Optimal single-electron feedback control

In a closed-loop controlled single-electron transistor (SET) the optimal feedback response is investigated, leading to a maximum suppression of shot-noise. Using a coupled quantum point contact (QPC) charge detector, the tunneling process is monitored in real-time and the fluctuations are fed back periodically to the tunneling barriers of the SET. The feedback response is applied proportional to the deviation from the target number of average transferred electrons. This leads to a strong suppression and temporal saturation of the cumulants of the full counting statistics. For the optimal feedback response, the saturation value of second cumulant is found to be given by target number. Astonishingly, the feedback works robust even for target numbers much smaller than one.