Quantum simulations of spin systems could enable the solution of problems which otherwise require infeasible classical resources. Such a simulation may be implemented using a well-controlled system of effective spins, such as a two-dimensional lattice of locally interacting ions. We propose here a layered planar rf trap design that can be used to create arbitrary two-dimensional lattices of ions. The design also leads naturally to ease of microfabrication. As a first experimental demonstration, we confine strontium-88 ions in a mm-scale lattice trap and verify numerical models of the trap by measuring the motional frequencies. We also confine 440 nm diameter charged microspheres and observe ion-ion repulsion between ions in neighboring lattice sites. Our design, when scaled to smaller ion-ion distances, is appropriate for quantum simulation schemes, e.g. that of Porras and Cirac (PRL 92 207901 (2004)). We note, however, that in practical realizations of the trap, an increase in the secular frequency with decreasing ion spacing may make a coupling rate that is large relative to the decoherence rate in such a trap difficult to achieve.
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