In this short communication we reply to the comment by Xu and Li (arXiv:2411.04132) on our first work on Dicke quantum batteries (Phys. Rev. Lett. 120, 117702 (2018)).
In the Letter [Physical Review Letters 120, 117702 (2018)], Ferraro \emph{et al.} claimed a quantum advantage in the Dicke quantum battery (QB), whereby N two-level systems (TLS) are coupled to a common photonic mode of a cavity. They argued that compared with the so-called Rabi QB, the Dicke QB exhibits a N quantum enhancement in the charging power because of the entanglement created by the common photonic mode. In this Comment, however, we demonstrate that the apparent N enhancement actually comes from the stronger cavity electric (or magnetic) field under the setup discussed in [Physical Review Letters 120, 117702 (2018)]. This is a trivial classical effect, and there is no true "quantum advantage" in the charging power of the Dicke QB. While somewhat similar questions regarding the origin of the claimed "quantum advantage" have been raised before, here we would like to make it clear that the N enhancement in [Physical Review Letters 120, 117702 (2018)] is purely a classical effect, not attributable to quantum entanglement or collective phenomena. Therefore, we believe that using the term "quantum battery" in this context may be inappropriate and misleading.
Quantum information theorems state that it is possible to exploit collective quantum resources to greatly enhance the charging power of quantum batteries (QBs) made of many identical elementary units. We here present and solve a model of a QB that can be engineered in solid-state architectures. It consists of N two-level systems coupled to a single photonic mode in a cavity. We contrast this collective model ("Dicke QB"), whereby entanglement is genuinely created by the common photonic mode, to the one in which each two-level system is coupled to its own separate cavity mode ("Rabi QB"). By employing exact diagonalization, we demonstrate the emergence of a quantum advantage in the charging power of Dicke QBs, which scales like sqrt[N] for N≫1.