Second-order Stark shifts exceeding 10$\,$GHz in electrically contacted SiV$^-$ centers in diamond

Negatively charged silicon vacancy centers (SiV$^-$) in diamond exhibit excellent spin coherence and optical properties, making them promising candidates for quantum technologies. However, the strain-induced inhomogeneous distribution of optical transition frequencies poses a challenge for scalability. We demonstrate electrical tuning of the SiV$^-$ center zero-phonon lines using in-plane contacts to apply moderate electric fields up to 45$\,$MV/m. The second-order Stark shift exceeds 10$\,$GHz, which is of the same order of magnitude as the 15$\,$GHz inhomogeneous distribution of SiV$^-$ observed in emitters embedded in optical nanostructures such as photonic crystal nanocavities. Analysis of individual SiV$^-$ centers shows significant variation in polarizabilities between defects indicating that the polarizability strongly depends on local parameters like strain. The observed polarizabilities are 3-25 times larger than those of tin vacancy centers, which we attribute to valence band resonances that delocalize the $e_u$ wavefunctions. Photoluminescence excitation measurements reveal that optical linewidths increase moderately with applied electric field strength. Our results demonstrate that large electrical Stark shifts can overcome the inhomogeneous distribution of transition frequencies, representing a significant step toward scalable SiV$^-$-based quantum technologies such as quantum repeaters.