Trembling motion of relativistic electrons in a magnetic field

TL;DR

This paper calculates the trembling motion (Zitterbewegung) of relativistic electrons in a magnetic field, showing it includes classical and quantum components, and proposes a simulation method using trapped ions.

Contribution

It demonstrates how magnetic fields influence Zitterbewegung and proposes a feasible simulation approach with trapped ions and laser excitations.

Findings

Zitterbewegung includes classical cyclotron and quantum interband frequencies.

Magnetic field makes ZB motion stationary and non-decaying.

Simulation of magnetic ZB effects using trapped ions is feasible.

Abstract

Zitterbewegung (ZB, the trembling motion) of free relativistic electrons in a vacuum in the presence of an external magnetic field is calculated. It is shown that the motion of an electron wave packet has intraband frequency components, corresponding to the classical cyclotron motion, and several interband frequency components corresponding to the Zitterbewegung. For a two-dimensional situation, the presence of a magnetic field makes the ZB motion stationary, i.e. not decaying in time. We show how to simulate the ZB in a magnetic field using trapped ions and laser excitations in the spirit of recently observed proof-of-principle ZB simulation by Gerritsma {\it et al.} Nature {\bf 463}, 68 (2010). It is demonstrated that, for the parameters of the Dirac equation simulated by the above experiment, the effect of a magnetic field on the Zitterbewegung is considerable.