Effect of electron-phonon interaction on the first excited energy level of a Gaussian GaAs quantum dot

The effect of electron-phonon interaction on the first excited state of a three-dimensional polar semiconductor quantum dot with Gaussian confinement is studied using the second-order Rayleigh-Schr¨odinger perturbation theory. An analytical expression for the first excited state polaronic correction is obtained under a plausible approximation. It is shown that this energy depends both on the strength and range of the Gaussian potential. Finally our theory is applied to a GaAs quantum dot and it is shown that the polaronic effect to the first excited level can be significantly large if the size of the dot is small. Since the information of the excited states is important for the study of decoherence phenomena, our results could be useful for quantum information processing.