Influence of an anisotropic parabolic potential on the quantum dot qubit

To study the influence of an anisotropic parabolic potential(APP)on the properties of a quantum dot(QD)qubit,we obtain the eigenenergies and eigenfunctions of the ground and first excited state of an electron,which is strongly coupled to the bulk longitudinal optical(LO)phonons,in a QD under the influence of an APP by the celebrated Lee–Low–Pines(LLP)unitary transformation and the Pekar type variational(PTV)methods.Then,this kind of two-level quantum system can be excogitated to constitute a single qubit.When the electron locates at the superposition state of its related eigenfunctions,we get the time evolution of the electron’s probability density.Finally,the influence of an APP on the QD qubit is investigated.The numerical calculations indicate that the probability density will oscillate periodically and it is a decreasing function of the effective confinement lengths of theAPPindifferentdirections.Whereasitsoscillatoryperiodisanincreasingoneandwilldiminishwithenhancing the electron–phonon(EP)coupling strength.