  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.
