Hyperfine Spectroscopy and Fast, All-Optical Arbitrary State Initialization and Readout of a Single, Ten-Level Ge73 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 <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>I</a:mi><a:mo>=</a:mo><a:mn>9</a:mn><a:mo>/</a:mo><a:mn>2</a:mn></a:math> <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mmultiscripts><c:mrow><c:mi>Ge</c:mi></c:mrow><c:mprescripts/><c:none/><c:mrow><c:mn>73</c:mn></c:mrow></c:mmultiscripts></c:mrow></c:math> nucleus. Here, we observe the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mrow><e:mmultiscripts><e:mrow><e:mi>GeV</e:mi></e:mrow><e:mprescripts/><e:none/><e:mrow><e:mn>73</e:mn></e:mrow></e:mmultiscripts></e:mrow><e:mtext> </e:mtext></e:mrow></e:math> hyperfine structure, perform nuclear spin readout, and optically initialize the <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mrow><g:mmultiscripts><g:mrow><g:mi>Ge</g:mi></g:mrow><g:mprescripts/><g:none/><g:mrow><g:mn>73</g:mn></g:mrow></g:mmultiscripts></g:mrow></g:math> spin into any eigenstate on a <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi mathvariant="normal">μ</i:mi><i:mi mathvariant="normal">s</i:mi></i:math> timescale and with a fidelity of up to <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mo>∼</m:mo><m:mn>84</m:mn><m:mo>%</m:mo></m:math>. Our results establish <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mrow><o:mmultiscripts><o:mrow><o:mi>GeV</o:mi></o:mrow><o:mprescripts/><o:none/><o:mrow><o:mn>73</o:mn></o:mrow></o:mmultiscripts></o:mrow></o:math> as an optically addressable high-spin quantum platform for a high-efficiency spin-photon interface as well as for foundational quantum physics and metrology.