Optomagnonics in dispersive media: magnon-photon coupling enhancement at the epsilon-near-zero frequency

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.