Abstract
We propose an alternative map from the the 2-dimensional charged Dirac oscillator in the background of a uniform perpendicular magnetic field onto a quantum optics model which contains both Jaynes-Cummings (JC) and Anti-Jaynes-Cummings (AJC) interactions. Different from previous work, we only introduce one kind of phonons and realize a symmetrical competition which is controlled by the magnetic field. Furthermore, we find that this model behaves as a quantum phase transition when a dimensionless parameter crosses its critical value. Several characteristics of quantum phase transition are exhibited explicitly.
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