Programmable 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 site-selective spin control across large rotating {}⁹Be⁺ 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(π) gate fidelity of 94.6% and nearest-neighbour crosstalk of 1.2%. We use this capability to prepare spatially structured spin patterns, generating a biskyrmion spin texture in a single-layer crystal, then extending the method to bilayer crystals we perform layer-selective addressing operations. We further demonstrate dual-quadrature Ramsey sensing by imprinting a relative π/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.