Properties of the two- and three-dimensional quantum dot qubit

On the condition of electric-longitudinal-optical(LO) phonon strong coupling in both two- and three-dimensional parabolic quantum dots(QDs),we obtain the eigenenergies of the ground state(GS) and the first excited state(ES),the eigenfunctions of the GS and the first ES by using a variational method of Pekar type.This system in QD may be employed as a quantum system-quantum bit(qubit).When the electron is in the superposition state of the GS and the first ES,we obtain the time evolution of the electron density.The relations of both the electron probability density and the period of oscillation with the electric-LO phonon coupling strength and confinement length are discussed.