高阶自旋噪音谱的量子理论及其在量子点自旋系统中的应用

As one of the candidates of quantum bit in the future quantum computer, quantum dot spin system is challenged by the quantum decoherence process due to the coupling to environment. How to understand the mechanism leading to spin decoherence has always been an important problem in both condensed matter physics and quantum computation. Because of the large number of nuclear spins and their complex dynamics, it becomes very challenging to solve the dynamics of quantum dot central spin. Starting from quantum master equation and taking into account of quantum measurement effect, this project will develop a quantum theory that enables us to calculate the higher order spin noise correlation, and apply it into the newly developed technique of higher order spin noise spectroscopy；Through the calculation of higher order spectroscopy of intrinsic spin fluctuation, we can describe in details the effect of different kinds of interactions on quantum spin dynamics；This project will discuss the relation between interactions such as anisotropy, quadrupole and dipole-dipole, and higher order spin noise spectroscopy in quantum dot spin system, and discover the underlying mechanism of spin decoherence. This project will provide a theoretical basis for deeper understanding of spin decoherence of quantum dot, instruct people to design and fabricate quantum dot spin device with long coherence time, and help the studies in other quantum spin systems.

量子点自旋系统作为未来量子计算机中量子比特的候选者之一，面临的主要挑战是跟外界环境耦合而造成的量子退相干效应。对自旋退相干的物理机制的理解成为凝聚态物理和量子计算领域的一个重要课题。由于核自旋数量巨大且有复杂的动力学过程，量子点中心自旋的动力学求解变得非常困难。本项目将从量子主方程出发，计入量子测量效应，发展一套计算高阶自旋噪音关联的量子理论，并应用到高阶自旋噪音谱这一新技术中；通过对本征自旋涨落的高阶谱的计算，精细刻画不同类型的相互作用对量子自旋动力学过程的影响；探讨量子点自旋系统中各向异性、电四极、磁偶极等相互作用跟高阶自旋噪音谱的内在联系，从而阐明自旋退相干的物理机制。本项目将为深入理解量子点自旋退相干效应提供理论基础，为制备具有长相干时间的量子点自旋器件提供理论指导，也为研究其它量子自旋系统的动力学过程提供有意义的借鉴。

在量子点自旋系统中，发展了计入量子测量效应下的全计数动力学理论，为计算高阶自旋涨落关联函数提供了理论工具；系统地研究了在连续的量子测量之下自旋的量子退相干效应，揭示了不同类型的相互作用，如连续测量的测量强度和外磁场强度，对量子自旋动力学过程的影响；建立了不同时刻下自旋测量结果的地推关系，以此发展了一套高效的数值计算方法，进而获得了在测量强度和磁场强度的参数空间中的自旋动力学的相图。在另一方面，发展了一套被驱动情况下的自旋动力学理论，找到了多状态的含时哈密顿量演化之后的解析解，并将其应用于在拓扑体系在缓慢淬灭下的动力学刻画；我们证明缓慢淬灭动力学下，拓扑不变量不仅可以通过带反转表面上的拓扑信息捕获，而且可以在自旋反转表面上捕获。本项目的研究为制备具有长相干时间的量子点自旋器件提供理论指导.