Quantum Dicke battery supercharging in the "bound luminocity" state

TL;DR

This paper analytically demonstrates a superlinear charging power law for a quantum battery based on the Dicke model, showing a power scaling of $N^{3/2}$ with the number of two-level systems, and compares it with recent numerical results.

Contribution

It derives an analytical superlinear law for quantum battery charging power in the Dicke model, advancing understanding of energy transfer dynamics in quantum systems.

Findings

Charging power scales as $N^{3/2}$

Charging time scales as $N^{-1/2}$

Analytical results match recent numerical findings

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 $P\sim N^{3/2}$ 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.