Generic mechanism of optimal energy transfer efficiency: a scaling theory of the mean first-passage time in exciton systems.

An asymptotic scaling theory is presented using the conceptual basis of trapping-free subspace (i.e., orthogonal subspace) to establish the generic mechanism of optimal efficiency of excitation energy transfer in light-harvesting systems. A quantum state orthogonal to the trap will exhibit noise-assisted transfer, clarifying the significance of initial preparation. For such an initial state, the efficiency is enhanced in the weak damping limit (⟨t⟩ ∼ 1/Γ), and suppressed in the strong damping limit (⟨t⟩ ∼ Γ), analogous to Kramers turnover in classical rate theory. An interpolating expression ⟨t⟩ = A/Γ + B + CΓ quantitatively describes the trapping time over the entire range of the dissipation strength, and predicts the optimal efficiency at Γ(opt) ∼ J for homogenous systems. In the presence of static disorder, the scaling law of transfer time with respect to dephasing rate changes from linear to square root, suggesting a weaker dependence on the environment. The prediction of the scaling theory is verified in a symmetric dendrimer system by numerically exact quantum calculations. Though formulated in the context of excitation energy transfer, the analysis and conclusions apply in general to open quantum processes, including electron transfer, fluorescence emission, and heat conduction.