Strong light-matter coupling is a necessary condition for exchanging information in quantum information protocols. It is used to couple different qubits (matter) via a quantum bus (photons) or to communicate different type of excitations, e.g. transducing between light and phonons or magnons. An unexplored, so far, interface is the coupling between light and topologically protected particle like excitations as magnetic domain walls, skyrmions or vortices. Here, we show theoretically that a single photon living in a superconducting cavity can be coupled strongly to the gyrotropic mode of a magnetic vortex in a nanodisc. We combine numerical and analytical calculations for a superconducting coplanar waveguide resonator and different realizations of the nanodisc (materials and sizes). We show that, for enhancing the coupling, constrictions fabricated in the resonator are beneficial, allowing to reach the strong coupling in CoFe discs of radius $200-400$ nm having resonance frequencies of few GHz. The strong coupling regime permits to exchange coherently a single photon and quanta of vortex excitations. Thus, our calculations show that the device proposed here serves as a transducer between photons and gyrating vortices, opening the way to complement superconducting qubits with topologically protected spin-excitations like vortices or skyrmions. We finish by discussing potential applications in quantum data processing based on the exploitation of the vortex as a short-wavelength magnon emitter.
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