When a quantum dot is embedded into a superconducting environment, it leads to the formations of localized Shiba states inside the gap. If the Coulomb interaction is sufficiently small, the Shiba states consist of a pair of singlet states and a doublet, that compete for the ground state and induce a quantum phase transition. In the presence of an external microwave field, the Shiba energy spectrum is significantly modified. Moreover, the transmission of the cavity inherits features that can pinpoint the exact location of the quantum critical point. In terms of methods used, our analytical calculations are supplemented by state of the art numerical renormalization group calculations.

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