
 out   0  ref
Function
Generator
νref Reference frequency
ν0 Xe precession freq.
fitting function
 (t )  tan 1
Phase [rad]
VX  cos( 2 ( ref  0 )t  (ref  0 ))
・Phase
Time [s]
Result
・Lock-in amplifier output signals
VY  sin( 2 ( ref  0 )t  (ref  0 ))
VY
Signal [V]
Xe
X
e
Lock-in Amplifier output
PhotoDiode
detector
 0 35.1Hz
f ( x)  2 ax  b
Δa = 9.310-9 Hz
freq. precision
VY (t )
VX (t )
Time [rad]
[From; T. Inoue et. al., Poster, INPC2010]
Frequency
Long term stability of the oscillation frequency
Solenoid current
Frequency
time (0 - 30,000 sec)
129Xe
cell temperature
At present,
there are a number of concerns:
・Do imperfections in spin detection, signal processing,
feedback field generation, ... affect the oscillation frequency?
・Does the presence of Rb atoms interfere the measurement?
・Does the low frequency operation really help in reducing the
spourious drifts?
These should be tested and investigated by using actual
setup.
Frequency pulling effect
●A phase deviation D in the
feedback field will induce a shift
in the Maser frequency.
Expt.
1

d
PT (t )    i w  w 0  iPz (t ) BT (t )
dt
 T2

BT t    ie i PT t 
1
 i w  w 0   e i Pz
T2
w  w0 
tan 
T2
Simulation
Ongoing developments
・Pumping laser
[T. Inoue, ... ]
[Inoue et al.]
・Double cell
[M. Tsuchiya, ... ]
・B0 stabilization
[T. Furukawa, ... ]
[Tsuchiya et al.]
NMOR magnetometry
B||
[Furukawa et al.]
φ
・Simulation study
[Hayashi et al.]
[H. Hayashi, T. Furukawa, ... ]
Paraffin coating
0.6
0.4
・Magnetometry
[T. Nanao, A. Yoshimi, ... ]
[Nanao, Yoshimi et al.]
0.2
0.0
z-0.2
fitting
-0.4
-0.6
-6.0 -4.0 -2.0
1
z 0.0
2.0
4.0 6.0
 d 
5
   4  10 G
dB

B 0
B 
HV application system preparation
[T. Inoue, ... ]
Picoammeter
Protection circuit
for picoammeter
High voltage
R : 1 MW
R : 1 MW
A
Cell
Transparent
electrode
HV
C : 2 nF
Leakage current test
- Cubic cell size : 20 mm × 20 mm × 20 mm
Pyrex glass (corning 7740)
- Transparent electrode : ITO (Indium Tin Oxide)
transmittance ~ 85%@795 nm
size : 30 mm × 30 mm × 1.75 mm
resistance : ~ 30 W
Leakage current [nA]
Xe cell for an E-field
a trial piece
spark
HV [kV]
HV application system preparation
Next step…
- Smaller cell (10 mm gap)
- Using 2 high voltage source (positive and negative)
- N2 or SF6 gas atmosphere
- Low pass filter for reducing the noise output by HV source …
Magnetic field stabilization
Current fluctuation
300nA,
~40ppm
In magnetic shield:
~28 mG magnetic field
with a solenoid coil
& stabilized current source
(applying 7mA current)
Current instability
= magnetic field fluctuation
→ Frequency instability
1.5mHz
~40ppm
Fluctuation of Xe precession
Frequency instability :
mostly due to current fluctuation
Previous current source
- stabilized current source
drift : <50nA in a few hour
Current
source
~ 7 mA
- slow & large drift (up to 1uA)
in long-term operation
A new current supply system
Feedback of current fluctuation
(measured with Dig. Voltmeter)
to correct the current drift
Current
source 1
~ 6.5 mA
Current
source 2
~ 0.5 mA
Digital
Voltmeter
Feedback
Two current sources
are installed in parallel
for setting resolutions
Using an accurate voltmeter
with a reference resistance
to obtain high resolutions
Performance of new current source
Stability improved !
Fluctuation:<1/200
This fluctuation is mainly
due to the accuracy of
current measurement.
Conclusion: The current stability is improved successfully (x200)
with the feedback of current fluctuation.
stability – limited by accuracies of current measurement
Future : More accurate measurement of current drift
→ More stabilized magnetic field for EDM measurement
Future
Spherical cell
・good symmetry
・Reflection
⇒ lowering of the
pumping efficiency?
Taper Amplifier
Optical Isolator
Cubic cells
Introduction of a narrow-line laser
(TA DFB, TOPTICA)
Power :
~ 430 mW
line width : ~ 4MHz
(cf. pressure broadening ~ 7.5 GHz)
20 times enhanced pumping efficiency
  ~ 107 sec -1
DFB Laser Diode
=> suppression of amplitude fluctuations
Setup
ポンピング
レーザー
Double cell for 129Xe gas
偏極度測定部分
ポンピング部分
pick-up
(偏極生成部分)
coil
保持磁場用
コイル
129Xe
: 227torr
N2 : 133torr
Rb
パイレックスガラス
SurfaSil コーティング
RF coil
偏極度測定装置
pick-up coil
Cell test bench
Current problems
pick-up coil 固定されていない
→測定の再現性が低い, 調整が困難, 振動に弱い
pick-up coil が振動
→NMRシグナルと同じ周波数であるRFシグナルを検出
→ノイズの発生
material：
PEEK
New system
・ Incorporation of anti-vibration system
・ Orthogonality adjustment mechanism for pick-up coil
High-precision, high-reproducibility
assesment system for 129Xe cells
trim coil
Simulation study of the frequency precision
Incorporate the phase and amplitude fluctuations of the maser signal.
Vx  A sin 
 n   n 1  2Dt   fluc   peri
A : シグナル振幅
ε : 振幅のゆらぎ
ν：測定周波数
φfluc：位相ゆらぎ
φperi：周期変動
Phasedeviation[rad]
A  A0   (t )
Signal [V]
Phase deviation[rad]
Time [s]
Time [s]
Time [s]
Simulation results
Frequency Precision[Hz]
Vx  A sin 
A  A0   (t )
 n   n 1  2Dt   fluc   peri
Experiment
Simulation
A ,  ,   ≈ the experiment
A  ≈ the experiment,  peri ≈ 0.5
A ,  ,   ≈ 1/10
2.3ｘ10-10 Hz
6.7ｘ10-11 Hz
2.0x10-11 Hz
←1.9x10-30 ecm
(E=10kV)
Time [s]
Half a day
1day
12days
Should reach a 10-10 Hz precision
in a 2-day measurement !!
Magnetometry； Non-linear MagnetoOptical Rotation (NMOR) on Rb atoms
Field precision required in EDM measurements
d A ~ 10
B +E
-28
(NMOR; Nonlinear Magneto-Optical Rotation)
ecm
@ E=10kV/cm
z
Required frequency precision
y
Resonant optical rotation
in Rb vapor
Linear polarized light
k
Rb atom
f  1 nHz
w+ t
B
x
Field
B  1 pG
D. Budker et al.,PRA 62 (2000) 043403.
B ~ 1 pG/ Hz
Optical Pumping magnetometers (Rb, Cs)： 30 pG/ √Hz
Advantages:
Magnetometry with SQUID：
2-3 fT/ √Hz = 20-30 pG /√Hz @ He temp.
50-60 fT/ √Hz = 0.5 – 0.6 nG/ /√Hz @ liq. N2 temp.
High-Q resonator → 0.08 fT/√Hz = 0.8 pG /√Hz
Narrow width
Operation at room temp.
low field
NMOR
原理
直線偏向光と原子の相互作用
1) 直線偏向光 により原子は alignment 状態になる
→ 原子集団の蒸気は linear dichroism を持つ
(F’=0)
+
gB
mF = -1 mF = 0 mF = +1
(F=1)
右・左円偏向成分に対する原子系屈折率
n w   1  20
Rotation angle (mrad)
0.6
0.4
0
2w  w0  g F  B Bz   i 0
0.2
0.0
直線偏向面の回転
-0.2
-0.4
l
2 g F  B Bz

0
  n  n  
2 2 g F  B Bz
-0.6
2
2l0


2
g

B
-10
-5
0 1   5 F B 10
z
0



0
l


2) 原子 alignment が磁場の周りを歳差運動する
→ dichroism の軸が回転する
3) 回転する dichroic 軸を持つ原子と入射直線偏光ビームとの
相互作用で偏光面が回転する
基底状態
1
 mF  1  mF  1 
2
1
 mF  1  mF  1 
 
2
0  mF  0
 
Summary
● Precession of 129Xe spins is maintained for unlimitedly long times, by
application of a feedback field generated from optically detected spins. The
merit of this optically coupled spin maser as a scheme for the EDM search is
the capability of operation at very low B0 fields, as mG or below.
● Frequency precision presently reached is 9.3 nHz, which corresponds to an
EDM sensitivity of 910-28 ecm (E=10kV/cm).
● There still remain drifts/fluctuations in the maser frequency that are correlated
with ambient temperature and noises. Improvements and further developments
are under progress.
・Reinforcement of 129Xe polarization by introducing a narrow-line high-power
TA-DFB pumping laser
・Stabilization of solenoid current
・Stabilization of cell temperature by means of a heat transfer fluid GALDEN
・Cell development for the E-field application
・Magnetometry with NMOR,
aiming at detection of d(129Xe) in a 1028 -1029 ecm regime.