Kerr Effect in Liquid Helium at Temperatures Below the Superfluid Transition

The electro-optical Kerr effect induced by a slowly varying electric field in liquid helium at temperatures below the $\lambda$ point is investigated. The Kerr constant of liquid helium is measured to be $(1.43\pm {0.02}^{(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})}\pm {0.04}^{(\mathrm{s}\mathrm{y}\mathrm{s})})\times {10}^{-20}(\mathrm{c}\mathrm{m}/\mathrm{V}{)}^2$ at $T=1.5\mathrm{K}$. Within experimental uncertainty, the Kerr constant is independent of temperature in the range $T=1.5\mathrm{K}$ to $2.17\mathrm{K}$, which implies that the Kerr constant of the superfluid component of liquid helium is the same as that of normal liquid helium. Pair and higher correlations of He atoms in the liquid phase account for about 23% of the measured Kerr constant. Liquid nitrogen was used to test the experimental setup; the result for the liquid nitrogen Kerr constant is $(4.38\pm 0.15)\times {10}^{-18}(\mathrm{c}\mathrm{m}/\mathrm{V}{)}^2$. Kerr effect can be used as a noncontact technique for measuring the magnitude and mapping out the distribution of electric fields inside these cryogenic insulants.

Figure 1

A schematic top view of the experimental apparatus.

Figure 2

The Kerr effect in liquid helium at $T=1.5\mathrm{K}$: induced ellipticity as a function of the electric field between the electrodes. Integration time for each point is 1000 s. Potential difference between the electrodes is shown on the upper scale. Larger electric fields were not applied because of breakdown in liquid helium.

Figure 3

The liquid helium Kerr constant in the temperature range $T=1.5\mathrm{K}$ to $T=2.17\mathrm{K}$. The electric field between the electrodes is $69\mathrm{k}\mathrm{V}/\mathrm{c}\mathrm{m}$, and the temperature is scanned up or down. Each point on the graph is obtained by averaging the Kerr effect-induced ellipticity readings over the interval of 0.1 K. The dashed line indicates the average over all the points, which agrees with the value of $K_{LHe}$ given in the text.