Electron-phonon dynamics in an ensemble of nearly isolated nanoparticles

We investigate the electron population dynamics in an ensemble of nearly isolated insulating nanoparticles, each nanoparticle modeled as an electronic two-level system coupled to a single vibrational mode. We find that at short times the ensemble-averaged excited-state population oscillates but has a decaying envelope. At long times, the oscillations become purely sinusoidal about a ‘‘plateau’’ population, with a frequency determined by the electron-phonon interaction strength and with an envelope that decays algebraically as t. We use this theory to predict electron-phonon dynamics in an ensemble of Y2O3 :Eu 31 nanoparticles.