Color centers in diamond have emerged as leading solid-state ``artificial atoms'' for a range of quantum technologies, from quantum sensing to quantum networks. Concerted research activities are now underway to identify new color centers that combine stable spin and optical properties of the nitrogen vacancy (${\mathrm{NV}}^{\ensuremath{-}}$) with the spectral stability of the silicon vacancy (${\mathrm{SiV}}^{\ensuremath{-}}$) centers in diamond, with recent research identifying other group-IV color centers with superior properties. In this paper, we investigate a class of diamond quantum emitters from first principles, the group-III color centers, which we show to be thermodynamically stable in a spin-1, electric-field-insensitive structure. From ab initio electronic structure methods, we characterize the product Jahn-Teller (pJT) effect present in the excited-state manifold of these group-III color centers, where we capture symmetry-breaking distortions associated with strong electron-phonon coupling. These predictions can guide experimental identification of group-III vacancy centers and their use in applications in quantum information science and technology.
Color centers in diamond have attracted much interest as candidates for optically active, solid-state quantum bits. Of particular interest are inversion-symmetric color centers based on group-IV impurities in diamond because they emit strongly into their zero-phonon lines and are insensitive to electric field noise to first order. Early studies of the negatively charged tin-vacancy (${\mathrm{SnV}}^{\ensuremath{-}}$) center in diamond have found the ${\mathrm{SnV}}^{\ensuremath{-}}$ to be a promising candidate: it has high quantum efficiency, emits strongly into its zero-phonon lines, and is expected to have a long
T2 spin coherence time at 4 K. To develop the ${\mathrm{SnV}}^{\ensuremath{-}}$ into a spin qubit requires further characterization, especially of the spin and optical properties of individual ${\mathrm{SnV}}^{\ensuremath{-}}$ in nanofabricated structures. In this work, we isolate single ${\mathrm{SnV}}^{\ensuremath{-}}$ centers in diamond nanopillars and characterize their emission properties and their spin response to a magnetic field. We observe narrow emission linewidths
<250 MHz, as well as a strong polarization dependence of each transition. We also find the Zeeman splitting under a magnetic field to be in good agreement with theoretical prediction. Our results pave the way toward future employment of single ${\mathrm{SnV}}^{\ensuremath{-}}$ centers as optically accessible quantum memories.