Temperature Effects of Parabolic Linear Bound Potential and Coulomb Bound Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in a parabolic quantum dot, we obtain the eigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method of Pekar type. This system in a quantum dot may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground state and the first-excited state, we obtain the time evolution of the electron density. The relations of the probability density of electron on the temperature and the electron-LO-phonon coupling constant and the relations of the period of oscillation on the temperature, the electron-LO-phonon coupling constant, the Coulomb binding parameter and the confinement length are derived. The results show that the probability density of electron oscillates with a period when the electron is in the superposition state of the ground and thefirst-excited state, and show that there are different laws that theprobability density of electron and the period of oscillation change with the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher. And it is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases with increasing the confinement length not only at lower temperatures but also at higher temperatures.     

Properties of Unsymmetrical Parabolic Confinement Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in unsymmetrical parabolic confinement potential quantum dot (QD), we obtain the eigenenergies of the ground state and the first-excited state, the eigenfunctions of the ground state, and the first-excited state by using variational method of Pekar type. This system in QD may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground state and the first-excited state, we obtain the time evolution of the electron density. The relations both the probability density of electron and the period of oscillation with the electron-LO-phonon coupling strength, the confinement strengths in the xy-plane and the z-direction are discussed.     

The energy levels of a two-electron two-dimensional parabolic quantum dot

This paper studies the two-electron total energy and the energy of the electron--electron interaction by using a variational method of Pekar type on the condition of electric--LO-phonon strong coupling in a parabolic quantum dot. It considers the following three cases: 1) two electrons are in the ground state; 2) one electron is in the ground state, the other is in the first-excited state; 3) two electrons are in the first-excited state. The relations of the two-electron total energy and the energy of the electron--electron interaction on the Coulomb binding parameter, the electron-LO-phonon coupling constant and the confinement length of the quantum dot are derived in the three cases.     

声子色散和库仑势对量子点中极化子基态能量的影响

本文在声子色散和库仑束缚势的影响下利用压缩态变分法计算了抛物量子点中弱耦合极化子的基态能量。采用的变分方法是基于逐次正则并且利用单模压缩态变换处理通常被我们所忽略的在第一次幺正变换中产生的声子产生湮灭算符的双线性项。计算得出了在考虑声子色散和库仑束缚势的情况下抛物量子点中弱耦合极化子的基态能量的数学表达式。讨论了在弱耦合情况下,受限长度,电子-声子耦合常数,色散系数,库仑结合参数与基态能量之间的依赖关系。     

抛物线性限制势二能级系统量子点量子比特的温度效应

应用Pekar变分方法,在抛物量子点中电子与体纵光学声子强耦合条件下,得出了电子的基态和第一激发态的本征能量及基态和第一激发态的本征波函数.以量子点中这样的二能级体系作为一个量子比特.当电子处于基态和第一激发态的叠加态时,计算出电子在时空中作周期性振荡的概率分布.并且得出了概率分布随温度及耦合强度的变化关系. 关键词： 量子点 量子比特 温度效应     

The influence of electric field on a parabolic quantum dot qubit

This paper calculates the time evolution of the quantum mechanical state of an electron by using variational method of Pekar type on the condition of electric--LO-phonon strong coupling in a parabolic quantum dot. It obtains the eigenenergies of the ground state and the first-excited state, the eigenfunctions of the ground state and the first-excited state This system in a quantum dot may be employed as a two-level quantum system qubit. The superposition state electron density oscillates in the quantum dot with a period when the electron is in the superposition state of the ground and the first-excited state. It studies the influence of the electric field on the eigenenergies of the ground state, the first-excited state and the period of oscillation at the different electron--LO-phonon coupling constant and the different confinement length.     

The decoherence of the triangular and Coulomb bound potential quantum dot qubit

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.     

Bound polaron in a two- and three-dimensional quantum dot for arbitrary electron–phonon coupling strength

A variational approach is presented for calculating the ground-state (GS) binding energies of an electron bound to a Coulomb impurity in a polar semiconductor quantum dot (QD) with parabolic confinement in both two and three dimensions. We perform calculations for the entire range of the electron-phonon coupling constant and the Coulomb binding parameter and for arbitrary confinement length. It is found that the polaronic effect is stronger in a two dimensions (2D) dot than in a three dimensions (3D) dot and this trend is more pronounced with the increase of the coupling constant. Furthermore, the GS binding energy increases with increasing the Coulomb binding parameter in both 2D and 3D QDs for the same electron–phonon coupling constant. The results also indicate that this effect becomes much more pronounced with decreasing dimensionality.     

VARIATIONAL CALCULATION ON GROUND-STATE ENERGY OF BOUND POLARONS IN PARABOLIC QUANTUM WIRES

Within the framework of Feynman path-integral variational theory, we calculate the ground-state energy of a polaron in parabolic quantum wires in the presence of a Coulomb potential. It is shown that the polaronic correction to the ground-state energy is more sensitive to the electron－phonon coupling constant than the Coulomb binding parameter, and it increases monotonically with decreasing effective wire radius. Moreover, compared to the results obtained by Feynman Haken variational path-integral theory, we obtain better results within the Feynman path-integral variational approach (FV approach). Applying our calculation to several polar semiconductor quantum wires, we find that the polaronic correction can be considerably large.     

抛物量子点中强耦合束缚极化子的性质

采用Pekar类型的变分方法研究了抛物量子点中强耦合束缚极化子的基态和激发态的性质。计算了束缚极化子的基态和激发态的能量、光学声子平均数。讨论了量子点的有效束缚强度和库仑束缚势对基态能量、激发态能量以及光学声子平均数的影响。数值计算结果表明:量子点中强耦合束缚极化子的基态和激发态能量及光学声子平均数均随量子点的有效束缚强度的增加而减小,基态、激发态能量随库仑束缚势的增加而减小,光学声子平均数随库仑束缚势的增加而增大。     

The ground-state lifetime of polaron in a parabolic quantum dot

This paper reports that the ground-state energy of polaron was obtained with strong electron-LO-phonon coupling by using a variational method of the Pekar type in a parabolic quantum dot. Quantum transition is occurred in the quantum system due to the electron-phonon interaction and the influence of temperature. That is the polaron transit from the ground-state to the first-excited state after absorbing a LO-phonon and it causes the change of the polaron lifetime. Numerical calculations are performed and the results illustrate that the ground-state lifetime of the polaron will increase with increasing the ground-state energy of polaron and decrease with increasing the electron-LO-phonon coupling strength, the confinement length of the quantum dot and the temperature.     

抛物量子点中弱耦合束缚极化子的相互作用能

研究了抛物量子点中弱耦合束缚极化子的性质,采用改进的线性组合算符和幺正变换方法导出了束缚极化子的振动频率、有效质量和相互作用能。讨论了量子点的有效受限长度、电子LO声子耦合强度和库仑场对抛物量子点中弱耦合极化子的振动频率、有效质量和相互作用能的影响。数值计算结果表明:弱耦合束缚极化子的振动频率和相互作用能随有效受限长度的减少而急剧增大,振动频率随库仑势以及电子LO声子耦合强度的增加而增加,而相互作用能随库仑势以及电子LO声子耦合强度的增加而减小。有效质量仅与电子LO声子耦合强度有关。     

库仑场对量子点中强耦合束缚极化子激发态性质的影响

采用线性组合算符和幺正变换方法研究量子点中强耦合束缚极化子的振动频率、第一内部激发态能量、激发能量和共振频率的性质。讨论了这些量随量子点的有效受限长度、电子-声子耦合强度和库仑束缚势的变化关系。通过数值计算结果表明:量子点中强耦合束缚极化子的振动频率、第一内部激发态能量、激发能量和共振频率随量子点的有效受限长度的减小而迅速增大,随库仑束缚势和电子-声子的耦合强度的增加而增大。     

抛物量子点中强耦合束缚磁极化子的性质

采用Pekar类型的变分方法研究了抛物量子点中强耦合束缚磁极化子的基态和激发态的性质.计算了束缚磁极化子的基态和激发态的能量、光学声子平均数以及束缚磁极化子的共振频率.讨论了这些量对回旋频率和有效束缚强度以及库仑束缚势的依赖关系.数值计算结果表明:量子点中强耦合束缚磁极化子的基态能量和共振频率以及光学声子平均数均随量子点的有效束缚强度的增加而减小,基态能量随库仑束缚势的增加而减小,随回旋频率的增加而增大.     

抛物量子点中强耦合束缚磁极化子的声子平均数

采用线性组合算符和幺正变换方法导出了强耦合束缚磁极化子的振动频率和声子平均数。讨论了量子点的有效受限长度、磁场、库仑场和电子-LO声子耦合强度对抛物量子点中强耦合束缚磁极化子振动频率和声子平均数的影响。数值计算结果表明:强耦合束缚磁极化子的振动频率和声子平均数均随量子点的有效受限长度、回旋共振频率的增加而减小,随库仑束缚势的增加而增加,声子平均数随电子-LO声子耦合强度增加而减小。     

库仑势对抛物量子点量子比特消相干的影响

采用Pekar类型的变分方法,在电子与体纵光学声子强耦合的条件下,计算得出了抛物量子点中电子的基态能量和第一激发态能量及其相应的本征波函数.量子点中这样的二能级体系可以作为一个量子比特.由于声子的自发辐射,造成量子比特的消相干,讨论了消相干时间与库仑结合参数,耦合强度,受限长度,色散系数的变化关系. 关键词： 量子点 量子比特 量子信息 消相干     

Hydrogenic impurity bound polaron in a parabolic quantum dot with arbitrary electron-phonon coupling strength

A variational approach is employed to obtain the ground and the first excited state binding energies of an electron bound to a hydrogenic impurity in a polar semiconductor quantum dot (QD) with symmetric parabolic confinement in both two and three-dimensions. We perform calculations for the entire range of the electron-phonon coupling constant and the Coulomb binding parameter and for arbitrary confinement length. It is found that the binding energy of ground and first excited state is larger in a two-dimension (2D) dot than in a three-dimension (3D) dot and this trend is more pronounced with the increase of the electron-phonon coupling constant for the same value of the Coulomb binding parameter and confinement length. Furthermore, the ground and the first excited state binding energy increases with increasing the Coulomb binding parameter in both 2D and 3D QDs for the same electron-phonon coupling constant.     

磁场对非对称量子点中束缚磁极化子性质的影响

采用线性组合算符和幺正变换方法研究磁场对非对称量子点中弱耦合束缚磁极化子性质的影响。导出量子点中弱耦合束缚磁极化子振动频率和基态能量随量子点的横向和纵向有效受限长度、库仑束缚势、磁场的回旋共振频率和电子-声子耦合强度的变化关系。数值计算结果表明:非对称量子点中弱耦合束缚磁极化子的振动频率和基态能量随量子点的横向和纵向有效受限长度的减小而迅速增大。振动频率随库仑束缚势和磁场的回旋共振频率的增加而增大。基态能量随库仑束缚势和电子-声子耦合强度的增加而减小。     

Temperature Effects of Parabolic Linear Bound Potential and Coulomb Bound Potential Quantum Dot Qubit

On the condition of electric-LO phonon strong coupling in a parabolic quantum dot, we obtain the eigenenergy and the eigenfunctions of the ground state and the first-excited state using the variational method of Pekar type. This system in a quantum dot may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground state and the first-excited state, we obtain the time evolution of the electron density. The relations of the probability density of electron on the temperature and the electron-LO-phonon coupling constant and the relations of the period of oscillation on the temperature, the electron-LO-phonon coupling constant, the Coulomb binding parameter and the confinement length are derived. The results show that the probability density of electron oscillates with a period when the electron is in the superposition state of the ground and the first-excited state, and show that there are different laws that the probability density of electron and the period of oscillation change with the temperature and the electron-LO-phonon coupling constant when the temperature is lower or higher. And it is obtained that the period of oscillation decreases with increasing the Coulomb bound potential and increases with increasing the confinement length not only at lower temperatures but also at higher temperatures.     

抛物量子点中强耦合束缚极化子的光学声子平均数

采用线性组合算符和幺正变换方法研究了在库仑场束缚下抛物量子点中强耦合束缚极化子的振动频率和光学声子平均数,并对其进行了数值计算。结果表明:强耦合束缚极化子的振动频率和光学声子平均数随量子点的有效受限长度的增加而减小,随电子-LO声子耦合强度的增强而增加,束缚极化子的振动频率随库仑势的增加而减小。