A resonantly enhanced relaxation rate in the Fenna-Matthews-Olson complex produces a resonantly suppressed dephasing rate.

The fourth-order time-convolutionless (TCL4) equation is used to calculate the Fenna-Matthews-Olson (FMO) complex's exciton transfer rate. We discovered resonant behavior based on a dimer model submerged in a bosonic bath with a pronounced vibrational mode. When the exciton energy difference nearly matches the vibrational frequency, the dephasing rate is strongly suppressed while the relaxation rate is strongly enhanced. This effect shows that the exciton transfer rate is boosted at the expense of suppressing the dephasing rate, which explains the complex's long-lasting quantum beat. Therefore, we reach the conclusion that the small dephasing rates in the complex are naturally selected in a Darwinian process. We also show that the resonant beat is a strongly non-Markovian effect, in the sense that it occurs only when the exciton subsystem and the bath with the vibration are in a correlated state, as opposed to the factorized initial state.