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