Single-atom dissipation and dephasing in Dicke and Tavis-Cummings quantum batteries

We study the influence of single-atom dissipation and dephasing noise on the performance of Dicke and Tavis-Cummings quantum batteries, where the electromagnetic field of the cavity hosting the system acts as a charger. For these models a genuine charging process can only occur in the transient regime. Indeed, unless the interaction with the environment is cut off, the asymptotic energy of the battery is solely determined by the environment and does not depend on the initial energy of the electromagnetic field. We numerically estimate the fundamental figures of merit for the model, including the time at which the battery reaches its maximum ergotropy, the average energy, and the energy that needs to be used to switch the battery-charger interaction on and off. Depending on the scaling of the coupling between the battery and the charger, we show that the model can still exhibit a subextensive charging time. However, for the Dicke battery, this effect comes with a higher cost when switching the battery-charger interaction on and off. We also show that as the number of battery constituents increases, both the Dicke and Tavis-Cummings models become asymptotically free, meaning the amount of energy that is not unitarily extractable becomes negligible. We obtain this result numerically and demonstrate analytically that it is a consequence of the symmetry under permutation of the model. Finally, we perform simulations for different values of the detuning, showing that the optimal regime for the Dicke battery is off-resonance, in contrast to what is observed in the Tavis-Cummings case.