  We consider a strongly correlated quantum dot, tunnel coupled to two
superconducting leads and capacitively coupled to a single mode microwave
cavity. When the superconducting gap is the largest energy scale, multiple
Shiba states are formed inside the gap. The competition of these states for the
ground state signals a quantum phase transition. We demonstrate that photonic
measurements can be used to probe such localized Shiba states. Moreover, the
quantum phase transition can be pinpointed exactly from the sudden change in
the transmission signal. Calculations were performed using the numerical
renormalization group approach.
