Charging quantum batteries via Otto machines: Influence of monitoring

The charging of a quantum battery by a four-stroke quantum machine that works either as an engine or a refrigerator is investigated. The presented analysis provides the energetic behavior of the combined system in terms of the heat- and workflows of the machine, the average, the variance of the battery's energy, as well as the coherent and incoherent parts of its ergotropy. To monitor the battery state, its energy is measured either after the completion of any cycle or after a prescribed number of cycles is carried out. The resulting battery performances greatly differ for those two cases. During the first charging epoch with an engine, the regular measurements speed up the charging, whereas the gain of ergotropy is more pronounced in the absence of measurements. In a later stage, the engine fails to work as such, while it still continues charging the battery that eventually reaches the maximally charged state in the absence of intermediate measurements and a suboptimally charged state for a periodically measured battery. For a refrigerator, the charging of the measured battery also proceeds faster during the first epoch. Only during the second stage, when the machine fails to extract heat from the cold bath, the influence of the measurements becomes less pronounced, leading to rather similar asymptotic states for the two measurement scenarios.