  The Stimulated Raman Adiabatic Passage (STIRAP) is applied to a system
coupled to a bath made of fully-interacting two-level systems, whose dynamics
is studied exploiting the generalized Cluster Correlation Expansion (gCCE)
theory. We specialize our analysis to a negatively charged silicon vacancy
(SiV-1) in non-purified 4H-SiC to assess the possibility of transferring
population between two states of the ground manifold, also taking into account
the interaction with a spherical nuclear spin bath formed by nuclei of 29Si and
13C. For this system, it is demonstrated that the presence of a small/medium
sized bath has no effect on the protocol, finding in particular a set of
parameter values for an efficient STIRAP process.
