Nonrelativistic limit in the 2+1 Dirac oscillator: a Ramsey-interferometry effect

Abstract

We study the nonrelativistic limit of a paradigmatic model in relativistic quantum mechanics, the two-dimensional Dirac oscillator. Remarkably, we find a different kind of Zitterbewegung which persists in this nonrelativistic regime, and leads to an observable deformation of the particle orbit. This effect can be interpreted in terms of a Ramsey-interferometric phenomenon, allowing an insightful connection between relativistic quantum mechanics and quantum optics. Furthermore, subsequent corrections to the nonrelativistic limit, which account for the usual spin-orbit Zitterbewegung, can be neatly understood in terms of a Mach-Zehnder interferometer.