Chirality quantum phase transition of a noncommutative planar Dirac oscillator

A map from the charged Dirac oscillator on a noncommutative plane interacting with a homogeneous magnetic field onto a quantum optics model is proposed. We find that both anti-Jaynes-Cummings (AJC) and Jaynes-Cummings (JC) interactions are included in this mapped quantum optics model. A competition between AJC and JC interactions will happen when the intensity of the magnetic field changes. Contrary to previous studies, the competition is symmetrical since the phonons that take part in the competition are only associated with the excitation of the Dirac oscillator. Furthermore, this model will experience a quantum phase transition when the intensity of the magnetic field crosses the critical point. However, the critical point is different from the one in the model of the charged nonrelativistic harmonic oscillator interacting with a homogenous magnetic field on a noncommutative plane. It also deviates from its commutative counterpart because of spatial noncommutativity. Some characteristics of the quantum phase transition are studied. Then we investigate the nonrelativistic limit of this model. Our results show that its nonrelativistic counterpart inherits similar properties of the chirality quantum phase transition from the relativistic one.