Quantum Dicke battery supercharging in the bound-luminosity state

Quantum batteries, which are quantum systems to be used for the storage and transformation of energy, have been recently attracting research interest. 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 an 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 the dynamics of coherent energy transfer between the superradiant condensate and the ensemble of two-level systems. Here, using our previous results, we have derived analytically the superlinear law for the quantum battery charging power PN^3/2 as a function of the number N of two-level systems in the battery, and also the N dependence for the charging time t₂N^-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 Dicke quantum battery charging is considered in detail.