We consider a collection of two level systems, such as qubits, embedded into a microwave cavity as a promising candidate for the realization of high power quantum batteries. In this perspective, the possibility to design devices where the conventional single-photon coupling is suppressed and the dominant interaction is mediated by two-photon processes is investigated, opening the way to an even further enhancement of the charging performance. By solving a Dicke model with both single- and two-photon coupling we determine the range of parameters where the latter unconventional interaction dominates the dynamics of the system leading to better performances both in the charging times and average charging power of the QB compared to the single-photon case. In addition, the scaling of the maximum stored energy, fluctuations and charging power with the finite number of qubits N is inspected. While the energy and fluctuations scale linearly with N, the quadratic growth of the average power leads to a relevant improvement of the charging performance of quantum batteries based on this scheme with respect to the purely single-photon coupling case. Moreover, it is shown that the charging process is progressively faster by increasing the coupling from the weak to the ultra-strong regime.
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