{\em Zitterbewegung} in Spin-Orbit Coupled Systems and Ehrenfest's Theorem

TL;DR

This paper uses Ehrenfest's theorem to derive and analyze the phenomenon of zitterbewegung in spin-orbit coupled systems, including electron gases and spinor Bose-Einstein condensates, highlighting conditions for its occurrence.

Contribution

It provides a simple Ehrenfest theorem-based derivation of zitterbewegung and extends the analysis to spinor BECs, predicting new velocity oscillations due to interactions.

Findings

Zitterbewegung occurs in the y-velocity component for wide initial wave packets in electron gases.

In spinor BECs, zitterbewegung can appear in the x-velocity component due to nonlinear interactions.

The derivation simplifies understanding of zitterbewegung in spin-orbit coupled quantum systems.

Abstract

We use Ehrenfest's theorem to provide a particularly simple derivation of the {\em zitterbewegung} in the dynamics of initial Gaussian wave packets in a two-dimensional electron gas. For initial packets which are very wide in the $y$-direction, the {\em zitterbewegung} is only in the $y$-component of the velocity. We extend our Ehrenfest theorem based calculation to the spin-orbit coupled spinor Bose-Einstein condensate (BEC) to predict that there can be {\em zitterbewegung} in the $x$-component of the velocity in this situation driven by a combination of the nonlinear interaction in the condensate and the splitting due to the spin-orbit coupling.