Quantum Dynamics Of Quantum-Dot And Nanomechanical-Resonator Systems

Quantum dots, artificial atoms or man-made submicron structures in solid, consti-tute a representative system for mesoscopic conductors and are platforms for quantum engineered devices, since many physical properties like tunnel coupling, energy spac-ing, etc. can be well controlled and varied. Quantum dots coupled in series also provide a perfect system to explore quantum coherence effects because the quantum superposi-tion of states in different dots has an immediate influence on the charge transfer. More-over, coupled quantum dots are also promising candidates for future implementations of quantum computation because of its relatively easy scalability. Recent technological advances have made it possible to confine, manipulate and measure a small number of electrons or just one electron in a single or double quantum dot. As a result, there has been considerable research activities related to quantum dots. Meanwhile, in recent years, nanomechanical resonators have become a very active area and are also attracting considerable attention because of their fundamental importance and potential applica-tions. Nanomechanical resonators with high resonance frequencies and large quality factors can be used, for example, to serve as ultrasensitive sensors in high-precision displacement measurement, detection of gravitational waves or mass detection, and to explore quantum effects such as superposition and entanglement at a macroscopic scale. Advances in nanofabrication techniques have made it possible to make devices in which nanomechanical resonators are connected to nanostructures such as quantum dots. The properties of these hybrid devices result from a combination of a macroscopic quantum phenomenon involving a small number of phonon in the cooled resonators and the ability to control single electrons, offered by quantum dots. Both manipulating and understanding these systems are therefore of great interest. Moreover, studying the backaction effects of a charge detector on this system is also of particular interest since they can help us better understand the experimental results.In this thesis, we investigate the quantum dynamics of the hybrid systems consisting of coupled double (triple) quantum dots and a nanomechanical resonator. Moreover, we also study the properties of quantum transport through the quantum dots systems as well as the effects of measurement backaction on these systems, which are induced by a nearby charge detector.Chapter1gives an overview of our investigated systems and their physical proper-ties, mainly including the fabrication of semiconductor quantum dots, the coupled dou-ble quantum dots, the coupled triple quantum dots, and the bunching and anti-bunching phenomena in electron transport.In Chapter2, we develop a master equation in the eigenstate representation by us-ing a simple double-quantum-dot model. This method has been used in our following chapters. Our approach presented here is not subject to either the large-bias condition or the low-temperature restriction. It is shown that our results under the large-bias ap-proximation are identical to those obtained using the many-body Schrodinger equation in the eigenstate representation.In Chapter3, we propose an approach for achieving ground state cooling of a nanomechanical resonator (NAMR) capacitively coupled to a triple quantum dot (TQD). The TQD is an electronic analog of a three-level atom in A configuration and allows an electron to enter lower-energy states and move out only from a higher-energy state. By tuning the degeneracy of the two lower-energy states in the TQD, an electron can be trapped in the dark state caused by the destructive quantum interference between tunnelings to the higher-energy state. Therefore ground state cooling of an NAMR can be achieved when an electron absorbs readily and repeatedly an energy quantum from the NAMR for excitation.In Chapter4, we propose a current correlation spectrum approach to probe the quan-tum behaviors of an NAMR. The NAMR is coupled to a double quantum dot (DQD) which acts as a quantum transducer and is further coupled to a quantum point contact (QPC). By measuring the current correlation spectrum of the QPC, shifts of the DQD energy levels which depend on the phonon occupation in the NAMR are determined. Quantum behaviors of the NAMR could thus be observed. In particular, the cooling of the NAMR into the quantum regime could be examined. In addition, the effects of the coupling strength between the DQD and the NAMR on these energy shifts are studied. We also investigate the impacts on the current correlation spectrum of the QPC due to the backaction from the charge detector on the DQD.In Chapter5, we investigate the influence of measurement backaction induced by a charge detector, i.e., QPC, on the full counting statistics (FCS) of voltage-biased quan-tum dots. We first study the FCS of electrons through single quantum dots with different quantum states and the related effects of measurement backaction. Also, we compare our results with the experimental ones and predict some new ones. Furthermore, we pay more attention to the effects of this measurement backaction on the FCS in a DQD. We show that this inevitable measurement backaction can essentially change the behav-ior of the FCS under certain conditions, e.g., changing the noise from sub-Poissonian to super-Poissonian and vice versa. When the measurement device is absent (i.e., the charge detector is decoupled to the DQD), we can recover the known results for both current and shot noise.Chapter6gives a summary of this thesis and an outlook of the further studies.