  A Cooper pair splitter consists of a central superconducting contact, S, from
which electrons are injected into two parallel, spatially separated quantum
dots (QDs). This geometry and electron interactions can lead to correlated
electrical currents due to the spatial separation of spin-singlet Cooper pairs
from S. We present experiments on such a device with a series of bottom gates,
which allows for spatially resolved tuning of the tunnel couplings between the
QDs and the electrical contacts and between the QDs. Our main findings are
gate-induced transitions between positive conductance correlation in the QDs
due to Cooper pair splitting and negative correlations due to QD dynamics.
Using a semi-classical rate equation model we show that the experimental
findings are consistent with in-situ electrical tuning of the local and
nonlocal quantum transport processes. In particular, we illustrate how the
competition between Cooper pair splitting and local processes can be optimized
in such hybrid nanostructures.
