Optimal Surface-Electrode Trap Lattices for Quantum Simulation with Trapped Ions

Trapped ions offer long internal state (spin) coherence times and strong inter-particle interactions mediated by the Coulomb force. This makes them interesting candidates for quantum simulation of coupled lattices. To this end it is desirable to be able to trap ions in arbitrary conformations with precisely controlled local potentials. We provide a general method for optimizing periodic planar radio-frequency electrodes for generating ion trapping potentials with specified trap locations and curvatures above the electrode plane. A linear-programming algorithm guarantees globally optimal electrode shapes that require only a single radio-frequency voltage source for operation. The optimization method produces final electrode shapes that are smooth and exhibit low fragmentation. Such characteristics are desirable for practical fabrication of surface-electrode trap lattices.