Generalized cluster correlation expansion theory for stimulated Raman adiabatic passage 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 by exploiting the generalized cluster correlation expansion (gCCE) theory. We specialize our analysis to a negatively charged silicon vacancy ($V_{\mathrm{Si}}^{-1}$) in nonpurified 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 ${}_{29}\mathrm{Si}$ and ${}_{13}C$. For this system, it is demonstrated that the presence of a small- or medium-sized bath has no effect on the protocol, finding in particular a set of parameter values for an efficient STIRAP process.