Relaxation of excited states of an emitter near a metal nanoparticle: An analysis based on superradiance theory

Methods of superradiance theory are employed for determining the relaxation rate of the excited state of a resonant emitter (atom, molecule, or quantum dot) near a metal nanoparticle under resonant excitation of plasmons in it, viz., modes of spatially uniform (dipole) harmonic oscillations of the electron density. Detuning from resonance and nonradiative loss suppressing radiation from the emitter near the nanoparticle surface are taken into account. The results are used to estimate the threshold conditions for generating a plasmon (“dipole”) nanolaser. It is shown that the threshold conditions of induced (laser) generation of plasmons for the emitter at a distance of 5–40 nm from an ellipsoidal nanoparticle are satisfied for relatively low emitter pumping rates (on the order of the rate of spontaneous emission of the emitter into the free space).