Optimal driving field for multipartite quantum battery coupled with a common thermal bath

For a many-atom battery coupled with a common thermal bath, the useful energy is maximized at an optimal number of the atoms for a fixed harmonic driving field, i.e., the so-called optimal building block see Chang et al. New J. Phys.23 103026 (2021). Here we consider the useful energy defined by the ergotropy and a continuous-wave driving field. For the single-atom case, we present analytical results of the increased energy and the ergotropy in the long-time limit (i.e., the steady-state ergotropy). It is found that there exists an optimal value of the driving-field strength. Such an observation holds for many-atom cases. Numerically, we show that the optimal strength increases linearly with the number N of the atoms. Using the optimal strength for each N, both the increased energy and the ergotropy increase monotonically with N.