一维纳米线中Majorana费米子的验证方案及其与超导量子比特耦合的研究

Quantum computer is one of the hottest topics in physics community. Its extraordinary computing capacity has encouraged many scientists to engage in how to make it. Topological quantum computation is a fault-tolerance computation model. However, there rarely has feasible physical system for topological qubit. 1-Dimension nanowire in proximity with s-wave superconductor is a hopeful system to do topological quantum computing because it may host Majorana fermion (MF), which is suitable to be topological qubit. The problem is that the existence of MF has not been confirmed in this system. In our project, we would construct a scheme based on fractional Josephson effect to verify its existence. First we calculate numerically the spectrum of a nanowire-Josephson junction in presence of magnetic field, and obtain the critical magnetic field, at which the phase transition between topological and non-topological phase happens. Then, we calculate the spectrum as the chemical potential change piecewisely. With this，we add a suitable voltage on the junction, and calculate the power spectrum with chemical potential in both phase, from which we will find the difference of the two phases. Besides, we would study how to coupling topological qubit and superconducting qubit including phase qubit and transmon. Take advantage of fractional Josephson effect, we first calculate the coupling matrix elements between them, and based on the coupling type, conceive the scheme of measuring topological qubit. Then, we would devise the approaches of controlling the coupling. Our study would pave a way for verifing the existence of MF，and make one step closer to realizing universal topological quantum computation using MF. In addition, our work could push forward the hybridization of topological and superconducting quantum computation.

量子计算机是最近二十年世界各国科学家努力实现的目标。拓扑量子计算是一种可容错的量子计算，但是目前缺少适合的物理系统。有人预言一维纳米线中存在可做拓扑比特的Majorana费米子，但还没得到实验证实。本项目拟研究如何利用约瑟夫森结来验证Majorana费米子的存在。首先我们计算在约瑟夫森结两端有和无Majorana费米子时系统低能谱线对外界参数的依赖关系，然后分别研究两种情形下结的约瑟夫森效应随参数的变化规律，最后分析两者之间的差异。我们的研究可为检验纳米线系统中能否出现Majorana费米子提供可行的方案。本项目还将研究Majorana费米子构成的拓扑比特与超导量子比特的耦合。我们先计算出拓扑比特与超导相位比特、电荷比特耦合算符的矩阵元，然后探索如何调控耦合和测量拓扑比特状态。该研究有助于实现普适拓扑量子计算，并促进它与超导量子计算的融合。

拓扑超导体是近十年来凝聚态领域的一个热点课题。它的边界上会衍生出一种奇异的准粒子，即马约拉纳费米子。由于这种粒子满足非阿贝尔统计规律，所以它在量子计算方面有非常重要的应用前景。但是马约拉纳费米子的存在还没有完全得到证实。分数约瑟夫森效应和非局域性是马约拉纳费米子的两大特征，但是实验上测量它们是很困难的。本课题研究了如何在一维半导体纳米线系统中探测马约拉纳费米子的这两个特性，并借此来证明这种粒子的存在。本项目研究发现：（1）分数约瑟夫森效应导致非常规的相位滑移现象。传统的约瑟夫森结里的相位滑移导致的相位差的变化是2pi，而在拓扑约瑟夫森结中是4pi。我们证明了这种新型相位滑移效应可以表征马约拉纳费米子，并且在实验上比直接测直流约瑟夫森效应更容易。（2）在拓扑约瑟夫森结中，拓扑平庸相的安德鲁束缚态和拓扑相的马约拉纳束缚态随磁场强度和结的穿透系数变化的行为有明显的不同，而且这些不同的根源是这些态有没有鲁棒的分数约瑟夫森耦合，以及是不是非局域分布的。为区分拓扑超导相和拓扑平庸相，我们提出用微波来探测这些态的变化趋势。我们的研究为在实验上证实马约拉纳费米子的存在提供了切实可行的方案，并为基于马约拉纳费米子的拓扑量子计算和信息处理奠定了良好的基础。