Generalized Cluster Correlation Expansion theory for STIRAP processes in the presence of a spin bath

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.