# Presentation: 211671

## Kerr Effect-based Measurement of the Electric Field

**Alex Sushkov**
**Dima Budker**
_**Valeriy Yashchuk**_
- (UC Berkeley)
*Neutron EDM Collaboration Meeting** *
*Los Alamos National Laboratory** *
*June 2, 2003*

**Kerr Effect-based Measurement ****of the ****Electric Field**

**:**

- Recent Developments

## Slide 2

## 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 d****n****=10****-28**** e ********cm**

- Electric field monitoring ~ 0.1% -1%

## The Kerr Effect 

- Uniaxial E-field-induced anisotropy:
-                        n = n-n= KE**0**2
- For input light polarized at 45o to E, the induced ellipticity:		      = Ln/ = (L /) KE**0**2
- 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

- Graduate student A. Sushkov

- Electrode Assembly

- Laser

- Home-made cryogenic HV cable

- HV cable- connector

- Copper electrodes l=38 mm gap=6 mm

- Thin-wall st. steel tube

## 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)

## LHe Kerr Constant Measurements

## Results: LHe Kerr constant (T1.3 K)

- 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)

## Modulation Polarimeter

**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 ******** J****2****(A) sin(2********t) + (1+********) ******** J****1****(A) sin(********t) + ...**

- (,)

- Lock-in Amplifier

## 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