Spin Qubits and Spin Decoherence in Graphene Quantum Dots

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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.