Propagation of waves along superfluid vortices trapping particles

Umberto Giuriato
Université Côte d'Azur, Observatoire de la Côte d’Azur, CNRS, Laboratoire Lagrange, 96 Boulevard de l'Observatoire, 06300, Nice, France.

Superfluids like liquid helium or ultracold atomic Bose-Einstein condensates are an exotic state of matter in which quantum effects appear on a macroscopic scale. One of the main features of superfluids is the presence of topological defects with quantised circulation, known as quantum vortices. These vorticity filaments can reconnect dissipating energy through sound emission and thus they play a central role in superfluid turbulence. At the same time, helicoidal waves (called Kelvin waves) can propagate along the vortex filaments and interact nonlinearly among themselves, contributing to the energy transfer towards small scales. An important experimental breakthrough occurred in 2006, when quantum vortices were directly visualised by using micrometer-sized hydrogen particles. Since these particles are trapped inside the vortex core they can be used to track the motion of vortices themselves. Thanks to this method, quantum vortex reconnections and Kelvin wave propagation have been observed. Nowadays, particles are still the main experimental tool used to visualise quantum vortices and to study their dynamics. Our aim is to study the propagation of waves along a superfluid vortex filament, when active particles are trapped inside its core. We perform numerical simulations of a self-consistent model based on the Gross-Pitaevskii (GP) equation, in which particles are described as localised potentials depleting the superfluid and following a Newtonian dynamics. In a former work we have shown that this model is able to reproduce the capture of a particle by a quantum vortex line. Now we study how the dynamics of a collection of particles (impurities) already set inside the vortex reflects the motion of the vortex itself. We measure the spatiotemporal spectra of the system, showing how the presence of particles induces a nontrivial modification of the vortex wave dispersion relation. In order to explain the numerical results, we develop a theory that mixes hydrodynamic equations and basic solid-state concepts. In particular, we point out a remarkable analogy with the propagation of electrons in a crystal lattice.