Effect of Parabolic Potential on Bipolaron

We apply a Feynman path-integral variational approach combining with the average for the relative motion to study the stability of bipolaron in a quantum dot. The binding energy is calculated in different parameters. We find that an optimum quantum potential favors the formation of bipolaron. Compared with other methods in literature, the present approach is better than Laudau Pekar one in all coupling regime and full path-integral one in the strong coupling regime.     

抛物势量子点中强耦合双极化子量子比特的性质

基于LLP幺正变换,采用Pekar型变分法得到了二维量子点中强耦合双极化子的基态和第一激发态的能量和波函数,进而构造了一个双极化子的量子比特。数值结果表明:在量子比特内,两电子的空间几率密度的时间振荡周期T0随电声子耦合强度α、量子点的受限强度ω0以及介质的介电常数比η的增加而减小;在量子比特内,两电子的空间几率密度Q随时间t、角坐标φ2及介电常数比η的变化而作周期性振荡;两电子在量子点中心附近区域出现的几率较大,而在远离量子点中心区域出现的几率很小。     

Effects of Thermal Lattice Vibration on the Effective Potential of Weak-Coupling Bipolaron in a Quantum Dot

Based on the Huybrechts' linear-combination operator,effects of thermal lattice vibration on the effective potential of weak-coupling bipolaron in semiconductor quantum dots are studied by using the LLP variational method and quantum statistical theory.The results show that the absolute value of the induced potential of the bipolaron increases with increasing the electron-phonon coupling strength,but decreases with increasing the temperature and the distance of electrons,respectively;the absolute value of the effective potential increases with increasing the radius of the quantum dot,electron-phonon coupling strength and the distance of electrons,respectively,but decreases with increasing the temperature;the temperature and electron-phonon interaction have the important influence on the formation and state properties of the bipolaron:the bipolarons in the bound state are closer and more stable when the electron-phonon coupling strength is larger or the temperature is lower;the confinement potential and coulomb repulsive potential between electrons are unfavorable to the formation of bipolarons in the bound state.     

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.     

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.     

双电子二维量子点基态能量的计算

分别利用微扰法、精确的对角化方法和变分法计算了双电子二维量子点的基态能量,与早期无约束的哈特利-福克研究结果比较,发现三参量的变分波函数是基态的极好表征.     

双电子平面量子点基态能量的计算

由于库仑作用,目前的研究还得不到双电子平面量子点基态波函数和基态能量的精确解析解.分别利用微扰法、精确对角化方法和变分法,计算双电子平面量子点的基态能量,与早期的无约束哈特利-福克研究结果比较,发现三参量的变分波函数是基态的极好表征.且能对多电子平面量子点的基态描述提供参考.     

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.     

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.     

Polaron Effect of a Two Electron Parabolic Quantum Dot

Polaron induced double electron in a quantum dot is investigated using the exact diagonalization techniques and the compact density-matrix approach. The dependence of nonlinear optical processes on the incident photon energies and the polaronic effect are brought out. The linear, third order non-linear optical absorption coefficients and the refractive index changes of singlet and triplet states as a function of photon energy are obtained with and without the inclusion of polaronic effect. It is found that the geometrical confinement and the effect of polaron have great influence on the optical properties of dots.     

Properties 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 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 quantum dot may be employed as a two-level quantum system-qubit. When the electron is in the superposition state of the ground- and the first-excited state, we obtain the time evolution of the electron density. The relation of the probability density of electron on the Coulomb binding parameter and the relations of the period of oscillation on the Coulomb binding parameter, the electron-LO-phonon coupling constant and the confinement length are derived.     

Effect of Magnetic Field on Internal Energy and Entropy of a Parabolic Cylindrical Quantum Dot

In the present work, the entropy and internal energy of a GaAs cylindrical quantum dot in the presence of an applied magnetic field is studied. For this purpose, the Tsallis formalism is applied to obtain internal energy and entropy. It is found that entropy and internal energy are continuous function and they are zero at special temperatures. Entropy maximum increases with increasing dot radius. Internal energy increases by increasing magnetic field.     

Ground and Excited States of Bipolarons in Two and Three Dimensions

The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The groundstate (GS) and excited-state energies of the Fr(o)hlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.     

Four-Electron Systems in a Coupled Double-Layer Quantum Dots

Making use of the method of few-body physics, the energy spectrum of a four-electron system consisting in a vertically coupled double-layer quantum dot as a function of the strength ofa magnetic field is investigated. Discontinuous ground-state transitions induced by an external magnetic field are shown. We find that, in the strong coupling case, the ground-state transitions depend not only on the external magnetic field B but also on the distance d between double-layer quantum dots. However, in the case of weak coupling, the ground-state transitions occur in the new sequence of the values of the magic angular momentum. Hence, the interlayer separation d and electron-electron interaction strongly affect the ground state of the coupled quantum dots.     

温度对抛物量子阱中极化子能量的影响

采用线性组合算符法和幺正变换法研究温度对抛物型量子阱中极化子基态能和基态结合能的影响. 通过理论推导得到极化子基态能和基态结合能的表达式. 结合量子统计力学中平均声子数的表达式, 得到极化子基态能量和基态结合能与温度的函数关系. 在不同温度下, 分别讨论了极化子基态能量和基态结合能与电子-声子耦合强度和阱宽的关系, 阱深取不同值时讨论了极化子基态能和基态结合能随温度的变化规律. 计算结果表明, 极化子的基态能量和基态结合能都是温度的递增函数.     

Ground and Excited States of Bipolarons in Two and Three Dimensions

The properties of large bipolarons in two and three dimensions are investigated by averaging over the relative wavefunction of the two electrons and using the Lee-Low-Pines-Huybrechts variational method. The ground-state (GS) and excited-state energies of the Fröhlich bipolaron for the whole range of electron-phonon coupling constants can be obtained. The energies of the first relaxed excited state (RES) and Franck-Condon (FC) excited state of the bipolaron are also calculated. It is found that the first RES energy is lower than the FC state energy. The comparison of our GS and RES energies with those in literature is also given.     

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。     

抛物量子点中强耦合磁极化子的性质

采用Pekar类型的变分方法研究了抛物量子点中强耦合磁极化子的基态和激发态的性质。计算了基态和激发态磁极化子的束缚能以及磁极化子的共振频率。讨论了这些量对回旋频率和有效限制强度的依赖关系,以及磁极化子光学声子平均数的性质,结果表明:由于Zeeman劈裂,抛物量子点中磁极化子的回旋共振频率劈裂为两支。基态和激发态磁极化子的束缚能以及磁极化子的共振频率都随回旋频率的增加而增大,随量子点的有效束缚强度的增大而减小。     

Spin Polaron in a Diluted Parabolic Magnetic Quantum Well

Theoretical investigations of spin polaron in a quantum well in the spin doping superlattice systems Cd_{1 - x_{in}} Mn_{x_{in}} Te / Cd_{1 - x_{out}}Mn_{x_{out}} Te are presented in this paper. A variational procedure within the effective mass approximation is employed in the presence of magnetic field to calculate the donor ionization energy. Spin polaronic shifts are estimated using a meanfield theory. The results show that the donor binding energy (i) Increases with the reduction in well sizes (ii) Decreases with the magnetic field is increased for a given well width (iii) Increases to a maximum value at 90 {\AA} and then decreases as the size of the well increases beyond 90 {\AA} and (iv) Spin polaronic shifts to the donor binding energy not only decrease in a magnetic field but also with the well width. The results are compared with the existing available literature.     

压力下GaN/Ga1-xAlxN量子点中杂质态的界面效应

考虑界面处导带弯曲,流体静压力以及有效质量随量子点位置的依赖性,采用变分法以及简化相干势近似,研究了无限高势垒GaN/Ga_1-xAl_xN球形量子点中杂质态的界面效应,计算了杂质态结合能随量子点尺寸、电子面密度以及压力的变化关系。结果表明,结合能随压力的增大呈线性增加的趋势,有效质量位置的依赖性以及导带弯曲对结合能有不容忽视的影响。