Enhancing coherent energy transfer between quantum batteries via a mediator.

We consider energy transfer processes between two quantum batteries (QBs), $i.e.$, two-level systems (TLSs). As a prototypical scenario we present a direct energy transfer between the first and second QB and we compare its performances with two mediated cases. The first one is when the energy from the first QB is transferred by a third TLS to the other QB, the second scenario is when the energy transfer is mediated by a cavity with a single photonic mode. We propose the analysis of the energy transfer process in resonance and off-resonance. The latter being really important for future experimental implementation, since it is really difficult to create TLSs with identical energy separation. As a result we observe that both in and off resonance we obtain better performances, concerning both the amount of energy and the time exploited to achieve the energy transfer, when we consider the cavity-mediated scenario.