Synthetic dissipation and cascade fluxes in a turbulent quantum gas

TL;DR

This study measures the direct energy cascade flux in a turbulent quantum Bose gas, demonstrating synthetic dissipation effects and the cascade front dynamics through tunable trap parameters and time-resolved observations.

Contribution

It introduces a method to directly measure fluxes in a turbulent quantum gas using synthetic dissipation and explores the cascade dynamics and zeroth law of turbulence.

Findings

Particle flux vanishes as $k_D^{-2}$ in the dissipationless limit.

Energy flux remains independent of the dissipation scale $k_D$.

Time-resolved data reveal the propagation of the cascade front.

Abstract

Scale-invariant fluxes are the defining property of turbulent cascades, but their direct measurement is a notorious problem. Here we perform such a measurement for a direct energy cascade in a turbulent quantum gas. Using a time-periodic force, we inject energy at a large lengthscale and generate a cascade in a uniformly-trapped Bose gas. The adjustable trap depth provides a high-momentum cutoff $k_{\textrm{D}}$, which realises a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius $k_{\textrm{D}}$, and the tunability of $k_{\textrm{D}}$ allows for a clear demonstration of the zeroth law of turbulence: we observe that for fixed forcing the particle flux vanishes as $k_{\textrm{D}}^{-2}$ in the dissipationless limit $k_{\textrm{D}}\rightarrow \infty$, while the energy flux is independent of $k_{\textrm{D}}$. Moreover, our time-resolved measurements give unique access to the pre-steady-state dynamics, when the cascade front propagates in momentum space.