Quantum simulation of 'zitterbewegung' in a single trapped ion under conditions of parity-keeping and parity-breaking

The motional trembling (‘zitterbewegung’) of a relativistic electron governed by Dirac equation was originally predicted by Schrodinger in the early days of quantum mechanics and simulated in a recent experiment with a single trapped ultracold ion. We investigate stable and instable confinements of a single trapped ion in a Paul trap under different conditions relevant to parity. Since our treatment involves neither restriction of Lamb-Dicke limit nor rotating-wave approximation, we may demonstrate different quantum dynamics of the single trapped ion in a wide range of the trapping parameters. We discuss the origin of the zitterbewegung which is relevant to the stability of the ion trapping.