Design of a Surface Trap for Freely Rotating Ion Ring Crystals

We present a design of an r.f. trap using planar electrodes with the goal to trap on the order of 100 ions in a small ring structure of diameters ranging between 100 $\mu$m and 200 $\mu$m. In order to minimize the influence of trap electrode imperfections due to the fabrication, we aim at trapping the ions around 400 $\mu$m above the trap electrodes. In view of experiments to create freely rotating crystals near the ground state, we numerically study factors breaking the rotational symmetry such as external stray electric fields, local charging of the trap electrodes, and fabrication imperfections. We conclude that these imperfections can be controlled sufficiently well under state-of-the-art experimental conditions to allow for freely rotating ion rings even at energies comparable to the ground state energy of the rotational degree-of-freedom.