This thesis aims to pave the way for the experimental study of many-body physics in a dense central spin system. It focuses on the development of both the highly coherent quantum-optical platform - a droplet-etched GaAs Quantum Dot (QD) - as well as the techniques to optically induce and probe the collective dynamics of its resident nuclear spin ensemble.

An all-optical quantum control of the electron spin is realised for the first time in a GaAs QD and subsequently used to refocus the strong hyperfine interaction between the spin and the nuclear ensemble. The measurement demonstrates a nearly hundred-fold improvement of the electron spin coherence over the state of the art in the conventional InGaAs QDs. This is owed to the reduced inhomogeneity of the nuclear quadrupolar interaction, and it further raises the prospects of turning the nuclear ensemble into a coherent quantum register - a host to collective non-classical phenomena.

To complement these results, I analyse a series of proof-of-concept experiments on initialising and addressing the nuclear quantum register in an InGaAs QD. These entail cooling and polarising the nuclear ensemble using strong electron-nuclear feedback, as well as driving the collective nuclear spin excitations via the electron-nuclear interaction. The asymmetry in the collective transition rates probed at a partial nuclear polarisation is used as an entanglement witness to demonstrate the formation of a nuclear dark state: a highly-entangled many-body state protected from being polarised by the nuclear wavefunction symmetry.

The thesis ends with a detailed proposal for controlling the structure of such nuclear entanglement exclusively via the electron spin. Specifically, the way to phase-engineer a many-body singlet state of the ensemble is outlined.

In the hope of guiding the next generations of physicists, the exposure of the core topics is aimed to be complete and pedagogical.