Considering a multi-pathway structure in a light-harvesting complex of photosynthesis, we investigate the role of energy-level mismatches between antenna molecules in transferring the absorbed energy to a reaction center. We find a condition in which the antenna molecules faithfully play their roles: Their effective absorption ratios are larger than those of the receiver molecule directly coupled to the reaction center. In the absence of energy-level mismatches and dephasing noise, there arises quantum destructive interference between multiple paths that restricts the energy transfer. On the other hand, the destructive interference diminishes as asymmetrically biasing the energy-level mismatches and/or introducing quantum noise of dephasing for the antenna molecules, so that the transfer efficiency is greatly enhanced to near unity. Remarkably, the near-unity efficiency can be achieved at a wide range of asymmetric energy-level mismatches. Temporal characteristics are also optimized at the energy-level mismatches where the transfer efficiency is near unity. We discuss these effects, in particular, for the Fenna-Matthews-Olson complex.
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