Optimal energy storage in the Tavis-Cummings quantum battery

The Tavis-Cummings (TC) model, which serves as a natural physical realization of a quantum battery, comprises ${N}_{b}$ atoms as battery cells that collectively interact with a shared photon field, functioning as the charger, initially containing ${n}_{0}$ photons. In this paper, we introduce the invariant subspace method to effectively represent the quantum dynamics of the TC battery. Our findings indicate that in the limiting case of ${n}_{0}\ensuremath{\gg}{N}_{b}$ or ${N}_{b}\ensuremath{\gg}{n}_{0}$, a distinct SU(2) symmetry emerges in the dynamics, thereby ensuring the realization of optimal energy storage. We also establish a negative relationship between the battery-charger entanglement and the energy storage capacity. As a result, we demonstrate that asymptotically optimal energy storage can be achieved in the scenario where ${N}_{b}={n}_{0}\ensuremath{\gg}1$. Our approach not only enhances our comprehension of the algebraic structure inherent in the TC model but also contributes to the broader theoretical framework of quantum batteries. Furthermore, it provides crucial insights into the relation between energy transfer and quantum correlations.