Optimal electrode geometries for 2-dimensional ion arrays with bi-layer ion traps

We investigate electrode geometries required to produce periodic 2-dimensional ion-trap arrays with the ions placed between two planes of electrodes. We present a generalization of previous methods for traps containing a single electrode plane to this new geometry, and show that for a given ion-electrode distance and applied voltages, the inter-ion distance can be reduced by a factor of up to 3 relative to single-plane traps. This represents an increase by a factor of 9 in the trap density and a factor of 27 in the exchange coupling between the oscillatory motion of neighboring ions. The resulting traps are also considerably deeper for bi-layer structures than for single-plane traps. These results could offer a useful path towards 2-dimensional ion arrays for quantum simulation. We also discuss issues with the fabrication of such traps.