Geometric quantum pumping in the presence of dissipation

The charge transported when a quantum pump is adiabatically driven by time-dependent external forces in presence of dissipation is given by the line integral of a pumping field $\mathbf{F}$. We give a general expression of $\mathbf{F}$ in terms of quantum correlation functions evaluated at fixed external forces. Hence, an advantage of our method is that it transforms the original time-dependent problem into an autonomous one. Yet another advantage is that the curl of $\mathbf{F}$ gives immediate visual information about the geometric structures governing dissipative quantum pumping. This can be used in a wide range of experimental cases, including electron pumps based on quantum dots and Cooper-pair pumps based on superconducting devices. Applied to a Cooper-pair sluice, we find an intriguing dissipation-induced enhancement of charge pumping, reversals of current, and emergence of asymmetries. This geometric method thus enables one to unveil a plethora of beneficial, dissipation-assisted operation protocols.