Turbulence in a superfluid in the zero temperature limit consists of a dynamic tangle of quantized vortex filaments. Different types of turbulence are possible depending on the level of correlations in the orientation of vortex lines. We provide an o
verview of turbulence in superfluid $^4$He with a particular focus on recent experiments probing the decay of turbulence in the zero temperature regime below 0.5 K. We describe extensive measurements of the vortex line density during the free decay of different types of turbulence: ultraquantum and quasiclassical turbulence in both stationary and rotating containers. The observed decays and the effective dissipation as a function of temperature are compared with theoretical models and numerical simulations.
We have studied the interaction of metastable $^4$He$_2^*$ excimer molecules with quantized vortices in superfluid $^4$He in the zero temperature limit. The vortices were generated by either rotation or ion injection. The trapping diameter of the mol
ecules on quantized vortices was found to be $96pm6$,nm at a pressure of 0.1,bar and $27pm5$,nm at 5.0 bar. We have also demonstrated that a moving tangle of vortices can carry the molecules through the superfluid helium.
In these torsional oscillator experiments the samples of solid $^4$He were characterized by measuring their thermal conducitvity. Polycrystalline samples of helium of either high isotopic purity or natural concentration of $^3$He were grown in an ann
ular container by the blocked-capillary method and investigated before and after annealing. No correlation has been found between the magnitude of the low-temperature shift of the torsional oscillator frequency and the amount of crystalline defects as measured by the thermal conductivity. In samples with the natural $^3$He concentration a substantial excess thermal conductivity over the usual $T^3$ dependence was observed below 120 mK.
