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

Abstract

We map the 2+1 Dirac–Moshinsky oscillator (2+1 DMO) coupled to an external isospin field onto the Jaynes–Cummings model (JCM), which describes the interaction between two two-level systems and a quantum single-mode field. We obtain the time-dependent wave function and the density matrix in two cases. As an initial state, we consider the quantum number state in the first case and the coherent state in the second case. We study the effect of the detuning parameter and the coherence angle on the entanglement and the population inversion. The obtained results show that the coherent state provides a better description than the number state for both the entanglement and the population inversion.