Adiabatic techniques offer some of the most promising tools for achieving high-fidelity control of the center-of-mass degree of freedom of single atoms. Because the main requirement of these techniques is to follow an eigenstate of the system, constraints on timing and field strength stability are usually low, especially for trapped systems. In this paper we present a detailed example of a technique to adiabatically transport a single atom between different waveguides on an atom chip. To ensure that all conditions are fulfilled, we carry out fully three-dimensional simulations of the system, using experimentally realistic parameters. We also detail our method for simulating the system in very reasonable time scales on a consumer desktop machine by leveraging the power of graphics-processing-unit computing

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