Parity-relevant zitterbewegung and quantum simulation by a single trapped ion

Zitterbewegung (ZB), the trembling of free relativistic electrons in a vacuum, could be simulated by a single trapped ion. We focus on the variations of ZB under different parity conditions and find no ZB in the case of odd or even parity. ZB occurs only for the admixture of the odd- and even-parity states. We also show that a similar role is played by the parity operator for the trapped ion in Fock-state representation and the space-inversion operator for a realistic relativistic electron. Although the ZB effect is invisible in a relativistic electron, preparation of the trapped ion in different parity states is a sophisticated job, which makes it possible to observe the parity-relevant ZB effects with currently available techniques.