Tunable and long-range energy transfer efficiency through a graphene nanodisk

Abstract

In this paper, we present a theoretical investigation of the energy transfer efficiency between a pair of quantum emitters placed in proximity to a conducting graphene nanodisk. The energy transfer efficiency quantifies the contribution of the energy transfer process to the relaxation of the donor quantum system, as compared to the spontaneous emission rate of the donor in the absence of the acceptor. We use in our calculations the Green's tensor formalism in the electrostatic limit. This approximation works very well for the nanodisks considered here, for which the radius is much smaller than the emission wavelength of the donor. The approximate analytical solutions obtained are used to investigate the decay rate of a single quantum emitter and the energy transfer rate between quantum emitters in the vicinity of the graphene nanodisk. We find that these rates are enhanced several orders of magnitude compared with their free-space values. We determine the resonance frequencies of the spontaneous emission rate of a single quantum emitter to a graphene nanodisk, and the energy transfer rate between a pair of quantum emitters in proximity to a graphene nanodisk. We identify the surface modes which give the largest contributions to the energy transfer function. We connect the resonance frequency values and their surface plasmon wave numbers, which depend on the radius of the graphene nanodisk, with the dispersion relation of an infinite graphene monolayer at the same chemical potential. Analyzing the distance dependence of these rates, we are able to fit the full numerical results with a simple analytical expression which depends only on the geometrical characteristics of the graphene nanodisk, i.e., its radius. We show that the interaction distance depends on the transition dipole moment orientation and the different order resonance frequencies. The interaction distance between a pair of quantum emitters increases from a free-space value of $20\phantom{\rule{0.28em}{0ex}}\text{nm}$ to reach values of 120 nm in the presence of a graphene nanodisk.