The effect of temperature and magnetic field on a quantum rod qubit

The Hamiltonian of a quantum rod (QR) with an ellipsoidal boundary is given after a coordinate transformation, which changes the ellipsoidal boundary into a spherical one. We obtain the eigenenergies and eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to the LO-phonon in a QR under an applied magnetic field by using the Pekar variational method. This system in QR may be employed as a two-level qubit. When the electron is in the superposition state of the ground and the first-excited states, we study the time evolution of the electron probability density. The relations of the probability density of electron on the temperature and the relations of the period of oscillation on the temperature and the cyclotron frequency of magnetic field are taken into consideration. The results show that the probability density of the electron oscillates in the QR with a oscillation period. It is found that the electron probability density and the oscillation period increase (decrease) with increasing temperature in lower (higher) temperature regime. The electron probability density increases (decreases) with increasing cyclotron frequency when the temperature is lower (higher). The oscillation period decreases with the increase of the cyclotron frequency.