Optimal efficiency of quantum transport in structured disordered systems with applications to light-harvesting complexes

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.