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

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%

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

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 ?

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

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

LHe Kerr Constant Measurements

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

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) + …

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

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:  = /4  max Kerr effect  = 0 or /2  zero Kerr effect

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