Mapping of the 2+1 Dirac-Moshinsky Oscillator Coupled to an External Isospin Field onto Jaynes-Cummings Model

In this paper, the 2+1 Dirac-Moshinsky oscillator (2+1 DMO) coupled to an external isospin field is mapped onto the Jaynes-Cummings model (JCM), which describes the interaction between two two-level systems and a quantum single-mode field. The time-dependent wave function and the density matrix are obtained in the two cases. In the first case, the quantum number state is considered, while in the second case, the coherent state is considered as an initial state. The effect of both the detuning parameter and the coherence angle are studied on the entanglement and on the population inversion. It has been shown that the coherent state gives good description than the number state for the entanglement and the population inversion.