  Micro and nanomechanical resonators with ultra-low dissipation have great
potential as useful quantum resources. The superfluid micromechanical
resonators presented here possess several advantageous characteristics:
straightforward thermalization, dissipationless flow, and in situ tunability.
We identify and quantitatively model the various dissipation mechanisms in two
resonators, one fabricated from borosilicate glass and one from single crystal
quartz. As the resonators are cryogenically cooled into the superfluid state,
the damping from thermal effects and from the normal fluid component are
strongly suppressed. At our lowest temperatures, damping is limited solely by
internal dissipation in the substrate materials, and reach quality factors up
to 913,000 at 13 mK. By lifting this limitation through substrate material
choice and resonator design, modelling suggests that the resonators should
reach quality factors as high as 10$^8$ at 100 mK, putting this architecture in
an ideal position to harness mechanical quantum effects.
