  Quantum emitters in diamond are leading optically-accessible solid-state
qubits. Among these, Group IV-vacancy defect centers have attracted great
interest as coherent and stable optical interfaces to long-lived spin states.
Theory indicates that their inversion symmetry provides first-order
insensitivity to stray electric fields, a common limitation for optical
coherence in any host material. Here we experimentally quantify this electric
field dependence via an external electric field applied to individual
tin-vacancy (SnV) centers in diamond. These measurements reveal that the
permanent electric dipole moment and polarizability are at least four orders of
magnitude smaller than for the diamond nitrogen vacancy (NV) centers,
representing the first direct measurement of the inversion symmetry protection
of a Group IV defect in diamond. Moreover, we show that by modulating the
electric-field-induced dipole we can use the SnV as a nanoscale probe of local
electric field noise, and we employ this technique to highlight the effect of
spectral diffusion on the SnV.
