  Semiconductor quantum dot molecules are considered as promising candidates
for quantum technological applications due to their wide tunability of optical
properties and coverage of different energy scales associated with charge and
spin physics. While previous works have studied the tunnel-coupling of the
different excitonic charge complexes shared by the two quantum dots by
conventional optical spectroscopy, we here report on the first demonstration of
a coherently controlled inter-dot tunnel-coupling focusing on the quantum
coherence of the optically active trion transitions. We employ ultrafast
four-wave mixing spectroscopy to resonantly generate a quantum coherence in one
trion complex, transfer it to and probe it in another trion configuration. With
the help of theoretical modelling on different levels of complexity we give an
instructive explanation of the underlying coupling mechanism and dynamical
processes.
