Interfaces of solid and liquid helium exhibit many physical phenomena. At very low temperatures the solid-liquid interface becomes mobile enough to allow a periodic melting-freezing wave to pro-pagate along the surface. These crystallization waves were experimentally confirmed in ^4He decades ago, but in ^3He they are only observable at extremely low temperatures (well below 0.5 mK). This presents a difficult technical challenge to create a measurement scheme with very low dissipation.
We have developed a method to use a quartz tuning fork to probe oscillating helium surfaces. These mechanical oscillators are highly sensitive to interactions with the surrounding medium, which makes them extremely accurate sensors of many material properties. By tracking the fork's resonant frequency with two lock-in amplifiers, we have been able to attain a frequency resolution below 1 mHz. The shift in resonant frequency can then be used to calculate the corresponding change in surface level, if the interaction between the fork and the helium surface is understood.
One of the main goals of this thesis was to create interaction models that could provide quantitative estimates for the calculations. Experimental results suggest that the liquid-vapour surface forms a column of superfluid that is suspended from the tip of the fork. Due to the extreme wetting properties of superfluids, the fork is also coated with a thin (∼ 300 Å) layer of helium. The added mass from this layer depends on the fork-surface distance. Oscillations of the surface level thus cause periodic change in the effective mass of the fork, which in turn modulates the resonant frequency. For the solid-liquid interface the interaction is based on the inviscid flow of superfluid around the moving fork. The added hydrodynamic mass increases when the fork oscillates closer to the solid surface. Crystallization waves below the fork will thus change the fork's resonant frequency.
We were able to excite gravity-capillary and crystallization waves in ^4He with a bifilarly wound capacitor. Using the quartz tuning fork detection scheme we measured the spectrum of both types of waves at 10 mK. According to the interaction models developed in this thesis, the surface level resolution of this method was ∼ 10 μm for the gravity-capillary waves and ∼ 1 nm for the crystallization waves. Thanks to the low dissipation (∼ 20 pW) of the measurement scheme, our method is directly applicable in future ^3He experiments.
