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Chinese Physics B

The optical phonon effect of quantum rod qubits

Cui-Tao Wang, Zhiyong Wu, Cui-Lan Zhao, Zhao-Hua Ding, Jing‐Lin Xiao

Published May 1, 2012• 3 citations
Publisher

Abstract

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given by using a coordinate transformation in which the ellipsoidal boundary is changed into a spherical one. Under the condition of strong electron—longitudinal optical phonon coupling in the rod, we obtain both the electron eigenfunctions and the eigenenergies of the ground and first-excited state by using the Pekar-type variational method. This quantum rod system may be used as a two-level qubit. When the electron is in the superposition state of the ground and first-excited states, the probability density of the electron oscillates in the rod with a certain period. It is found that the oscillation period is an increasing function of the ellipsoid aspect ratio and the transverse and longitudinal effective confinement lengths of the quantum rod, whereas it is a decreasing function of the electron—phonon coupling strength.

DOI
10.1088/1674-1056/21/5/057108

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We investigate the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to LO-phonon in an asymmetric quantum dot (QD) by using variational method of Pekar type. The present system may be used as a two-level qubit. When the electron is in the superposition state of the ground and the first excited states, the probability density of the electron oscillates in the QD with a certain period. It is found that the oscillation period is an increasing function of the transverse and the longitudinal effective confinement lengths of the QD, whereas it is a decreasing one of the electron–phonon coupling strength.
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 the APP in different directions. Whereas its oscillatory period is an increasing one and will diminish with enhancing the electron—phonon (EP) coupling strength.
On the basis of Lee-Low-Pines( LLP) unitary transformation,the eigenenergy and eigenfunction of the ground-state and the first excited state of the strong-coupling bipolaron in two-dimensional quantum dot( QD) were obtained by using the variational method of Pekar type. A qubit was formed by overlaying both the ground state and the first excited state of the bipolaron system. Numerical calculations indicate that the oscillating period T0 of qubits decreases with the increasing the electron-phonon coupling strength α,the confinement strength ω0of the quantum dot,and the dielectric constant ratio η; the distribution of the probability density Q of the electrons in quantum dot oscillates periodically with time t,angle coordinate φ2,and the dielectric constant ratio η,and there is a maximum at near the center and zero away from the center of quantum dot.
We study the eigenenergies and the eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to the LO-phonon in a quantum dot with triangular bound potential by using the Pekar variational method. This system may be used as a two-level qubit. Our numerical results indicate that the decoherence rate will decrease with increasing the confinement length of the quantum dot (QD) and decrease with increasing electron-LO-phonon coupling constant. The influences of the polar angle on the decoherence rate are dominant when the coupling constant increases, while the effects of the polar angle on that are strong when the confinement length increases. Meanwhile, the decoherence rate varies periodically with respect to the polar angle.
We study the eigenenergies and eigenfunctions of the ground and first-excited states of an electron which is strongly coupled to an LO-phonon in a quantum dot with a triangular bound potential and Coulomb bound potential by using the Pekar variational method. This system may be used as a two-level qubit. Phonon spontaneous emission causes the decoherence of the qubit. Numerical calculations are performed on the decoherence rate as a function of the polar angle, the Coulomb binding parameter, the coupling strength, the confinement length of the quantum dot and the dispersion coefficient.