Quantum Dicke battery supercharging in the bound-luminosity state

Physical Review A: Atomic, Molecular, and Optical physics. 2024. Vol. 109. No. 2. Article 022210.

S. S. Seidov, Mukhin S. I.

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 tc ∼ 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.

Keywords: Dicke model, Quantum battery