All-optical control of Nuclear spin qudits in Neutral atoms

The large nuclear spins of alkaline-earth atoms enable a natural qudit encoding. The nuclear spin is isolated from the environment, which makes it robust against unwanted noise but also renders it difficult to control. Previous works have proposed magnetic-field based control techniques for universal control as well as optical techniques enabling partial control of the spin manifold. In this work, we propose and analyze several all-optical control protocols for nuclear spin qudits and perform a comparative study. First, we address the fundamental question of universal controllability for these schemes, accounting for the control Hamiltonians, the number of control parameters, and the control sequences. Second, we corroborate these analytical results with numerical simulations demonstrating the preparation of arbitrary single-qudit states and the implementation of arbitrary single-qudit gates. Finally, we examine the quantum speed limits of these control schemes and derive lower bounds on gate times. Our results establish the feasibility of fast optical nuclear-spin control in alkaline-earth neutral atoms.