Single-qudit control in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mi>Sr</mml:mi> <mml:mprescripts/> <mml:none/> <mml:mn>87</mml:mn> </mml:mmultiscripts> </mml:math> via optical nuclear electric resonance

Optical nuclear electric resonance (ONER) was recently proposed as a fast and robust single-qubit gate mechanism in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mmultiscripts> <a:mi>Sr</a:mi> <a:mprescripts/> <a:none/> <a:mn>87</a:mn> </a:mmultiscripts> </a:math> . Here, we demonstrate through numerical simulations that ONER can be extended to single-qudit control, addressing multiple one-level hyperfine transitions within the ten-dimensional nuclear-spin manifold. We identify suitable operating regimes and show that ONER enables high-fidelity spin manipulations, with simulated π-gate fidelities exceeding 99.9%, while maintaining coherence under realistic parameter fluctuations. These results establish a proof of principle for optical qudit control in <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"> <b:mmultiscripts> <b:mi>Sr</b:mi> <b:mprescripts/> <b:none/> <b:mn>87</b:mn> </b:mmultiscripts> </b:math> and delineate practical parameter ranges for future experiments, highlighting ONER as a promising pathway toward high-dimensional quantum information processing.