How trapped particles interact with and sample superfluid vortex excitations

Abstract

Particles have been used for more than a decade to visualize and study the dynamics of quantum vortices in superfluid helium. In this work we study how the dynamics of a collection of particles set inside a vortex reflects the motion of the vortex. We use a self-consistent model based on the Gross-Pitaevskii equation coupled with classical particle dynamics. We find that each particle oscillates with a natural frequency proportional to the number of vortices attached to it. We then study the dynamics of an array of particles trapped in a quantum vortex and use particle trajectories to measure the frequency spectrum of the vortex excitations. Surprisingly, due to the discreetness of the array, the vortex excitations measured by the particles exhibit bands, gaps, and Brillouin zones, analogous to the ones of electrons moving in crystals. We then establish a mathematical analogy where vortex excitations play the role of electrons and particles that of the potential barriers constituting the crystal. We find that the height of the effective potential barriers is proportional to the particle mass and the frequency of the incoming waves. We conclude that large-scale vortex excitations could be in principle directly measured by particles and novel physics could emerge from particle-vortex interaction.

Quantum vortex reconnections mediated by trapped particles

“…We refer to [27][28][29]33 for further details about the model, where it has been recently adopted to study extensively the interaction between particles and quantum vortices.…”

“…1, for a neutral particle of size a p = 4.3ξ and initial vortex separation d = 10ξ. During the motion of the dipole, the particle starts to precede about the filament because of Magnus effect 28,30,38 . At the same time, the two vortices start to bend, until the filament without particle reconnects with the surface of the sphere at time t − rec .…”

“…Remarkably, such window turns out to be the same in the rescaled units regardless of the particle size. Note how before the reconnection the momentum of the trapped particle oscillates weakly about a constant average, because of the Magnus precession induced by the vortex 28 . If the invariance (6) really holds, the net particle momentum increment after the detachment in the rescaled units is expected to coincide for particles of different radius but same relative mass M. However, a small mismatch can be observed, which is probably due to the interaction between the particle and the vortex by which it is trapped before the reconnection.…”

“…Unlike the vortex-filament method or the HVBK model, the full dynamics of vortices emerges naturally, including the reconnection events. Particles modeled as highly repulsive potentials have been successfully implemented in the GP framework, allowing for an extensive study of the capture process 27 , the interaction between trapped particles and Kelvin waves 28 , and the Lagrangian properties of quantum turbulence 29 . Recently, the dynamics of particles trapped inside GP vortices has been addressed also in two dimensions 30 .…”

Stochastic motion of finite-size immiscible impurities in a dilute quantum fluid at finite temperature

“…In this article, we couple the PGP equation with a minimal model for impurities, which are described as localized repulsive potentials with classical degrees of freedom 13,36 . It has been recently utilized systematically to investigate the interaction between particles and quan-tum vortices at very low temperature [37][38][39][40] . We stress that this minimal model is suitable for extensive numerical simulations and Monte-Carlo sampling.…”