Quantum Dicke battery supercharging in the "bound luminocity" state

Quantum batteries, which are quantum systems to be used for storage and transformation of energy, are attracting research interest recently. A promising candidate for their investigation is the Dicke model, which describes an ensemble of two-level systems interacting with a single-mode electromagnetic wave in a resonator cavity. In order to charge the battery, a coupling between the ensemble of two-level systems and resonator cavity should be turned off at a certain moment of time. This moment of time is chosen in such a way, that the energy gets fully stored in the ensemble of two-level systems. In our previous work we have investigated a "bound luminosity" superradiant state of the extended Dicke model and found analytical expressions for dynamics of coherent energy transfer between superradiant condensate and the ensemble of the two-level systems. Here, using our previous results, we have derived analytically the superlinear law for the quantum battery charging power $P\sim N^{3/2}$ as function of the number $N$ of the two-level systems in the battery, and also $N$-dependence for the charging time $t_c\sim N^{-1/2}$. The $N$-exponent $3/2$ of the charging power is in quantitative correspondence with the recent result ${1.541}$ obtained numerically by other authors. The physics of the Dicke quantum battery charging is considered in detail