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