The accurate characterization of eigenmodes and eigenfrequencies of two-dimensional ion crystals provides the foundation for the use of such structures for quantum simulation purposes. We present a combined experimental and theoretical study of two-d
imensional ion crystals. We demonstrate that standard pseudopotential theory accurately predicts the positions of the ions and the location of structural transitions between different crystal configurations. However, pseudopotential theory is insufficient to determine eigenfrequencies of the two-dimensional ion crystals accurately but shows significant deviations from the experimental data obtained from resolved sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and the effect is understood from the dynamics of two-dimensional ion crystals in the Paul trap. The results represent initial steps towards an exploitation of these structures for quantum simulation schemes.
We report on transport operations with linear crystals of 40Ca+ ions by applying complex electric time-dependent potentials. For their control we use the information obtained from the ions fluorescence. We demonstrate that by means of this feedback t
echnique, we can transport a predefined number of ions and also split and unify ion crystals. The feedback control allows for a robust scheme, compensating for experimental errors as it does not rely on a precisely known electrical modeling of the electric potentials in the ion trap beforehand. Our method allows us to generate a self-learning voltage ramp for the required process. With an experimental demonstration of a transport with more than 99.8 % success probability, this technique may facilitate the operation of a future ion based quantum processor.
