The quantum network model with real variables is usually used to describe theexcitation energy transfer (EET) in the Fenna-Matthews-Olson(FMO) complexes. Inthis paper we add the quantum phase factors to the hopping terms and find thatthe quantum phase factors play an important role in the EET. The quantum phasefactors allow us to consider the space structure of the pigments. It is foundthat phase coherence within the complexes would allow quantum interference toaffect the dynamics of the EET. There exist some optimal phase regions wherethe transfer efficiency takes its maxima, which indicates that when thepigments are optimally spaced, the exciton can pass through the FMO withperfect efficiency. Moreover, the optimal phase regions almost do not changewith the environments. In addition, we find that the phase factors are usefulin the EET just in the case of multiple-pathway. Therefore, we demonstratethat, the quantum phases may bring the other two factors, the optimal space ofthe pigments and multiple-pathway, together to contribute the EET inphotosynthetic complexes with perfect efficiency.
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