1. Kerr Effect-based Measurement of the Electric Field:
Recent Developments
Alex Sushkov
Dima Budker
Valeriy Yashchuk
(UC Berkeley)
Neutron EDM Collaboration Meeting
Los Alamos National Laboratory
June 2, 2003

3. Electric field monitoring ~ 0.1% -1%
E-field requirements
Homogeneity over cell volume
Stability over 500 s < 1 %
Reversibility
This reduces E-field-related systematics to < 510-10 Hz,
i.e. one tenth of the EDM shift for dn=10-28 e cm
Electric field monitoring ~ 0.1% -1%

4. The Kerr Effect  n = n-n= KE02
Uniaxial E-field-induced anisotropy:
n = n-n= KE02
For input light polarized at 45o to E, the induced ellipticity:  = Ln/ = (L /) KE02
Circular analyzer 
Achievable sensitivity:   10-8 rad Hz-1/2

5. Electric Field Measurement
Kerr constant for LHe estimated from experimental data for He at 300K: K  1.710-20(cm/V)2
Electric field: E0 = 50 kV/cm
Sample length: L = 10 cm
Induced ellipticity:   10-5 rad
A 1s measurement gives accuracy (  10-8 rad Hz-1/2):
E0/E0  510-4
? Kerr constant for superfluid He ?
? Polarimeter sensitivity ?

6. Test set-up at Berkeley
Cryostat (T  1.4 K)
with optical access
Laser
Thin-wall st. steel tube
Home-made cryogenic HV cable
Copper electrodes l=38 mm gap=6 mm
HV cable- connector
Graduate student A. Sushkov
Electrode Assembly

7. Results: LN2 Kerr constant
Measurement:
K = 4.2(1)10-18 (cm/V)2
Literature result:
K = 4.010-18 (cm/V)2
K.Imai et. al., Proceedings of the 3rd Int. Conf. On Prop. and App. Of Diel. Mat., 1991 Japan)
E = 60 kV/cm
max

8. LHe Kerr Constant Measurements

9. Results: LHe Kerr constant (T1.3 K)
Measurement:
K = 2.45(13)10-20 (cm/V)2
Theoretical value:
K = 2.010-20 (cm/V)2
(1s, 2s, 2p levels)
E = 50 kV/cm
max

10. Modulation Polarimeter
(,)
Lock-in Amplifier
Home-made diode laser: battery current supply, 780 nm
Photo-Elastic Modulator: frequency = 50kHz,
phase modulation amplitude 0A
Polarizers: nearly crossed, opening angle   1
Sample: introduces rotation , ellipticity ; ,  1
The polarimeter signal: 2 + 2  J2(A) sin(2t) + (1+)  J1(A) sin(t) + …

11. Polarimeter Performance
Noise: 310-7 rad/(Hz)1/2
Drift: 10-5 rad in 500 seconds

12. Possible improvements
Light interference on optical elements due to
laser frequency drift and temperature fluctuation
(currently the suspected cause of the large drifts seen in the polarimeter)
 Anti-reflection coating
Laser frequency stabilization
Temperature stabilization
Imperfections of windows
(give an offset ellipticity of  2 degrees, which can fluctuate due to stresses)
 Find windows with small stress-optic coefficient
Photo-elastic modulator imperfections
(give an offset ellipticity of  1 degree drifting with temperature)
 Find $$$
Kerr effect modulation
(modulate the angle  of the incoming linear polarization with respect to the electric field:  = /  max Kerr effect  = 0 or /2  zero Kerr effect

13. Electric Field Measurement Sensitivity
Kerr constant for LHe K = 2.510-20(cm/V)2
Electric field: E0 = 50 kV/cm
Sample length: L = 10 cm
Induced ellipticity:  = 310-5 rad
A 1s measurement gives accuracy (  310-7 rad Hz-1/2):
E0/E0  510-3
NEXT STEPS:
Polarimeter drift and sensitivity improvement
LHe Kerr-constant temperature dependence measurement