Hyperfine Spectroscopy and Fast, All-Optical Arbitrary State Initialization and Readout of a Single, Ten-Level 73Ge Vacancy Nuclear Spin Qudit in Diamond

A high-spin nucleus coupled to a color center can act as a long-lived memory qudit in a spin-photon interface. The germanium vacancy (GeV) in diamond has attracted recent attention due to its excellent spectral properties and provides access to the ten-dimensional Hilbert space of the I = 9/2 73Ge nucleus. Here, we observe the 73GeV hyperfine structure, perform nuclear spin readout, and optically initialize the 73Ge spin into any eigenstate on a mu s timescale and with a fidelity of up to -84%. Our results establish 73GeV as an optically addressable high-spin quantum platform for a high-efficiency spin-photon interface as well as for foundational quantum physics and metrology.