Optical perspective on the time-dependent Dirac oscillator

TL;DR

This paper explores the optical analog of the time-dependent Dirac oscillator, analyzing how temporal frequency modulations affect angular momentum, spin-orbit entanglement, and Zitterbewegung, revealing both aperiodic and analytically solvable dynamics.

Contribution

It introduces a novel optical model for the time-dependent Dirac oscillator and studies its dynamic properties, including angular momentum and entanglement effects, with exact solutions for certain cases.

Findings

Time modulations cause notable changes in Zitterbewegung.

Certain time dependencies lead to aperiodic evolution of observables.

Analytical solutions are possible for specific frequency modulations.

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.