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Topological pumping assisted by Bloch oscillations

Adiabatic quantum pumping in one-dimensional lattices is extended by adding a tilted potential to probe better topologically nontrivial bands. This extension leads to almost perfectly quantized pumping for an arbitrary initial state selected in a band of interest, including Bloch states. In this approach, the time variable offers not only a synthetic dimension as in the case of the Thouless pumping, but it assists also in the uniform sampling of all momenta due to the Bloch oscillations induced by the tilt. The quantized drift of Bloch oscillations is determined by a one-dimensional time integral of the Berry curvature, being effectively an integer multiple of the topological Chern number in the Thouless pumping. Our study offers a straightforward approach to yield quantized pumping, and it is useful for probing topological phase transitions.