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 pressuredependent density. Our precision measurements suggest 3D microwave cavities are a promising choice for refining previously measured values in helium, with potential applications in metrology.

Superfluid 4 He (He-II) is a widely studied model system for exploring finite-size effects in strongly confined geometries. Here we study He-II confined into mm-scale channels of 25 and 50 nm height, at arbitrarily high pressures using a nanofluidic Helmholtz resonator. We find that the superfluid density is measurably suppressed in the confined geometry from the transition temperature down to 0.6 K. Importantly, this suppression can be accounted for by roton-like thermal excitation with an energy gap of 5 K. This finding sheds light on the unexplained lack of finite-size scaling of suppression of the superfluid density. Additionally, the strong confinement allows for observation of the Kosterlitz-Thouless transition for the first time at arbitrary pressure.