Precision measurements of the zero temperature dielectric constant and density of liquid $^4$He

TL;DR

This study uses microwave cavity resonances to precisely measure the dielectric constant and density of superfluid helium-4 at near-zero temperature, revealing discrepancies with prior data and highlighting the method's potential for metrology.

Contribution

It introduces a high-precision microwave cavity technique for measuring helium-4's dielectric constant and density at ultra-low temperatures, addressing previous measurement discrepancies.

Findings

Discrepancy between low and high frequency dielectric constant measurements.

Pressure-dependent density values differ from previous reports.

Microwave cavities show promise for helium property metrology.

Abstract

The resonant frequencies of three-dimensional microwave cavities are explicitly dependent on the dielectric constant of the material filling the cavity, making them an ideal system for probing material properties. In particular, dielectric constant measurements allow one to extract the helium density through the Clausius-Mossotti relation. By filling a cylindrical aluminum cavity with superfluid helium, we make precision measurements of the dielectric constant of liquid $^4$He at saturated vapor pressure for range of temperatures 30 -- 300 mK and at pressures of 0-25.0 bar at 30 mK, essentially the zero temperature limit for the properties of $^4$He. After reviewing previous measurements, we find systematic discrepancy between low and high frequency determination of the dielectric constant in the zero-temperature limit and moderate discrepancy with previously reported values of pressure-dependent density. Our precision measurements suggest 3D microwave cavities are a promising choice for refining previously measured values in helium, with potential applications in metrology.