  Cooper pair splitting (CPS) is a process in which the electrons of naturally
occurring spin-singlet pairs in a superconductor are spatially separated using
two quantum dots. Here we investigate the evolution of the conductance
correlations in an InAs CPS device in the presence of an external magnetic
field. In our experiments the gate dependence of the signal that depends on
both quantum dots continuously evolves from a slightly asymmetric Lorentzian to
a strongly asymmetric Fano-type resonance with increasing field. These
experiments can be understood in a simple three - site model, which shows that
the nonlocal CPS leads to symmetric line shapes, while the local transport
processes can exhibit an asymmetric shape due to quantum interference. These
findings demonstrate that the electrons from a Cooper pair splitter can
propagate coherently after their emission from the superconductor and how a
magnetic field can be used to optimize the performance of a CPS device. In
addition, the model calculations suggest that the estimate of the CPS
efficiency in the experiments is a lower bound for the actual efficiency.
