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Generic scaling laws, such as the Kolmogorov's 5/3-law, are milestoneachievements of turbulence research in classical fluids. For quantum fluidssuch as atomic Bose-Einstein condensates, superfluid helium, and superfluidneutron stars, turbulence can also exist in the presence of a chaotic tangle ofevolving quantized vortex lines. However, due to the lack of suitableexperimental tools to directly probe the vortex-tangle motion, so far little isknown about possible scaling laws that characterize the velocity correlationsand trajectory statistics of the vortices in quantum-fluid turbulence (QT).Acquiring such knowledge could greatly benefit the development of advancedstatistical models of QT. Here we report an experiment where a tangle ofvortices in superfluid $^4$He are decorated with solidified deuterium tracerparticles. Under experimental conditions where these tracers follow the motionof the vortices, we observed an apparent superdiffusion of the vortices. Ouranalysis 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 ofrandom walkers. Instead, a previously unknown power-law scaling of thevortex-velocity temporal correlation is uncovered as the cause. This findingmay motivate future research on hidden scaling laws in QT.

Superdiffusion of quantized vortices uncovering scaling behavior of quantum turbulence