1. Our approach to EDM
Earth’s field New physics
10-16
(μnHo/E) Statistical < 10-27 e·cm
n EDM
e EDM ✦ Increase UCN density*
10-18
∼
∼
10-24 Systematic < 10-27 e·cm
EDM
10-25 ✦ Buffer gas nuclear spin
upper limit
10-26 comagnetometer*
statistical 1.5×10-26 ✦ Spherical coil*
10-27
systematic 0.7×10-26
10-28 ✦ R2 ×1/10*
e·cm ✦ Meissner shield
* our work
Japanese collaborators
Y. Masuda, S.C. Jeong, Y. Watanabe, T. Adachi (KEK)
K. Asahi (TIT)
K. Matsuta, M. Mihara, R. Matsumiya, D. Nishimura (Osaka)
K. Hatanaka , I. Tanihata (RCNP)

2. EDM (dn) measurement
n spin s
Ho E
1 μT 10 kV/cm
UCN bottle

3. EDM (dn) measurement
n spin s
1st RF pulse
γH1t = π/2
Ho E
1 μT 10 kV/cm
UCN bottle

4. EDM (dn) measurement
n spin s
ωotc RF phase
ωotc precession phase
ωo: 2μnHo ± 2dnE
Ho E
1 μT 10 kV
t : precession time
/cm c
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s UCN bottle

5. EDM (dn) measurement
n spin s
2nd π/2 ωtc RF phase
RF pulse
ωotc precession phase
for neutron ωo: 2μnHo ± 2dnE
Ho E
polarimetry 1 μT 10 kV
t : precession time
/cm c
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s UCN bottle
Pncos(ω-ωo)tc
RF frequency ω

6. EDM (dn) measurement
n spin s
2nd π/2 ωtc RF phase
RF pulse
ωotc precession phase
for neutron ωo: 2μnHo ± 2dnE
Ho E
polarimetry 1 μT 10 kV
t : precession time
/cm c
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s UCN bottle
Pncos(ω-ωo)tc
E reversal for extraction of dn
RF frequency ω
δdsta = h/{2PnEtc√N}
Pn : UCN polarization
N : number of UCN

7. tc=
Ramsey resonance t
100ms
t
Effect of Pncos(ω-ωo)tc two coherent RF pulses
%!!!
(ω-ωo)tc = -5π -π π 5π
31,3,:6.1.0,-/66501,.4,"µ;!
)*+,-./012,34156,30378956!
-3π 3π
$!!!
#!!!
"!!!
-4π
-2π 0 2π 4π
!!
&!!! &&!! '!!! '&!! (!!!
<65=/50-8,>?9@!

8. Systematic error of ILL EDM
1st π/2 2nd π/2
RF pulse RF pulse
ωtc RF phase
ωotc precession phase
n spin s
Ho E
1 μT 10 kV /cm
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s
EDM cell

9. Systematic error of ILL EDM
1st π/2 2nd π/2
RF pulse RF pulse
ωtc RF phase
ωotc precession phase
n spin s
Ho E
1 μT 10 kV /cm
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s
∂Ho/∂z = 1 nT/m
EDM cell

10. Systematic error of ILL EDM
1st π/2 2nd π/2
RF pulse RF pulse
ωtc RF phase
ωotc precession phase
n spin s
Ho E
1 μT 10 kV /cm
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s
∂Ho/∂z = 1 nT/m
E×v/c2
Phase shift arises from transverse fields, (∂Ho/∂z)R/2 andEDM cell
z
E
Ho y
UCN spin x

11. Systematic error of ILL EDM
1st π/2 2nd π/2
RF pulse RF pulse
ωtc RF phase
ωotc precession phase
n spin s
Ho E
1 μT 10 kV /cm
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s
∂Ho/∂z = 1 nT/m
E×v/c2
Phase shift arises from transverse fields, (∂Ho/∂z)R/2 andEDM cell
z
E
Ho y
vxyE/c2
γ(vxyE/c2)τ
τ = 2R/vxy
vxy << 2π/ω0
UCN spin x

12. Systematic error of ILL EDM
1st π/2 2nd π/2
RF pulse RF pulse
ωtc RF phase
ωotc precession phase
n spin s
Ho E
1 μT 10 kV /cm
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s
∂Ho/∂z = 1 nT/m
E×v/c2
Phase shift arises from transverse fields, (∂Ho/∂z)R/2 andEDM cell
z
E
Ho y
vxyE/c2 γ(∂H0z/∂z)(R/2)τ ×
γ(vxyE/c2)τ
τ = 2R/vxy
(∂H0z/∂z)(R/2) vxy << 2π/ω0
UCN spin x

13. Systematic error of ILL EDM
1st π/2 2nd π/2
RF pulse RF pulse
ωtc RF phase
ωotc precession phase
n spin s
Ho E
1 μT 10 kV /cm
(ω-ωo)tc
Neutron precession
S = exp{i(μ·H0 + dn·E)/h·t}
μ, dn ∝ s
∂Ho/∂z = 1 nT/m
E×v/c2
Phase shift arises from transverse fields, (∂Ho/∂z)R/2 andEDM cell
z
E Motion induced phase shift
Ho y in cylindrically symmetric Ho
vxyE/c2 γ(∂H0z/∂z)(R/2)τ ×
Δω∝
γ(vxyE/c2)τ
γ(∂H0z/∂z)(R/2)τ)·γ(vxyE/c2)τ /τ
τ = 2R/vxy = γ2(∂H0z/∂z)(R2/c2)·E
(∂H0z/∂z)(R/2) vxy << 2π/ω0
x false EDM
UCN spin

14. Motion induced systematic error
Geometric Phase Effect (GPE)
Pendlebury et al, Phys. Rev A70(2004), Golub and Lamoreaux, Phys. Rev A71(2005)
For cylindrical symmetric field
for for
UCN atom
dafn = -h/4 (∂H0z/∂z)/H0z2 vxy2/c2 = 1×10-27 e·cm
dafHgn = h/8 ⎮γnγHg⎮ (∂H0z/∂z) R2/c2 = 5×10-26 e·cm
for 199Hg at H0z = 1 μT, ∂H0z/∂z = 1 nT/m and R = 0.5 m

15. Nuclear spin magnetometer
dafNn = - /4·γn JNγN (∂H0z/∂z)·R2/c2
= 5×10-26 e·cm for 199Hg, ∂H0z/∂z = 1 nT/m, R = 0.5 m
σa at ρ for
Isotope JN g (γN=gμN/h)
2200 m/s τ=1/(σaρv)=500 s
n 1/2 -1.913
199Hg
1/2 0.5026 2150 b (3x1010/cc, photon)
(ILL)
3He
1/2 -2.128 5333 b 1012/cc, SQUID
(SNS)
129Xe
1/2 -0.777 21 b 2.5x1014/cc, SQUID
(Ours)
133Cs
7/2 2.579 29 b
(PSI)

16. Our idea for the suppression of the false EDM

17. Our idea for the suppression of the false EDM
R= Ho(UCN)/Ho(199Hg) = 1±∆h<∂H0z/∂z>/H0z
∆h = hav(UCN) - hav(199Hg) = 3 mm
Pendlebury et al

18. Our idea for the suppression of the false EDM
R= Ho(UCN)/Ho(199Hg) = 1±∆h<∂H0z/∂z>/H0z
∆h = hav(UCN) - hav(199Hg) = 3 mm
Pendlebury et al

19. Our idea for the suppression of the false EDM
R= Ho(UCN)/Ho(199Hg) = 1±∆h<∂H0z/∂z>/H0z
∆h = hav(UCN) - hav(199Hg) = 3 mm
Pendlebury et al
Earth’s rotation has serious effect
because sign of γ199Hg is opposite to γn.
drot = 2.5×10-26 e·cm, Golub
Sign of γ129Xe is the same as γn.
129Xe is not serious.

20. Our idea for the suppression of the false EDM
R= Ho(UCN)/Ho(199Hg) = 1±∆h<∂H0z/∂z>/H0z
∆h = hav(UCN) - hav(199Hg) = 3 mm Suppression by atomic collision
Pendlebury et al
199Hg-4He
Earth’s rotation has serious effect
because sign of γ199Hg is opposite to γn.
drot = 2.5×10-26 e·cm, Golub
Sign of γ129Xe is the same as γn.
129Xe is not serious.

21. Our idea for the suppression of the false EDM
R= Ho(UCN)/Ho(199Hg) = 1±∆h<∂H0z/∂z>/H0z
∆h = hav(UCN) - hav(199Hg) = 3 mm Suppression by atomic collision
Pendlebury et al
129Xe-129Xe 199Hg-4He
0.0005
Earth’s rotation has serious effect
because sign of γ199Hg is opposite to γn. 129Xe
drot = 2.5×10-26 e·cm, Golub λ = 1/nσ << 0.05 cm
Sign of γ129Xe is the same as γn. n = 2.5×1014/cc, σXe-Xe >> 838Å2
129Xe is not serious.

22. 129Xe-SQUID (or SERF) magnetometer
Dipole field B = μ0/4π (3r(μ·r) - μr2)/r5
= 0.98×10-13 T at r = 0.1 m
129Xe
μ = -3.9239×10-27 J/T
n = 2.5×1017/liter
μ
S = 0.01 m2
Φ = 0.47 Φ0 cos(ω0t) Tm2
Φ0 = h/2e = 2.067833667×10-15 Tm2

23. 129Xe-SQUID (or SERF) magnetometer
Dipole field B = μ0/4π (3r(μ·r) - μr2)/r5
= 0.98×10-13 T at r = 0.1 m
129Xe
SQUID Tristan Tech.
BMS-L LTS μ = -3.9239×10-27 J/T
sensitivity 1fT, n = 2.5×1017/liter
5μΦ0/√Hz
(or spin-exchange μ
relaxation free SERF Cs
magnetometer)
S = 0.01 m2
Φ = 0.47 Φ0 cos(ω0t) Tm2
Φ0 = h/2e = 2.067833667×10-15 Tm2

24. Discharge problem
Townsend discharge is triggered by photoelectric current I0
avalanche effect
I = I0 eαnd
αn : first Townsend ionization coefficient d : distance between the plate
Electric grow discharge
P = 0.1 ~ 1 torr : N = 3.5×(1016 ~ 1015)/cc
Grow discharge disappears at
P = 0.01 torr : N = 3.5×1014/cc

25. Discharge problem
129Xe Ne Magneto Optical Trap,
λ = 1/nσ << 0.05 cm Phys.Rev.A78(2008)042712,
n = 2.5×1014/cc σNe-He 164Å2, σNe-Ne 500Å2,
σXe-Xe >> 838Å2 σNe-Ar 838Å2
Townsend discharge is triggered by photoelectric current I0
avalanche effect
I = I0 eαnd
αn : first Townsend ionization coefficient d : distance between the plate
Electric grow discharge
P = 0.1 ~ 1 torr : N = 3.5×(1016 ~ 1015)/cc
Grow discharge disappears at
P = 0.01 torr : N = 3.5×1014/cc

26. Thermoelectron ?
Work function Electron emission
from electrode
I(T) ∝ T2 e-W/kT
kT = 25.8×10-3 eV
at 300K
= 14.2×10-3 eV
at 165K
W ~4 eV
I(165K)/I(300K)
= 0.3×e-127
= 3×10-56
low temperature may
suppress discharge

27. We built a spherical coil for Ho coil 2008
z
r0 d
three dimensional dipole
dz ~ (Ni/6)(r0/r)2cos
i
divB = 0
r0
uniform z-directed field
~ -(Ni/3)(r/r0)cos

28. We built a spherical coil for Ho coil 2008
z
r0 d
three dimensional dipole
dz ~ (Ni/6)(r0/r)2cos
i
divB = 0
r0
uniform z-directed field
~ -(Ni/3)(r/r0)cos
place in a superconductor shielding

29. We have built
a Ramsey resonance apparatus
Spherical coil 2008~2009
Door valve
Spin flipper
Polarizer/analyzer
Rotary valve
UCN detector

30. We have built
a Ramsey resonance apparatus
Spherical coil 2008~2009
Door valve
π/2 RF coil
Spin flipper
Polarizer/analyzer
Rotary valve
EDM cell
UCN detector

31. High voltage will be
applied in FY2010
+250 kV
-250 kV

32. Comparison with world’s EDM
magnetic
EDM cell H0 field magnetometer
shielding
small spherical coil μ metal 129Xe buffer gas
Ours room
temperature cylindrical superconductor co-magnetometer
Sussex large solenoid μ metal n at E=0
RAL He-II cylindrical superconductor magnetometer
large cosθ coil μ metal 3He
SNS
He-II non cylindrical superconductor co-magnetometer
large cosθ coil Cs multi-
PSI room μ metal
magnetometer
temperature non cylindrical