  Silicon carbide is a very promising platform for quantum applications because
of extraordinary spin and optical properties of point defects in this
technologically-friendly material. These properties are strongly influenced by
crystal vibrations, but the exact relationship between them and the behavior of
spin qubits is not fully investigated. We uncover the local vibrational modes
of the Si vacancy spin qubits in as-grown 4H-SiC. We apply the resonant
microwave field to isolate the contribution from one particular type of
defects, the so-called V2 center, and observe the zero-phonon line together
with seven equally-separated phonon replicas. Furthermore, we present
first-principles calculations of the photoluminescence lineshape, which are in
excellent agreement with our experimental data. To boost up the calculation
accuracy and decrease the computation time, we extract the force constants
using machine learning algorithms. This allows us to identify dominant modes in
the lattice vibrations coupled to an excited electron during optical emission
in the Si vacancy. The resonance phonon energy of 36 meV and the Debye-Waller
factor of about 6% are obtained. We establish experimentally that the
activation energy of the optically-induced spin polarization is given by the
local vibrational energy. Our findings give insight into the coupling of
electronic states to vibrational modes in SiC spin qubits, which is essential
to predict their spin, optical, mechanical and thermal properties. The approach
described can be applied to a large variety of spin defects with spectrally
overlapped contributions in SiC as well as in other 3D and 2D materials.
