  Disordered quantum networks, as those describing light-harvesting complexes,
are often characterized by the presence of antenna structures where the light
is captured and inner structures (reaction centers) where the excitation is
transferred. Antennae often display distinguished coherent features: their
eigenstates can be separated, with respect to the transfer of excitation, in
the two classes of superradiant and subradiant states. Both are important to
optimize transfer efficiency. In absence of disorder superradiant states have
an enhanced coupling strength to the RC, while subradiant ones are basically
decoupled from it. Disorder induces a coupling between subradiant and
superradiant states, thus creating an indirect coupling to the RC. We consider
the problem of finding the maximal excitation transfer efficiency as a function
of the RC energy and the disorder strength, first in a paradigmatic three-level
system and then in a realistic model for the light-harvesting complex of purple
bacteria. Specifically, we focus on the case in which the excitation is
initially on a subradiant state, showing that the optimal disorder is of the
order of the superradiant coupling. We also determine the optimal detuning
between the initial state and the RC energy. We show that the efficiency
remains high around the optimal detuning in a large energy window, proportional
to the superradiant coupling. This allows for the simultaneous optimization of
excitation transfer from several initial states with different optimal
detuning.
