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

Weyl semimetals are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band. According to lattice theory, Weyl cones must come in pairs, with the minimum number of cones being two. A semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM). Here we report the experimental realization of an IWSM band by engineering 3D spin-orbit coupling for ultracold atoms. The topological Weyl points are clearly measured via the virtual slicing imaging technique in equilibrium and are further resolved in the quench dynamics. The realization of an IWSM band opens an avenue to investigate various exotic phenomena that are difficult to access in solids.

We study the decay mechanism of the gapped lowest-lying axial excitation of a quasipure atomic Bose-Einstein condensate confined in a cylindrical box trap. Owing to the absence of accessible lower-energy modes, or direct coupling to an external bath, this excitation is protected against one-body (linear) decay, and the damping mechanism is exclusively nonlinear. We develop a universal theoretical model that explains this fundamentally nonlinear damping as a process whereby two quanta of the gapped lowest excitation mode couple to a higher-energy mode, which subsequently decays into a continuum. We find quantitative agreement between our experiments and the predictions of this model. Finally, by strongly driving the system below its (lowest) resonant frequency, we observe third-harmonic generation, a hallmark of nonlinear behavior.