  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.
