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

TL;DR

This paper investigates how parity conditions influence Zitterbewegung (ZB) in a simulated relativistic electron using a trapped ion, revealing that ZB occurs only with mixed parity states and proposing feasible experimental observations.

Contribution

It demonstrates the parity-dependent behavior of ZB in a trapped ion simulation, highlighting the role of parity states in quantum relativistic effects.

Findings

ZB disappears for pure odd or even parity states.

ZB occurs only with superpositions of parity states.

Proposes experimental methods to observe parity-related ZB effects.

Abstract

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.