Programmable coherent site-selective spin control in rotating Penning-trap ion crystals
Large ion crystals in Penning traps provide a platform for quantum simulation and sensing with hundreds of spins, but their continuous rigid-body rotation has so far limited flexible local qubit control. Here we demonstrate programmable coherent site-selective spin control across large rotating ${}^{9}\mathrm{Be}^{+}$ crystals in a Penning trap. A tightly focused off-resonant laser beam drives local $R_z$ phase rotations via differential AC Stark shifts. Beam steering synchronised with crystal rotation enables addressing of arbitrary ions throughout the crystal. Ramsey-based characterisation shows $R_z(\pi)$ gate fidelity of 0.950(4) and nearest-neighbour crosstalk error of 0.021(6). We demonstrate preparing spatially structured spin patterns, generating a biskyrmion spin texture in a single-layer crystal, and then extend the method to bilayer crystals where we perform layer-selective addressing operations. We further demonstrate dual-quadrature Ramsey sensing by imprinting a relative $\pi/2$ phase shift between spatial sub-ensembles, enabling simultaneous measurement of orthogonal spin components within a single experimental realisation. These results establish programmable local control in large rotating ion crystals, opening new routes for engineering spatially structured quantum states in multidimensional trapped-ion systems.