Electron spins in quantum dots and other solid-state defect spins are one of the main systems investigated for the possible implementation of quantum information processing. To this end, the interaction of the spins with their environment needs to be controlled. We study, in particular, the interaction of the defect spin with the surrounding nuclear spins.

We show that the fast control achievable for the electron spin and the slow dynamics of the mesoscopic nuclear spin bath allows to decouple the central spin from the bath and to drive and monitor interesting quantum many-body bath phenomena such as superradiance-like dynamics and steady-state phase transitions in the nuclear spin system.