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

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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.