Spin qubits and entanglement in semiconductor nanostructures, as well as spin decoherence due to the hyperfine interaction and the spin-orbit coupling

我们的目标是从理论上理解半导体纳米结构(如量子点)中单自旋的量子相位相干性的基本原理。为此，将研究导致退相干(相干性损失)的相关物理过程以及可以增强电子自旋相干性的过程。对于电子自旋，主要的消相干机制之一是与周围的核自旋的超精细耦合。尽管如此，电子自旋-核自旋系综动力学和自旋相干的核态准备仍有许多方面尚不清楚，需要进一步研究。因此，该项目第三阶段的重点仍然是半导体中的电子-核自旋相互作用问题。除了基本的科学理解外，自旋退相干与其核自旋环境的关系的理论模型也很重要，因为半导体结构中的电子自旋已被确认为用于量子信息处理的量子比特。用超算符法等解析方法来模拟单自旋的退相干是合适的。我们得到了在量子点中制备与单个电子自旋耦合的核自旋系综的一些解析结果，以及对几百个核自旋的核自旋制备方案的一些数值模拟，以及对相干电子自旋Landau-Zener-Stück elberg振荡的描述，这与实验符合得很好。我们现在所处的位置是，我们已经建立的分析和数值方法可以进一步发展和推广，以便对最近和未来的核自旋操纵实验进行更定量的描述。

We aim at a theoretical understanding of the fundamentals of quantum phase coherence of single spins in semiconductor nanostructures such as quantum dots. To this end, the relevant physical processes leading to decoherence (loss of coherence) and processes that can enhance the electron spin coherence will be investigated. For electron spins, one of the dominant decoherence mechanisms is the hyperfine coupling to the surrounding nuclear spins. Still, there are many aspects of the electron spin-nuclear spin ensemble dynamics and nuclear state preparation for spin coherence that are not understood and require further investigation. Therefore, the emphasis of the third phase of this project remains on the problem of electron-nuclear spin interactions in semiconductors. Besides the fundamental scientific understanding, theoretical modeling of spin decoherence in dependence of its nuclear spin environment is also important because electron spins in semiconductor structures have been identified as qubits for quantum information processing. To model decoherence of single spins, analytical methods such as the superoperator formalism are suitable. We have obtained some analytical results on the preparation of an ensemble of nuclear spins coupled to a single electron spin in a quantum dot, and some numerical simulations of a nuclear-spin preparation scheme with a few hundred nuclear spins, as well as a description of coherent electronnuclear spin Landau-Zener-Stückelberg oscillations, which agrees well with experiment. We are now at the point where the analytical and numerical methods that we have established can be further developed and generalized, in order to obtain a more quantitative description of recent and future nuclear-spin manipulation experiments.