  Unravelling the nature of energy transport in multi-chromophoric
photosynthetic complexes is essential to extract valuable design blueprints for
light-harvesting applications. Long-range exciton transport in such systems is
facilitated by a combination of delocalized excitation wavefunctions (excitons)
and remarkable exciton diffusivities. The unambiguous identification of the
exciton transport, however, is intrinsically challenging due to the system's
sheer complexity. Here we address this challenge by employing a novel
spectroscopic lab-on-a-chip approach: A combination of ultrafast coherent
two-dimensional spectroscopy and microfluidics working in tandem with
theoretical modelling. This allowed us to unveil exciton transport throughout
the entire hierarchical supramolecular structure of a double-walled artificial
light-harvesting complex. We show that at low exciton densities, the outer
layer acts as an antenna that supplies excitons to the inner tube, while under
high excitation fluences it protects the inner tube from overburning. Our
findings shed light on the excitonic trajectories across different sub-units of
a multi-layered supramolecular structure and underpin the great potential of
artificial light-harvesting complexes for directional excitation energy
transport.
