Pair-amplitude dynamics in strongly coupled superconductor–quantum dot hybrids

We consider a three-terminal system consisting of a quantum dot strongly\ncoupled to two superconducting reservoirs in the infinite gap limit and weakly\ncoupled to a normal metal. Using a real-time diagrammatic approach, we\ncalculate the dynamics of the proximity-induced pair amplitude on the quantum\ndot. We find that after a quench the pair amplitude shows pronounced\noscillations with a frequency determined by the coupling to the\nsuperconductors. In addition, it decays exponentially on a time scale set by\nthe coupling to the normal metal. Strong oscillations of the pair amplitude\noccur also when the system is periodically driven both in the adiabatic and\nfast-driving limit. We relate the dynamics of the pair amplitude to the\nJosephson and Andreev current through the dot to demonstrate that it is an\nexperimentally accessible quantity.\n