Hyperfine dephasing of electron spin qubits in GaAs quantum dots

GaAs量子点中的电子自旋已经证明了它们作为半导体量子比特的可行性，但是这些器件中退相干的一个重要来源是电子与主晶格的核自旋的超精细相互作用。虽然在理解和减少其影响方面取得了很大进展，但本项目仍有几个问题需要通过实验加以解决。一项主要任务是详细研究动态解耦的有效性。我们之前已经证明，这种技术可以通过重复反转量子比特状态将退相时间延长到至少200µs，但限制因素尚不清楚，理论上预计时间会更长。此外，我们将研究由于电场的四极耦合导致的核自旋失相也限制了电子相干性的猜想。如果它是正确的，通过选择最佳的外场方向，相干时间的显著增强是预期的。项目的后半部分将集中在有关核自旋浴性质的更基本的问题上。到目前为止，所有的实验都可以用一个由大约10^6个原子核组成的经典模型来解释，但考虑到它的介观性质，如果能观察到量子效应，那就很有趣了。我们将探讨通过经典谱密度的描述在多大程度上是适当的，以及这个谱看起来会是什么样子。此外，我们将直接探索是否可以检测到量子比特对核自旋的反向作用。这种反向作用是量子力学定律所要求的，也是不确定性关系的核心。因此，它将成为量子力学行为的一个定性标志。为此，我们将测量量子位的连续单次测量之间的相关性，以及它们如何依赖于两次测量之间对量子位的操纵。我们早期的理论和实验工作证明了这种新型测量概念的可行性。

Electron spins in GaAs quantum dots have proven their viability as semiconductor qubits, but one important source of decoherence in these devices is the hyperfine interaction of the electrons with the nuclear spins of the host lattice. While much progress has been made in understanding and reducing its effect, several questions that will be addressed experimentally in this project remain. One major task is a detailed study of the effectiveness of dynamical decoupling. We have shown earlier that this technique can extend the dephasing time to at least 200 µs by repeatedly inverting the qubit state, but the limiting factors are not understood, and much longer times are expected theoretically. Furthermore, we will investigate the conjecture that dephasing of nuclear spins due to quadrupole coupling to electric fields also limits electron coherence. If it is correct, a significant enhancement of the coherence time by choosing an optimal orientation of the external field is expected.The second half of the project will focus on more fundamental questions concerning the properties of the nuclear spin bath. So far, all experiments can be explained with a classical model of this bath consisting of about 10^6 nuclei, but given its mesocopic nature it is interesting if quantum effects can be observed. We will explore to what extent a description via a classical spectral density is adequate, and what this spectrum would look like. Furthermore, we will directly probe whether a back action of the qubit on the nuclear spins can be detected. Such a back action is required by the laws of quantum mechanics and lies at the heart of the uncertainty relation. It would thus be a qualitative hallmark of quantum mechanical behavior. To this end, we will measure the correlations between successive single shot measurements of the qubit and how they depend on the manipulation of the qubits between the two measurements. Our earlier theoretical and experimental work demonstrates the viability of this novel measurement concept.