Supplementary file 1_Optical perspective on the time-dependent Dirac oscillator.pdf

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 et al., [Phys. Rev. A 76, 041,801(R) (2007)]. 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 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. Our work has potential implications for simulating relativistic phenomena in optical platforms.