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

Abstract

Trapped ions offer long internal state (spin) coherence times and strong interparticle 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.

Ideal multipole ion traps from planar ring electrodes

“…We conclude this section by noting that the optimization of electrode shapes for construction of a multipole trap may be done in a more sophisticated way using the approach of Schmied et al [23]. For the lowest-order trap, the results of such calculations agree with ours [26].…”

Optical trapping of an ion

“…Finally, two-and three-dimensional optical lattices might provide an alternative approach for ion trap architectures [12,21,25,26]. One can consider, for example, to implement QS with trapped ions [27,28] in larger, higher-dimensional systems with the Coulomb force providing long range interaction beyond nearest neighbors.…”

Surface-electrode point Paul trap

“…The ability to fabricate these traps in a scalable fashion makes them attractive for realizing large arrays of single ions in independent traps that may be utilized for a quantum processor, provided the individual ions can be interconnected, e.g., through optical fibers [14][15][16]. On this aspect, the axial symmetry of the trap lends itself well to integration of such fibers and potentially other optical elements that also possess axial symmetry.…”