量子点系统的动力学和输运性质研究

【作者】 刘玉申；

【导师】 陈灏；

【作者基本信息】 复旦大学 ， 理论物理， 2007， 博士

【摘要】 本论文主要涵盖了三方面的工作，可分为三部分。第一部分是有关含时双量子点系统的动力学性质的研究，这一部分的推导主要采用紧束缚Hubbard模型。在第二部分，利用非平衡态格林函数的方法，我们讨论了通过单个包含电子-电子相互作用的量子点的非弹性输运性质。在第三部分，我们同样利用非平衡态格林函数的方法，研究了包含两个耦合的量子点，对称隧穿耦合到电极的AB环的输运性质，在这里量子点之间的库仑相互作用被考虑进去。第一部分为第1章共分7节。第1节简略地描述了量子点系统。第2节介绍了含时介观物理体系的研究背景。激光技术的迅速发展，为我们研究激光和物质相互作用引起的一些非线性性质打开了方便之门。第3节我们系统的介绍了用于研究周期含时哈密顿量的一个好的数值方法：Floquet理论方法。在第4节我们研究了在周期外场驱动下，双电子在不对称耦合的量子点分子的动力学行为。数值结果显示动态局域化和Rabi振荡现象也出现在这个量子系统。在第5节我们研究了在一个周期外场驱动下对称量子点分子中的激子的动力学行为。在较强的电子和空穴库仑相互作用的下，我们理论上分析了这个系统，指出动态局域化产生的条件。电子和空穴的相互库仑吸引相互作用在形成纠缠态中扮演着一个重要的角色。我们提供的近似结果和来自Floquet理论的数值结果符合的很好。在第6节我们研究了在随机脉冲下，在量子点分子中的激子的动力学行为。当两个局域化态的Rabi振荡发生，最大纠缠贝尔态被形成在这个量子点分子。最后在第7节我们给出工作小结以及工作展望。第二章包括8节。在第1节我们简单介绍一下通过量子点系统量子输运的研究背景。第2节给出了格林函数的定义。在第3节，我们列举了三个简单的完全可解的模型：粒子之间无相互作用模型，共振能级模型和Einstein模型。在第4节中，我们介绍了在处理介观系统的输运性质时用到的Keldysh技术，它是研究含时或非含时量子点系统输运性质的一个重要的方法。一个光子辅助隧穿模型被介绍在第5节中。在第6节，我们介绍了一个声子辅助隧穿模型。第7节也就是本章的重点，我们利用非平衡态格林函数方法和正则变换，研究了低温下单个量子点的非弹性输运性质。在这里我们考虑了电子-电子的相互作用，电子-声子，电子-光子相互作用。时间平均占据数，时间平均电导以及时间平均电流被自洽计算得到。时间平均电导随着外场强度和入射电子能量的变化也被研究。由于电荷的积累，两种声子发射峰可能同时存在在这个系统。在最后一节我们对工作做了总结和展望。第三章包含了6节。在第1节，我们简单介绍了通过两个量子点输运研究背景。在第2节，我们给出将要研究的一个理论模型。两个平行耦合的单能级量子点被连在电极上。在第3节，我们用运动学方法计算了两个点中的格林函数。在第4节，用Keldysh格林函数，一个隧穿电流公式被给出。在第5节，我们介绍了数值结果和讨论。工作总结和展望被写在最后一小节中。更多还原

【Abstract】 This dissertation mainly includes three parts. The first part presents the theoretical research on dynamics property of the time-dependent double quantum dots system. The results of this part are mainly obtained by using the tight-bonding Hubbard model. The second part discusses the electronic inelastic transport through a quantum dot in the presence of the electron-electron interaction by using the Keldysh nonequilibrium Green function approach. In the third part, we study electronic transport properties of an Aharonov-Bohm ring with embedded coupled double quantum dots connected to two electrodes in a symmetrical parallel configuration in the presence of strong interdot Coulomb interaction by using the Keldysh nonequilibrium Green function approach.The first part is composed of seven subsections. The first subsection simply introduces quantum dots system. In the second subsection, we introduce the background of the study on the time-dependent mesoscopic system. The development of laser technologies open the doorway for studying the new quantum effects in nonlinear quantum systems which interact with strong electromagnetic field. In the third subsection, we introduce a good approach (Floquet theory) to study of quantum systems with their Hamiltonian being a periodic function in time. In the 4th subsection, we study the dynamics of the two interacting electrons in an asymmetric double coupled quantum dot under an ac electric field. The numerical results demonstrate that the dynamical localization and Rabi oscillation still excite in the system. In the 5th subsection, we investigate the dynamical behaviors of an interacting electron - hole pair in a double coupled quantum dot molecule under an ac electric field. We theoretically analyze the phenomenon of localization of an exciton in the quantum system under the strong Coulomb interaction, and indicate the conditions that dynamical localization occurs. The attractive Coulomb interaction plays an important role in forming the entangled states of the system. In the 6th subsection, we theoretically analyze the dynamical behaviors of an interacting electron - hole pair in a double coupled quantum dot molecule in radiation pulses. It is found the maximally entangled Bell states can be prepared when a resonant transfer occurs between two localized states. A summary and prospec-tion are given in 7th subsection. The second part includes 8 subsections. The first subsection briefly introduces the background of the study on the transport through the quantum dot system. In the second subsection, the definitions of Green functions are introduced. The third subsection introduces three exactly solvable models : free-particle model, resonant-level model and Einstein model. In the 4th subsection, we introduce the nonequilibrium keldysh technologies, which is an important approach to study the transport properties of the time-dependent or time-independent quantum dots system. Photon- assisted tunneling processes are introduced in the 5th subsection. In the 6th subsection a phonon-assisted model is given. The 7th subsection is the important part in the second chapter. We study the low-temperature inelastic transport properties of a single quantum dot with the on-site Coulomb repulsive interaction, the electron-phonon interaction and the electron-photon interaction by using the nonequilibrium Green function(NEGF) approach and the canonical transformation. The time-averaged occupation number, the time-averaged differential conductance and time-averaged current are calculated self-consistently in the quantum dot. The variation in the differential conductance with the frequency of the external field and the incident electron energy is presented. It is found that the two kinds of phonon-emission peaks may coexist in the time-averaged differential conductance spectrum due to the charge accumulations. In the last subsection the summary and prospection are present.The third part includes 6 subsections. The first subsection briefly introduces the background of the study on the transport through the double quantum dots system. In the second subsection, we give a model consists of two single-level coupled quantum dots attached in a parallel configuration to the leads. In the third subsection, we calculate the Green’s function of the two dots by using the standard equation-of-motion technique. In the 4th subsection, we give tunneling current formula by using the Keldysh Green function. Numerical results and discussion are given in the 5th subsection. The summary and prospect are written in the last subsection.更多还原