Extended Dicke quantum battery with interatomic interactions and driving field

We investigate the charging process of quantum battery (QB) systems in an extended Dicke model with both atomic interactions and an external driving field. We focus on the effects of the atomic interaction and the external driving field on the charging performance of QB and find that the maximum stored energy of QB has a critical phenomenon. We analyze the critical behavior and obtain the analytical expression of the critical atomic interaction. The dependence of the maximum stored energy, the energy quantum fluctuations and the maximum charging power on the number $N$ of the two-level systems are also discussed. In particular, for the maximum charging power, we obtain the quantum advantage of the QB, which approximately satisfies a superlinear scaling relation $P_{max}\propto N^{\alpha}$, where scaling exponent $\alpha$ varies with the number $N$ of the two-level systems. In the ultra-strong coupling regime, the atomic interaction can lead to a faster battery charging, and the quantum advantage $\alpha = 1.88$ can be achieved. While in the deep-strong coupling regime, the quantum advantage of the QB's maximum charging power is the same as that of the Dicke QB, i.e., $\alpha=1.5$