Adiabatic Pumping in a Generalized Aubry-Andre Model Family with Mobility Edges

The adiabatic pumping between left and right end modes in a generalized Aubry-Andre model family with mobility edges by resorting to two end-bulk-end channels is investigated. It is shown that the system can be in an intermediate regime mixed with localized and extended phases as the mobility edge is introduced. One of the channels can remain intact even when the parameter determining the localization-delocalization transition exceeds the threshold of the paradigmatic Aubry-Andre model, leading to that the parametric condition for successful pumping is relaxed. Moreover, it is found that widening the region of the hybrid phase can further enhance the effect of the mobility edge. The pumping result is also quantified based on the fidelity and check the corresponding pumping process to validate these observations. Furthermore, another channel to realize a flexible adiabatic pumping among four types of generalized end modes is engineered. This work enables the potential application of mobility edges in strong-quasidisorder-immune quantum state transfer.