Engineering Zeeman-manifold quintets using state-dependent light shifts in neutral atoms
We present a general method for engineering qudits through individually addressable transitions between Zeeman sublevels, achieved by combining a large linear Zeeman shift with a state-dependent light shift. This approach lifts the degeneracy between adjacent states while simultaneously tuning their energy splittings into the radio-frequency (RF) domain, enabling coherent manipulation within the Zeeman manifold using experimentally accessible drive frequencies. As a concrete realization, we investigate the implementation of an $SU(5)$ quintet encoded in the Zeeman sublevels of the long-lived $^3\mathrm{P}_2$ state of neutral $\mathrm{^{88}Sr}$ atoms confined in far-detuned, $\sigma^{-}$-polarized optical tweezers. Using realistic experimental parameters, we numerically demonstrate full control of the quintet manifold, including initialization into a specific $SU(5)$ basis state via a multi-photon transfer, coherent state- and site-selective single-qudit rotations driven by RF fields, and fast state-selective optical readout. Our simulations predict state-preparation fidelities of $\mathcal{F} \simeq 0.99$ within less than $1~$us, single-qudit gate fidelities of $F$ $\simeq 0.99$ with $\pi$-pulse durations of $\sim1.4~$us, and fast destructive imaging with durations below $10~$us under ideal conditions. These results establish a broadly applicable framework for high-fidelity control of Zeeman sublevel-encoded qudits and highlight the $^3\mathrm{P}_2$ manifold in strontium as a promising platform for scalable qudit-based quantum technologies.