  The efficiency of natural light harvesting systems is largely determined by
their ability to transfer excitations from the antenna to the energy trapping
center before recombination. Exciton diffusion length similarly limits organic
photovoltaics and demands bulk heterojunction architectures. Dark state
protection, achieved by coherent coupling between subunits within the antenna,
can significantly reduce radiative recombination and enhance the efficiency of
energy trapping. In this work we extend the dark state concept to the
double-excitation manifold by studying the dynamical flow of excitations. We
show the lowest double-excitation state carries minimal oscillator strength but
relaxation to this state from higher lying double excitations can be relatively
rapid such that the lowest double excitation state can act as a dynamical dark
state protecting excitation from radiative recombination. This mechanism is
sensitive to topology and operates differently for chain and ring structures,
while becoming more pronounced in both geometries when the size of the antenna
increases. When the exciton-exciton annihilation (EEA) mechanism is considered,
the double-excitation population is quickly depleted and the dynamics changes
dramatically. However the efficiency and output power are still significantly
different from those calculated using the single-excitation manifold alone,
justifying the necessity of considering the double-excitation manifold.
Remarkably, in certain scenarios, the EEA can even increase the overall light
harvesting efficiency by bringing population down from the double-excitation
dark states to the single-excitation manifold.
