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 boundluminosity 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 P similar to N3/2 as a function of the number N of two -level systems in the battery, and also the N dependence for the charging time tc similar to 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 Dicke quantum battery charging is considered in detail.