Extended Dicke quantum battery with interatomic interactions and driving field

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