1. Alex Sushkov Dima Budker Valeriy Yashchuk (UC Berkeley) Kerr Effect-based Measurement of the Electric Field

2. Kerr Effect Kerr effect: appearance of birefringence in an initially isotropic medium, induced by an applied external electric field:  n = n || -n  = KE 2 For input light polarized at 45 o to E, the induced ellipticity:  =  L  n/ = (  L/ )KE 2 K is related to hyperpolarizability  : P =  E +  E 3 /6 + …

3. Why do it? Measure the magnitude of an electric field. Measure the spatial and temporal dependence of an electric field. Investigate the structure of liquid helium: - pair and higher correlations of atoms in the liquid, - Kerr virial coefficients, - effect of temperature and superfluidity.

4. Experimental Setup ArXiv: physics/0403143

5. Some apparatus details Cryogenics: Janis pumped helium cryostat with optical access, T min = 1.5 K. High-voltage cables: carbon steel wire insulated with teflon heat-shrink. Breakdown in LHe: - breakdown in LHeII at 70 kV/cm - no breakdown in LHeI observed up to 130 kV/cm. Polarimeter: - 785 nm diode laser, - electro-optic modulator, - lock-in detection at 50 kHz, - room-T sensitivity  10 -7 rad/Hz 1/2.

6. Results: LN 2 Measured Kerr constant for LN 2 at 73 K: K = (4.38  0.15)  10 -18 (cm/V) 2 Published value: (K.Imai et. al., Proceedings of the 3rd Int. Conf. On Prop. and App. Of Diel. Mat., 1991 Japan) K = 4.3  10 -18 (cm/V) 2 (no error given)

7. Results: LHe Measured Kerr constant for LHe at 1.5 K: K = (1.43  0.02 (stat)  0.04 (sys) )  10 -20 (cm/V) 2

8. T-dependence: LHe Within the experimental error, the LHe Kerr constant does not depend on temperature in the range 1.5 K to 2.2 K.

9. Theoretical interpretation Superfluidity: absence of temperature dependence means that superfluidity does not affect the Kerr constant of LHe. He atom hyperpolarizability:  = (44.2  0.8) atomic units (Tammer et al.)  K LHe  (1.10  0.02)  10 -20 (cm/V) 2 Van der Waals complexes: polarizability anisotropy of complexes of two or more He atoms contribute 23% to K LHe.

10. Measuring the electric field in the neutron EDM experiment Electric field requirements:  E = 50 kV/cm.  1% uniformity over the cell volume.  < 1% drift over 500 seconds.  diagnostics for the HV test set-up. Signal to be measured: assuming sample length L = 30 cm, the Kerr ellipticity is   2  10 -5 rad. Sensitivity: with sensitivity 10 -7 rad/Hz 1/2, we get  E/E  5  10 -3 in a 1 second measurement. Challenge: achieve this sensitivity at 300mK.

11. A cold magnetometer Goal: shot-noise limited sensitivity of  B ~ 3  10 -13 Gauss/Hz 1/2