Quantum phase transition and chaos of anomalous Dicke model in the thermodynamic limit

We study the anomalous Dicke model from two different perspectives including the quantum theory and semiclassical approximation method. Due to the competition between both bidirectional couplings in this appealing model, it exhibits three distinct phases, i.e. the normal phase, the superradiant electric phase and magnetic phase, respectively. We study its critical behaviors (CBs) under either the ideal or realistic conditions, and then acquire its ground-state wave function and quantum variation with different coupling strengths to character these CBs. As long as the coupling strengths being modulated, its wave function undergoes rotation and compression, and especially in the superradiant phase, the center of the wave function is also shifted. Quantum squeezing behavior also occurs near the critical points of the coupling strengths. Utilizing the semiclassical approximation, we also study its potential energy and the Poincaré sections, and which results also present remarkable phase-transition and chaotic behaviors, respectively. Different from the traditional Dicke model, this model shows more abundant physical features and multi-parameter regulation mechanism, and we believe that these behaviors can be simulated or realized in different experimental platforms in the future.