Quench dynamics in the Jaynes-Cummings-Hubbard and Dicke models

Both the Jaynes-Cummings-Hubbard (JCH) and Dicke models can be thought of as idealised models of a quantum battery. In this paper we numerically investigate the charging properties of both of these models. The two models differ in how the two-level systems are contained in cavities. In the Dicke model, the $N$ two-level systems are contained in a single cavity, while in the JCH model the two-level systems each have their own cavity and are able to pass photons between them. In each of these models we consider a scenario where the two-level systems start in the ground state and the coupling parameter between the photon and the two-level systems is quenched. Each of these models display a maximum charging power that scales with the size of the battery $N$ and no super charging was found. Charging power also scales with the square root of the average number of photons per two-level system $m$ for both models. Finally, in the JCH model, the power was found to charge inversely with the square root of the photon-cavity coupling $\kappa$.