Dynamical current correlations in Cooper pair splitters based on proximized quantum dots

Entanglement of electrons is studied by means of current–current correlations in two Cooper pair splitter devices: with one and two proximized quantum dots (1QD and 2QD), in presence of intra- and inter-dot Coulomb interactions, and weakly coupled with metallic electrodes. The 1QD system, where Cooper pairs can be transmitted to the same or split to different normal electrodes, is contrasted with the 2QD device, where double occupancy of a single quantum dot is forbidden and transport is only through an inter-dot singlet due to non-local crossed Andreev reflection processes deep in the superconducting energy gap. Separating the current correlation function into components for partial currents of electrons and holes through various Andreev bound states, one can see bunching and antibunching of split particles: inter-level components between electron and hole currents flowing to different electrodes are positive, while intra-level electron–electron or hole–hole components are negative, respectively. Spectral decomposition of the frequency-dependent current cross-correlation is performed to get better insight into mechanisms of entanglement and dynamics of split Cooper pairs, and to extract various charge fluctuation processes with different relaxation times, related to electron and hole currents flowing through the Andreev bound states. Only low frequency polarization fluctuations are seen in the current cross-correlations, while various negative and positive high frequency (charge fluctuations) components compensate each other in the symmetric system.