Influence of Hydrogen-like impurity and thickness effect on quantum transition of a two-level system in an asymmetric Gaussian potential quantum dot

Considering hydrogen-like impurity and the thickness effect, the eigenvalues and eigenfunctions of the electron ground state and first exited state in a quantum dot (QD) are derived by using the Lee-Low-Pines-Pekar variational method with a parabolic confinement potential well (PCPW) and an asymmetric Gaussian functional confinement potential well (AGFCPW) serving as the transverse and longitudinal confinement potential, respectively. Based on the above two states, a two-level system is constructed. Then, the electron quantum transition affected by a magnetic field is discussed in terms of the two-level system theory. The numerical calculations indicate that the electron transition probability Q deceases with the range R-0 of the PCPW decreasing. With R-0 decreasing, the amplitude of the transition probability Q decreases greatly when R-0 is small (R-0 < 2:5r(p)), but the decrease becomes small when R-0 is large (R-0 > 2:5r(p)). The transition probability Q decreases with the dielectric constant ratio eta increasing. For different values of the well width L of the AGFCPW, the change forms of the transition probability Q with the well width L are different: the transition probability Q decreases monotonically with the decreasing of the well width L when L is large (L > 1:3r(p)), which is similar to the trend of the transition probability Q changing with the range R-0 of the PCPW, but the oscillation of the transition probability Q is small with the decreasing of the well width L when L is small (L < 1:3r(p)). Whereas, both changes are consistent basically when the range of the confinement potential (the value of R-0 or L) is large since the AGFCPW can be approximated by the PCPW when z/L << 1. For the electronic state and its change in the QD with a confinement potential, in any case, the results are rough without regard to the influence arising from the thickness of the QD. This shows that the AGFCPW is more accurate than the PCPW in reflecting the real confinement potential. This conclusion is in accordance with the experimental results. In addition, the transition probability Q decreases with increasing V-0. The amplitude of the transition probability Q decreasing with increasing the dielectric constant ratio eta is enlarged with reducing the coupling strength alpha. This indicates that the phonon (the polarization of the medium) effect cannot be ignored when investigating the change of the electronic state in the QD. The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency omega(c). The external magnetic field is a kind of inducement causing the quantum transition of electronic state. The transition probability Q periodically oscillates and goes up with increasing the cyclotron frequency omega(c), and is affected dramatically by the coupling strength alpha : with increasing the coupling strength alpha, the oscillation period of Q increases, but the oscillation amplitude decreases. In a word, the transition probability of the electron is influenced significantly by some physical quantities, such as the coupling strength alpha, the dielectric constant ratio eta, the resonant frequency of the magnetic field omega(c), the well depth V0, and the well width L of AGFCPW.