  We study the silicon vacancy in 3C SiC as a color center of interest in the
field of Quantum Technologies, focusing on its magnetic interaction with the
SiC nuclear spin bath containing Si29 and C13 nuclei in their natural isotopic
concentration. We calculate the system energetic and magnetic properties with
ab initio methods based on the Density Functional Theory, identifying the
neutral charge state of the silicon vacancy as the most favorable for p doped
3C SiC systems. We thereon evaluate the Free Induction Decay and the Hahn echo
sequence on the electron spin interacting with the nuclear spin bath. Here, the
Electron Spin Echo Envelope Modulation phenomenon, due to single nuclear spin
flipping processes, and the overall decay are highlighted in the context of the
Cluster Correlation Expansion theory. We find a non exponential coherence
decay, which is a typical feature of solid state qubits subjected to low
frequency 1/f noise from the environment.
