  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.
