Spin purity of the quantum dot confined electron and hole in an external magnetic field

We investigate experimentally and theoretically the temporal evolution of the spin of the conduction band electron and that of the valence band heavy hole, both confined in the same semiconductor quantum dot. We use all-optical pulse techniques to perform complete tomographic measurements of the spin as a function of time after its initialization and study the total spin purity (coherence), measured here. In the important limit of a weak externally applied magnetic field, comparable in strength to the Overhauser field due to fluctuations in the surrounding nuclei spins, the measured spin purity performs complex temporal oscillations. We use a central-spin model encompassing the spin's Zeeman and the hyperfine interactions to reproduce the measured results quantitatively. Our studies are essential for designing and optimizing quantum-dot-spin-based entangled multiphoton sources that set stringent limitations on the magnitude of the externally applied field.