Optimization of two-dimensional ion trap arrays for quantum simulation

The optimization of two-dimensional (2D) lattice ion trap geometries for trapped ion quantum simulation is investigated. The geometry is optimized for the highest ratio of ion-ion interaction rate to decoherence rate. To calculate the electric field of such array geometries a numerical simulation based on a 'Biot-Savart like law' method is used. In this article we will focus on square, hexagonal and centre rectangular lattices for optimization. A method for maximizing the homogeneity of trapping site properties over an array is presented for arrays of a range of sizes. We show how both the polygon radii and separations scale to optimize the ratio between the interaction and decoherence rate. The optimal polygon radius and separation for a 2D lattice is found to be a function of the ratio between radio-frequency (rf) voltage and drive frequency applied to the array. We then provide a case study for Yb-171(+) ions to show how a 2D quantum simulator array could be designed.