Controlling observables in normal, hybrid and Josephson junctions

The theory of time-dependent quantum transport addresses the question: How do electrons flow through a junction under the influence of an external perturbation as time goes by? In this article, we invert this question and search for a time-dependent bias such that the system behaves in a desired way. Our system of choice consists of quantum dots coupled to normal or superconducting leads. We present results for junctions with normal leads where the current, the density or a molecular vibration is optimised to follow a given target pattern. For junctions with two superconducting leads, where the Josephson effect triggers the current to oscillate, we investigate what happens if the frequency of the Josephson oscillation comes close to the frequency of the molecular vibration. Furthermore we show how to suppress the Josephson oscillations by suitably tailoring the bias. In a second example involving superconductivity, we consider a Y-shaped junction with two quantum dots coupled to one superconducting and two normal leads. This device is used as a Cooper pair splitter to create entangled electrons on the two quantum dots. We maximise the splitting efficiency with the help of an optimised bias.