Effects of quantum deformation on the Jaynes-Cummings and anti-Jaynes-Cummings models

The theory of non-Hermitian systems and the quantum deformations have attracted a great deal attention in past decades. In general, Hamiltonians are constructed by an ad hoc manner. Here, we study ($2+1$) Dirac oscillator show that context $\ensuremath{\kappa}$-deformed Poincar\'e-Hopf algebra its Hamiltonian is but has real eigenvalues. non-Hermiticity stems from algebra. From mapping Bermudez et al., Phys. Rev. A 76, 041801(R) (2007), propose $\ensuremath{\kappa}$-Jaynes-Cummings $\ensuremath{\kappa}$-anti-Jaynes-Cummings models, which describe interaction between two-level system with quantized mode optical cavity context. We find $\ensuremath{\kappa}$ deformation modifies Zitterbewegung frequencies collapses revivals oscillations. particular, total angular momentum $z$ direction not conserved anymore, as direct consequence deformation.