The Dirac Oscillator in the Context of Jaynes-Cummings and Anti-Jaynes-Cummings Models for Vortex Analysis in (2+1)-Dimensional Space-time

Abstract

This study investigates the two-dimensional Dirac oscillator in (2+1)-dimensional spacetime under the influence of a perpendicular magnetic field, focusing on specific transitions in the magnetic quantum numbers m\(\varvec{>0}\) and m\(\varvec{<0}\). These transitions are characterized by the exchange of chiral creation and annihilation operators, which define two distinct directions associated with the magnetic field, termed right and left operators. We explore the behavior of spin-polarized electron vortices through these operators, applying the Jaynes-Cummings (JC) and Anti-Jaynes-Cummings (AJC) models to analyze quantum transitions. Utilizing the rotating wave approximation, we perform rotational coupling transformations \(\varvec{T_{\pm }}\) and counter-rotating transformations \(\varvec{L_{\pm }}\), leading to the derivation of the transformed Hamiltonians \(\varvec{H_{DOAJC}^{L_{\pm }}}\) and \(\varvec{H_{DOJC}^{T_{\pm }}}\). These results provide a deeper understanding of the dynamics and coupling mechanisms in the Dirac oscillator influenced by a magnetic field.