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In this paper, the 2+1 Dirac-Moshinsky oscillator (2+1 DMO) coupled to anexternal isospin field is mapped onto the Jaynes-Cummings model (JCM), whichdescribes the interaction between two two-level systems and a quantumsingle-mode field. The time-dependent wave function and the density matrix areobtained in the two cases. In the first case, the quantum number state isconsidered, while in the second case, the coherent state is considered as aninitial state. The effect of both the detuning parameter and the coherenceangle are studied on the entanglement and on the population inversion. It hasbeen shown that the coherent state gives good description than the number statefor the entanglement and the population inversion.

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