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Realization of strong synthetic magnetic fields in driven optical latticeshas enabled implementation of topological bands in cold-atom setups. Amilestone has been reached by a recent measurement of a finite Chern numberbased on the dynamics of incoherent bosonic atoms. The measurements of thequantum Hall effect in semiconductors are related to the Chern-numbermeasurement in a cold-atom setup, however, the design and complexity of the twotypes of measurements are quite different. Motivated by these recentdevelopments, we investigate the dynamics of weakly interacting incoherentbosons in a two-dimensional driven optical lattice exposed to an externalforce, which provides a direct probe of the Chern number. We consider arealistic driving protocol in the regime of high driving frequency and focus onthe role of weak repulsive interactions. We find that interactions lead to theredistribution of atoms over topological bands both through the conversion ofinteraction energy into kinetic energy during the expansion of the atomic cloudand due to an additional heating. Remarkably, we observe that the moderateatomic repulsion facilitates the measurement by flattening the distribution ofatoms in the quasi-momentum space. Our results also show that weak interactionscan suppress the contribution of some higher-order non-topological terms infavor of the topological part of the effective model.

Dynamics of weakly interacting bosons in optical lattices with flux