Superadiabatic theory for Cooper pair pumping under decoherence

We introduce a method where successive coordinate transformations are applied to decrease the error in the adiabatic master equation resulting from truncation in the local adiabatic parameter. Our method reduces the nonphysical behaviour stemming from the lack of complete positivity. The strong environment-induced relaxation at high Cooper pair pumping frequencies leads to adiabatic ground-state pumping only in the lowest-order approximation. We illustrate the robustness of the frequency where the adiabaticity breaks down using the high-order theory and show the emergence of an optimal environmental coupling strength, for which ideal pumping is preserved for the highest frequency. Finally, we study the effect of quantum interference on the pumped current and give an estimate for the relaxation rate of an experimentally measured system.