Superdiffusion of quantized vortices uncovering scaling behavior of quantum turbulence

TL;DR

This study experimentally demonstrates superdiffusion in quantum vortex tangles within superfluid helium, revealing a new power-law scaling of vortex velocity correlations that advances understanding of quantum turbulence.

Contribution

It uncovers a previously unknown power-law scaling of vortex-velocity correlations in quantum turbulence through experimental observation of vortex superdiffusion.

Findings

Vortex superdiffusion observed in superfluid helium.

Superdiffusion caused by velocity correlation scaling, not Lévy flights.

Discovery of a new power-law scaling law in quantum turbulence.

Abstract

Generic scaling laws, such as the Kolmogorov's 5/3-law, are milestone achievements of turbulence research in classical fluids. For quantum fluids such as atomic Bose-Einstein condensates, superfluid helium, and superfluid neutron stars, turbulence can also exist in the presence of a chaotic tangle of evolving quantized vortex lines. However, due to the lack of suitable experimental tools to directly probe the vortex-tangle motion, so far little is known about possible scaling laws that characterize the velocity correlations and trajectory statistics of the vortices in quantum-fluid turbulence (QT). Acquiring such knowledge could greatly benefit the development of advanced statistical models of QT. Here we report an experiment where a tangle of vortices in superfluid $^4$He are decorated with solidified deuterium tracer particles. Under experimental conditions where these tracers follow the motion of the vortices, we observed an apparent superdiffusion of the vortices. Our analysis shows that this superdiffusion is not due to L\'{e}vy flights, i.e., long-distance hops that are known to be responsible for superdiffusion of random walkers. Instead, a previously unknown power-law scaling of the vortex-velocity temporal correlation is uncovered as the cause. This finding may motivate future research on hidden scaling laws in QT.