  The study of quantum vortex dynamics in He II holds great promise to refine
quantum-fluid models. Bose-Einstein condensates, neutron stars or even
superconductors exhibit quantum vortices, whose interactions are a key element
of dissipation in these systems. These quantum objects have their velocity
circulation around their core quantized and, in He II, a core as thin as a
helium atom. They have been observed experimentally by indirect means, such as
second sound attenuation or electron bubble imprints on photo sensitive
material, and for the last twenty years, decorating cryogenic flows with
particles has proved to be a powerful method to study these vortices. However,
in these recent particle visualization observations, experimental stability,
initial condition, stationarity and reproducibility are elusive or fragmented
and 2d dynamical analysis are performed although most of the considered flows
are inherently 3d. Here we show that we are able to visualize these vortices in
the canonical and higher symmetry case of a stationary rotating superfluid
bucket. Using direct visualization, we quantitatively verify Feynman's rule
linking the resulting quantum vortex density to the imposed rotational speed.
Our statistically meaningful results demonstrate that decorated quantum
vortices behave as Feynman predicted. It follows that hydrogen flakes are good
tracers of quantum vortices for stationary cases in He II. The observed vortex
lattices are analogous to Abrikosov lattices found in superconductors and
Bose-Einstein condensates. Moreover, these lattices aligned with the rotation
axis can play the role of a well-defined and controlled initial condition for
dynamical cases. We make the most of this stable configuration by observing
collective wave mode propagation along quantum vortices and quantum vortex
interactions in rotating He II. These results provide a new experimental
baseline for models to evolve towards a better description of all
quantum-fluids.
