Direct and third-body mediated resonance energy transfer in dimensionally constrained nanostructures

The process of resonance energy transfer (RET) in a nanostructure influenced by a vicinal, nonabsorbing third body is studied within the framework of molecular quantum electrodynamics. Direct RET and the influence of neighboring matter have been studied previously, mainly for molecules. However, a complete study or unified understanding of direct and indirect RET in nanostructures with different dimensionalities is still lacking. Therefore, there is a strong need for a complete theory that models RET for the cases of quantum wells, nanowires, and quantum dots. We construct a detailed picture of excitation energy transfer in nanostructures and how it is affected by another quantum object, which includes the derivation of quantum amplitudes based on second- and fourth-order time-dependent perturbation theories, and the derivation of transfer rates and distance dependencies, providing a complete picture and understanding of RET in nanostructures. The results of the derivations indicate that the dimensionality of the nanostructure determines the controllability of the RET rate. Furthermore, third-body mediation leads to a nonvanishing RET in the coupling of nanowire to nanowire and quantum dot to quantum dot.