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. In particular, the coherence of the spin purity in the limit of a weak externally applied magnetic field, comparable in strength to the Overhauser field due to fluctuations in the surrounding nuclei spins. We use an all-optical pulse technique to measure the spin evolution as a function of time after its initialization. We show for the first time that the spin purity performs complex temporal oscillations which we quantitatively simulate using a central spin model. Our model encompasses the Zeeman and the hyperfine interactions between the spin and the external and Overhauser fields, respectively. Our novel studies are essential for the design and optimization of quantum-dot-based entangled multi-photon sources. Specifically, cluster and graph states, which set stringent limitations on the magnitude of the externally applied field.
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