Optimal efficiency of quantum transport in a disordered trimer

Disordered quantum networks, such as those describing light-harvesting complexes, are often characterized by\r\nthe presence of peripheral ringlike structures, where the excitation is initialized, and inner structures and reaction\r\ncenters (RCs), where the excitation is trapped and transferred. The peripheral rings often display distinguished\r\ncoherent features: Their eigenstates can be separated, with respect to the transfer of excitation, into two classes of\r\nsuperradiant and subradiant states. Both are important to optimize transfer efficiency. In the absence of disorder,\r\nsuperradiant states have an enhanced coupling strength to the RC, while the subradiant ones are basically\r\ndecoupled from it. Static on-site disorder induces a coupling between subradiant and superradiant states, thus\r\ncreating an indirect coupling to the RC. The problem of finding the optimal transfer conditions, as a function of\r\nboth the RC energy and the disorder strength, is very complex even in the simplest network, namely, a three-level\r\nsystem. In this paper we analyze such trimeric structure, choosing as the initial condition an excitation on a\r\nsubradiant state, rather than the more common choice of an excitation localized on a single site. We show that,\r\nwhile the optimal disorder is of the order of the superradiant coupling, the optimal detuning between the initial\r\nstate and the RC energy strongly depends on system parameters: When the superradiant coupling is much larger\r\nthan the energy gap between the superradiant and the subradiant levels, optimal transfer occurs if the RC energy\r\nis at resonance with the subradiant initial state, whereas we find an optimal RC energy at resonance with a virtual\r\ndressed state when the superradiant coupling is smaller than or comparable to the gap. The presence of dynamical\r\nnoise, which induces dephasing and decoherence, affects the resonance structure of energy transfer producing\r\nan additional incoherent resonance peak, which corresponds to the RC energy being equal to the energy of the\r\nsuperradiant state