Vortex-Enhanced Zitterbewegung in Relativistic Electron Wave Packets

TL;DR

Zitterbewegung in free electrons is challenging to observe due to its sub-Compton amplitude and dispersion. The authors construct exact relativistic vortex electron wave packets as coherent superpositions of positive- and negative-energy Dirac states to reveal ZBW within a structured state. They demonstrate that the ZBW amplitude is amplified by a factor $\eta = \sqrt{l}$, yielding $r_{ZB} = \sqrt{l} r_{ZB}^{(Huang)}$, and unify Gaussian and BG vortex beams within a single framework. This work provides a concrete route to observing relativistic quantum dynamics in structured electron beams and informs the design of experiments in TEM and ultrafast electron optics.

Abstract

Zitterbewegung (ZBW), the trembling motion predicted by the Dirac equation, has long remained unobservable in free electrons due to its sub-Compton scale. We elaborately construct a relativistic vortex electron wave packet as a coherent superposition of both positive- and negative-energy Dirac states and derive their space-time dynamics. Our analysis demonstrates that introducing orbital angular momentum provides a mechanism for amplifying the ZBW amplitude far beyond that of conventional Gaussian packets, while maintaining coherence. The resulting relativistic vortex states unify Gaussian and Bessel-Gaussian models within a single framework and opens new possibilities for observing relativistic quantum dynamics in structured electron wave packets.