On the condition of strong electron-LO phonon coupling in an asymmetrical Gaussian potential quantum well (AGPQW) with a hydrogen-like impurity at the origin of the coordinate, we calculate the eigenenergies and the eigenfunctions of the ground and the first excited states (GFES) by using a variational method of Pekar type. A single qubit can be realized in this two-level quantum system. We calculate the time evolution and the change of the coordinate of the electron's probability density. When the electron is in the superposition state of the GFES, the electron's probability density oscillates in the AGPQW with a certain period T 0 = 20.716 fs. It turns out that due to the presence of the asymmetrical Gaussian potential in the growth direction of the QW, the electron probability density shows a single peak configuration in the coordinate range of z > 0, whereas it equals to zero in the range of z < 0. There is only one peak if the confinement is a two-dimensional symmetric structure in the x y plane of the QW. The oscillating period is a decreasing function of the strength of the Coulombic impurity potential, the height of the AGPQWs and the polaron radius. It is also a decreasing function of the above quantities for R < 0.24 nm, but becomes an increasing one for R > 0.24 nm. It has a minimum when R = 0.24 nm.
By employing a variational method of Pekar type, we study the eigenenergies and the corresponding eigenfunctions of the ground and the first-excited states of an electron strongly coupled to electron-LO in a RbCl quantum pseudodot (QPD) with a hydrogen-like impurity at the center. This QPD system may be used as a twolevel quantum qubit. The expressions of electron's probability density versus time and the coordinates, and the oscillating period versus the Coulombic impurity potential and the polaron radius have been derived. The investigated results indicate 1 that the probability density of the electron oscillates in the QPD with a certain oscillating period of T 0 = 7.817fs, 2 that due to the presence of the asymmetrical potential in the z direction of the RbCl QPD, the electron probability density shows double-peak configuration, whereas there is only one peak if the confinement is a two-dimensional symmetric structure in the x y plane of the QPD, 3 that the oscillation period is a decreasing function of the Coulombic impurity potential, whereas it is an increasing one of the polaron radius.
We study the eigenenergies and eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to longintudinal-optical phonon in an asymmetric quantum dot with a hydrogen-like impurity by using variational method of Pekar type. A single qubit can be realized in this two-level quantum system. The electron probability density oscillates in the asymmetric quantum dot with a certain period of T 0 = 10.958 fs when the electron is in the superposition state of the ground and the first excited states. Moreover, due to the presence of the different harmonic potentials, the dependence way of the probability density of the electron on the coordinate of z is different from that on the coordinates of x and y. It is found that the oscillating period increases with decreasing Coulombic impurity potential and the polaron radius.
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