Exploring global symmetry-breaking superradiant phase via phase competition

Superradiant phase transitions play a fundamental role in understanding the mechanism of collective light-matter interaction at the quantum level. Here we investigate multiple superradiant phases and phase transitions with different symmetry-breaking patterns in a two-mode V-type Dicke model. Interestingly, we show that there exists a quadruple point where one normal phase, one global symmetry-breaking superradiant phase and two local symmetry-breaking superradiant phases meet. Such a global phase results from the phase competition between two local superradiant phases and can not occur in the standard $\Lambda$- and $\Xi$-type three-level configurations in quantum optics. Moreover, we exhibit a sequential first-order quantum phase transition from one local to the global again to the other local superradiant phase. Our study opens up a perspective of exploring multi-level quantum critical phenomena with global symmetry breaking.