Mono-parametric quantum charge pumping: interplay between spatial   interference and photon-assisted tunneling
  We analyze quantum charge pumping in an open ring with a dot embedded in one of its arms. We show that cyclic driving of the dot levels by a \textit{single} parameter leads to a pumped current when a static magnetic flux is simultaneously applied to the ring. Based on the computation of the Floquet-Green's functions, we show that for low driving frequencies $\omega_0$, the interplay between the spatial interference through the ring plus photon-assisted tunneling gives an average direct current (dc) which is proportional to $\omega_0^{2}$. The direction of the pumped current can be reversed by changing the applied magnetic field. 
Luis E. F. Foa Torres