Using methods of condensed matter and statistical physics, we examine the transport of excitons through the Fenna-Matthews-Olson (FMO) complex from a receiving antenna to a reaction center. Writing the equations of motion for the exciton creation/annihilation operators, we are able to describe the exciton dynamics, even in the regime when the reorganization energy is of the order of the intra-system couplings. In particular, we obtain the well-known quantum oscillations of the site populations. We determine the exciton transfer efficiency in the presence of a quenching field and protein environment. While the majority of the protein vibronic modes are treated as a heat bath, we address the situation when specific modes are strongly coupled to excitons and examine the effects of these modes on the quantum oscillations and the energy transfer efficiency. We find that, for the vibronic frequencies below 16 meV, the exciton transfer is drastically suppressed. We attribute this effect to the formation of polaronic states where the exciton is transferred back and forth between the two pigments with the absorption/emission of the vibronic quanta, instead of proceeding to the reaction center. The same effect suppresses the quantum beating at the vibronic frequency of 25 meV. We also show that the efficiency of the energy transfer can be enhanced when the vibronic mode strongly couples to the third pigment only, instead of coupling to the entire system.
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