  Reaching strong light-matter coupling in solid-state systems has been long
pursued for the implementation of scalable quantum devices. Here, we put
forward the concept of a platform capable of achieving strong coupling between
magnetic excitations (magnons) and optics based in an epsilon-near-zero medium,
that's it, a medium in which the permittivity is close to zero. We adopt a
phenomenological approach to quantize the electromagnetic field inside a
dispersive magnetic medium and obtain a Hamiltonian describing the interaction
between photons and magnons and the frequency-dependent coupling. We predict
that, in the epsilon-near-zero regime, the single-magnon photon optomagnonic
coupling can be comparable to the uniform magnon's frequency for small magnetic
volumes. For state-of-the-art illustrative values, this would correspond to
achieving the single-magnon strong coupling regime, where the coupling rate is
larger than all the decay rates. Finally, we show that the non-linear energy
spectrum intrinsic to this coupling regime regime can be probed via the
characteristic multiple magnon sidebands in the photon power spectrum.
