We study the effects of cotunneling and a non-uniform Zeeman splitting on the stationary and transient leakage current through a double quantum dot in the Pauli spin blockade regime. We find that the stationary current due to cotunneling vanishes at
low temperature and large applied magnetic field, allowing for the dynamical preparation of a pure spin ground state, even at large voltage bias. Additionally, we analyze current that flows between blocking events, characterized, in general, by a fractional effective charge $e^*$. This charge can be used as a sensitive probe of spin relaxation mechanisms and can be used to determine the visibility of Rabi oscillations.
We analyze nuclear spin dynamics in quantum dots and defect centers with a bound electron under electron-mediated coupling between nuclear spins due to the hyperfine interaction (J-coupling in NMR). Our analysis shows that the Overhauser field genera
ted by the nuclei at the position of the electron has short-time dynamics quadratic in time for an initial nuclear spin state without transverse coherence. The quadratic short-time behavior allows for an extension of the Overhauser field lifetime through a sequence of projective measurements (quantum Zeno effect). We analyze the requirements on the repetition rate of measurements and the measurement accuracy to achieve such an effect. Further, we calculate the long-time behavior of the Overhauser field for effective electron Zeeman splittings larger than the hyperfine coupling strength and find, both in a Dyson series expansion and a generalized master equation approach, that for a nuclear spin system with a sufficiently smooth polarization the electron-mediated interaction alone leads only to a partial decay of the Overhauser field by an amount on the order of the inverse number of nuclear spins interacting with the electron.
In this article we review our work on the dynamics and decoherence of electron and hole spins in single and double quantum dots. The first part, on electron spins, focuses on decoherence induced via the hyperfine interaction while the second part cov
ers decoherence and relaxation of heavy-hole spins due to spin-orbit interaction as well as the manipulation of heavy-hole spin using electric dipole spin resonance.
