Helium is the epitome of quantum mechanics because of its small mass and inertness to react. It does not freeze even till absolute zero – unless higher pressure is applied. This unique feature makes liquid and solid helium the purest substances as all other impurities would be frozen out and absorbed by interfaces, with the only exception being its own isotopic impurities, namely ³He in ⁴He or vice versa. The isotopic impurities are extremely mobile and feature with different quantum statistics, therefore even a tiny amount can significantly change properties of liquid or solid helium.

Furthermore, their distribution and behavior are highly sensitive to environment, making their dynamics hard to predict. This is one of the main reasons that quantitative studies on their effects on helium properties are still lacking.

Recently, a group of researchers led by Prof. CHENG Zhigang from the Institute of Physics of the Chinese Academy of Sciences, in collaboration with Prof. John Beamish from University of Alberta, proposed a novel and convenient technique for in-situ measurement of isotopic impurity concentration in liquid helium.

Even with almost the same polarizability, atomic volumes of the two isotopes of helium are different by about 30%. Based on Clausius-Mossotti relation, this leads to a distinct contrast in their dielectric constants, hence dielectric constant of a ³He/⁴He mixture can be used as a measure of its impurity concentration.

The researchers immersed a concentric capacitance in liquid helium, its dielectric constant can be measured in real-time via capacitance. Liquid pressure was simultaneously measured in order to exclude the capacitance change contributed by pressure variations. Without sophisticated instrument, the resolution can easily reach 40 ppm by only using a commercial capacitance bridge. Resolution can be improved by one or two orders of magnitude if more careful homemade bridge is employed.

To test the technique, the researchers prepared solid-liquid coexisting ⁴He samples, and systematically doped ³He impurities. Using the technique, they observed the aggregation of ³He atoms in the liquid phase at low temperatures, and they migrated to solid phase once temperature was raised.

With the benefit of real-time measurement, the dynamics of the migration could be quantitatively studied: the diffusion time constant decreased as temperature was increased, and the behavior can be explained by a thermally activated process, the extracted activation energy suggests that ³He atoms diffuse along grain boundaries in the solid phase.

This novel technique advances the state-of-the-art in monitoring isotopic impurities in liquid helium with unprecedented resolution. With simple design and setup, the technique can be conveniently generalized to a broad range of experimental studies. It enables quantitative studies on dynamics of isotopic impurities and their impact on helium properties.

This study was published on Physical Review Research entitled "In situ monitoring distribution and migration of ³He in liquid-solid ⁴He mixtures".

The study was supported by the Key Research Program of Frontier Sciences, CAS, the National Key R&D Program of China, the National Science Foundation of China, and a grant from NSERC Canada.