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 171Yb+ ions to show how a 2D quantum simulator array could be designed.