Collective charging of an organic quantum battery

We study the collective charging of a quantum battery (QB) consisting of a one-dimensional molecular aggregate and a coupled single-mode cavity, to which we refer as an ``organic quantum battery" since the battery part is an organic material. The organic QB can be viewed as an extension of the so-called Dicke QB [D. Ferraro \emph{et al}., Phys. Rev. Lett. \textbf{120}, 117702 (2018)] by including finite exciton hopping and exciton-exciton interaction within the battery. We consider two types of normalizations of the exciton-cavity coupling when the size of the aggregate $N$ is increased: (I) The cavity length also increases to keep the density of monomers constant, (II) The cavity length does not change. Our main findings are that: (i) For fixed $N$ and exciton-cavity coupling, there exist optimal exciton-exciton interactions at which the maximum stored energy density and the maximum charging power density reach their respective maxima that both increase with increasing exciton-cavity coupling. The existence of such maxima for weak exciton-cavity coupling is argued to be due to the non-monotonic behavior of the one-exciton to two-exciton transition probability in the framework of second-order time-dependent perturbation theory. (ii) Under normalization I, no quantum advantage is observed in the scaling of the two quantities with varying $N$. Under normalization II, it is found that both the maximum stored energy density and the maximum charging power density exhibit quantum advantages compared with the Dicke QB.