受约束量子点系统的电子结构的理论研究

The interest in quantum dot systems has increased considerably over the years in many branches of physics, such as atoms and molecules under extremely high pressure introduced by spatial confinement, natural and artificial atoms in laser plasma environment or external electromagnetic filed, various custom-designed semiconductor nanostructures, etc. In this project, we will focus on the electronic structure of confined multi-electron quantum dot systems in different confinement models, more specifically, we will investigate the impenetrable spherical box confined quantum dot in weakly coupled plasmas. In such a quantum system, the interaction between charged particles is produced by the combination effect of Debye screened Coulomb potential and spherical box confinement potential. Considerable theoretical researches available in the literature have been concentrated on the one-electron problems, while investigations on multi-electron systems are quite scarce. In this work, we will focus our attention on the two- and three-electron quantum dot systems. By utilizing different types of explicitly correlated multi-electron wavefunctions, we will analytically calculate the multi-electron integrals including various kinds of confinement potentials and apply Löwdin’s canonical orthogonalization method to reduce the basis sets. Then we can accurately calculate the energy levels, wavefunction distribuions, oscillator strengths, photoionization cross sections, interelectronic quantum entanglement, and effective pressures for quantum dots under different confinement conditions. Finally, we will develop a highly efficient, flexible, and robust computational package to provide accurate atomic data for relevant areas.

对量子点系统的研究近年来在物理学的各个领域都引起了人们广泛的兴趣，如空间约束产生高压下的原子和分子、等离子体或电磁场环境中的自然原子和人工原子、特需制造的各种半导体纳米结构等。本项目将研究在多种约束条件下的多电子量子点系统所具有的电子结构，具体研究对象为弱耦合等离子体中的不可穿透球形盒约束量子点。在这种系统中，带电粒子间相互作用同时受到屏蔽库伦势和球形盒约束势的影响。目前现有的理论研究大多集中在单电子问题，对多电子问题的研究还很不充分。在本项目中，我们拟利用多种高关联波函数，解析地求解在多种约束势作用下的多电子势能积分，并利用全局正交化方法约化基函数，精确地计算双电子及三电子量子点系统的能级结构、波函数分布、振子强度、光电离截面、电子间量子纠缠、以及不同约束条件下的有效压强等物理性质。通过开发一套高效可靠的适用于各种外界条件的计算程序，为相关领域提供精确的原子数据。

对弱耦合等离子体和空间球形约束势作用下的原子体系的结构理论研究，有利于帮助我们理解外部环境对原子的电子结构的影响，通过对系统能级、电子波函数及其相关物理量随环境参数的变化进行分析，为我们深入理解电子间的关联效应提供了新的方法和手段。本项目中，我们分别研究了基于Debye屏蔽库伦势模型的弱耦合等离子体环境和不可穿透球形约束势作用下的单电子和双电子原子系统，精确地计算了原子在不同外界环境参数下的能级分布与电子波函数的变化，并通过对坐标空间和动量空间中电子几率分布信息熵的研究，对电子分布的局域性与不确定性等量子特性进行定量描述。通过发展多种理论方法和数值计算程序，我们能够对各种外界条件下的原子结构性质进行理论预测，为原子分子物理、等离子体物理、量子信息等领域提供重要的原子数据。