Direct visualization of the quantum vortex density law in rotating 4He

Abstract: 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.