Spin Qubits and Spin Decoherence in Graphene Quantum Dots

石墨烯量子点是研究量子与经典交叉的独特材料体系。其原因在于主动降低该量子耗散系统的浴自由度是可行的。根据定义，一个量子耗散系统由一个小的量子系统和一个相互耦合的大量子系统组成。在石墨烯量子点中，系统可以是单个电子的自旋（在点内捕获），而其自由度将是宿主材料中13C原子的核自旋。这种耦合是由超精细相互作用介导的。在13C原子自然丰度为1%的情况下，典型尺寸的石墨烯量子点的自由度数量仍然相当大。然而，同位素纯化使我们能够减少13C含量相对于不携带任何核自旋的12C含量。因此，原则上可以不断降低浴槽自由度。我们想研究石墨烯量子点中电子自旋和核自旋的动力学。从量子计算和基础物理学的角度来看，这一分析都很有趣。为此，我们将采用数值方法（基于精确对角化）和解析方法（基于Nakajima-Zwanzig方程）的结合。我们期望发现有趣的新物理学，特别是在中间数量的浴自由度的交叉状态下，例如，与自旋退相干和弛豫有关。

Graphene quantum dots are a unique material system to study the quantum to classical crossover. The reason is the feasibility to actively reduce the bath degrees of freedom in this quantum dissipative system. A quantum dissipative system consists by definition of a small quantum system and a larger bath that are coupled to each other. In graphene quantum dots, the system could be the spin of a single electron (captured inside the dot) and the bath degrees of freedom would then be the nuclear spins of the 13C atoms of the host material. The coupling is mediated by the hyperfine interaction. At natural abundance of 1% 13C atoms, the number of bath degrees of freedom in a typically sized graphene quantum dot would still be quite large. However, isotopic purification enables us to reduce the 13C content with respect to the 12C content that does not carry any nuclear spin at all. Therefore, it is in principle possible to constantly reduce the bath degrees of freedom.We would like to study the dynamics of the electron spin as well as the nuclear spins in a graphene quantum dot. This analysis is interesting both from a quantum computing as well as a fundamental physics point of view. To do so, we will employ a combination of numerical methods (based on exact diagonalization) and analytical methods (based on the Nakajima-Zwanzig equation). We expect to discover interesting new physics especially in the crossover regime of an intermediate number of bath degrees of freedom, for instance, related to spin decoherence and relaxation.