Abstract
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 works 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∼ 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∼ 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.