Statistics of Tunneling Events in Three-Terminal Hybrid Devices with Quantum Dot

We investigate statistics of the tunneling events in the short time limit in terms of the waiting time distribution (WTD), defined as the probability for a delay time between two subsequent transitions of particles, and consider it for a quantum dot (QD) strongly coupled to a superconducting and weakly coupled to two normal electrodes. Our study focuses on the WTD in the subgap transport, when coherent exchange of the Cooper pairs occurs between the QD and the superconductor. The dynamics can be described in terms of a Markovian generalized master equation for the reduced density matrix. We observe coherent oscillations between the Andreev bound states in the correlated jumps, both for the local and non-local WTDs. In addition the analysis of the transient currents give us some insight into dominant relaxation processes in short time scales.