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arXiv · 2512.18904

Optical perspective on the time-dependent Dirac oscillator

Thiago T. Tsutsui·Alison A. Silva·Antonio S. M. de Castro·Fabiano M. Andrade
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Abstract

The Dirac oscillator is a relativistic quantum system, characterized by its linearity in both position and momentum. Moreover, considering $(1{+}1)$ and $(2{+}1)$ dimensions, the system can be mapped onto the Jaynes-Cummings and anti-Jaynes-Cummings models, as illustrated in an exact manner by Bermudez \emph{et al.} [\href{ https://doi.org/10.1103/PhysRevA.76.041801}{Phys. Rev. A 76, 041801(R)}]. Using the optical counterparts of the Dirac oscillator, we analyze an extension of the model that incorporates a time-dependent frequency. We focus on the consequences of these time modulations on the angular momentum observables and spin-orbit entanglement. Noticeable changes in the \emph{Zitterbewegung} are found. We show that a specific choice of time dependence yields aperiodic evolution of the observables, whereas an alternative choice allows analytical solutions.

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Thiago T. Tsutsui, Alison A. Silva, Antonio S. M. de Castro, Fabiano M. Andrade. 2025-12-21. Optical perspective on the time-dependent Dirac oscillator. https://arxiv.org/abs/2512.18904

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