Engineering spin-spin interactions with global beams

Trapped-ion quantum simulators typically generate spin-spin interactions by resonantly coupling to the normal modes of the ion crystal motion. The most common choice leads to a scaling of interaction strength with distance like a power law. In this work, we attempt to generalize on the accessible interaction graphs, if only global Raman beams are used, i.e. without individual addressing of each ion. We find that interesting cases other than power laws can be generated under conditions. We explore these conditions and speculate limitations for 1D and 2D ion crystals.