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Cavity quantum electrodynamics with mesoscopic topological superconductors

We study one-dimensional $p$-wave superconductors capacitively coupled to a microwave stripline cavity. By probing the light exiting from the cavity, one can reveal the electronic susceptibility of the $p$-wave superconductor. We analyze two superconducting systems: the prototypical Kitaev chain, and a topological semiconducting wire. For both systems, we show that the photonic measurements, via the electronic susceptibility, allows us to determine the topological phase transition point, the emergence of the Majorana fermions, and the parity of their ground state. We show that all these effects, which are absent in effective theories that take into account the coupling of light to Majorana fermions only, are due to the interplay between the Majorana fermions and the bulk states of the superconductors.