Fundamental efficiency bound for coherent energy transfer in nanophotonics

We derive a unified quantum theory of coherent and incoherent energy transfer between two atoms (donor and acceptor) valid in arbitrary Markovian nanophotonic environments. Our theory predicts a fundamental bound $\eta_{max} = \frac{\gamma_a}{\gamma_d + \gamma_a}$ for energy transfer efficiency arising from the spontaneous emission rates $\gamma_{d}$ and $\gamma_a$ of the donor and acceptor. We propose the control of the acceptor spontaneous emission rate as a new design principle for enhancing energy transfer efficiency. We predict an experiment using mirrors to enhance the efficiency bound by exploiting the dipole orientations of the donor and acceptor. Of fundamental interest, we show that while quantum coherence implies the ultimate efficiency bound has been reached, reaching the ultimate efficiency does not require quantum coherence. Our work paves the way towards nanophotonic analogues of efficiency enhancing environments known in quantum biological systems.