Time-resolved measurements of the anomalous Hall velocity

The anomalous velocity is a purely intrinsic interference effect that gives rise to many fascinating transport phenomena in solids, including the anomalous Hall effect (AHE), the spin Hall effect (SHE), and their quantized versions. However, measuring the anomalous velocity in real solid-state materials is challenging as a direct observation of electron wave-packet dynamics is generally impeded by inherent short times for scattering.

Here, we report on direct measurements of the anomalous Hall velocity for bosonic superfluids in an accelerated optical boron-nitride lattice. By tracing the coherent evolution of Bloch states in momentum space, we precisely extract the time-dependent anomalous velocity along different paths in reciprocal space and infer the associated local Berry curvature. Using this method, we demonstrate geometric pumping and a bosonic counterpart of the valley Hall effect for condensates in the second Bloch band, where atoms in different valleys experience net anomalous transport in opposite directions.