  In the modern understanding of turbulence, a central concept is the existence
of cascades of excitations from large to small lengthscales, or vice-versa.
This concept was introduced in 1941 by Kolmogorov and Obukhov, and the
phenomenon has since been observed in a variety of systems, including
interplanetary plasmas, supernovae, ocean waves, and financial markets. Despite
a lot of progress, quantitative understanding of turbulence remains a challenge
due to the interplay of many lengthscales that usually thwarts theoretical
simulations of realistic experimental conditions. Here we observe the emergence
of a turbulent cascade in a weakly interacting homogeneous Bose gas, a quantum
fluid that is amenable to a theoretical description on all relevant
lengthscales. We prepare a Bose-Einstein condensate (BEC) in an optical box,
drive it out of equilibrium with an oscillating force that pumps energy into
the system at the largest lengthscale, study the BEC's nonlinear response to
the periodic drive, and observe a gradual development of a cascade
characterised by an isotropic power-law distribution in momentum space. We
numerically model our experiments using the Gross-Pitaevskii equation (GPE) and
find excellent agreement with the measurements. Our experiments establish the
uniform Bose gas as a promising new platform for investigating many aspects of
turbulence, including the interplay of vortex and wave turbulence and the
relative importance of quantum and classical effects.
