  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 admixture of the odd and even parity states. We also
show the similar role 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.
