Synthetic dissipation and cascade fluxes in a turbulent quantum gas

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 $k_{\text{D}}$, which realises a synthetic dissipation scale. This gives us direct access to the particle flux across a momentum shell of radius $k_{\text{D}}$, and the tunability of $k_{\text{D}}$ allows for a clear demonstration of the zeroth law of turbulence: we observe that for fixed forcing the particle flux vanishes as $k_{\text{D}}^{-2}$ in the dissipationless limit $k_{\text{D}}\to \infty$, while the energy flux is independent of $k_{\text{D}}$. Moreover, our time-resolved measurements give unique access to the pre-steady-state dynamics, when the cascade front propagates in momentum space.

Main text: 4 pages, 4 figures. Supplementary Material: 2 pages, 3 figures