Impurity Effect of Asymmetric Gaussian Potential Quantum Well Qubit

Abstract

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.

Coulomb Impurity Potential RbCl Quantum Pseudodot Qubit

“…For this reason, the energy space between the GFES increases with increasing Coulombic impurity potential and then the oscillating period decreases. This result is similar to the case of the asymmetric Gaussian potential quantum well [13]. It also can be seen that the oscillating period decreases as the polaron radius decreases because the energy spacing between the GFES increases.…”

“…It also can be seen that the oscillating period decreases as the polaron radius decreases because the energy spacing between the GFES increases. This result is the opposite of asymmetric Gaussian potential [13].…”

“…(1) are the same with Ref. [13]. V (r ) is the PHP [14] that includes both harmonic QD potential and antidot potential.…”

“…Following the Pekar [15][16][17] variational method and the Ref. [13], for the strongcoupling of electron-phonon, carrying out the Lee-Low-Pines unitary transformation to Eq. (1).…”

Influence of temperature on ground state energy of bound polaron in asymmetric Gaussian potential quantum well in presence of electromagnetic field

“…In equation (1), the physical quantities are identical with those in [34]. -b r expresses the CIP about the hydrogen-like impurity and the electron.…”