Quantum Biology, Photosynthesis, and Resonance Energy Transfer

Quantum biology is the subfield of physics concerned with natural systems where quantum mechanics is necessary in order to fully explain biological functions. The precise boundary between this subject and those closely related to it is difficult to define clearly. However, the transfer of energy across chlorophylls during photosynthesis is, by the accounts of contemporary research, a paradigmatic model for quantum effects in biology. Underlying this phenomenon is a process known as \textit{F\ orster resonance energy transfer} (FRET), and the quantum mechanical formalism necessary to understand this process extends beyond the standard undergraduate physics curriculum. Thus, we present an overview of this formalism by building upon accessible first principles. We then give a broad description of photosynthesis in which we identify the key molecular structures needed in light-harvesting complexes for resonant energy transfer to occur. Theoretical motivation for FRET is provided in detail before a partial derivation of the FRET rate expression is given using quantum dynamical mapping with coupling to an environmental bath. This work illustrates precisely how biological processes can be innately quantum mechanical