Superstrong coupling of a microwave cavity to yttrium iron garnet magnons

Multiple-post reentrant 3D lumped cavity modes have been realized to design the concept of discrete Whispering Gallery and Fabry-Perot-like Modes for multimode microwave Quantum Electrodynamics experiments. Using a magnon spin-wave resonance of a submillimeter-sized Yttrium-Iron-Garnet sphere at milliKelvin temperatures and a four-post cavity, we demonstrate the ultra-strong coupling regime between discrete Whispering Gallery Modes and a magnon resonance with strength of 1.84 GHz. By increasing the number of posts to eight and arranging them in a D$_4$ symmetry pattern, we expand the mode structure to that of a discrete Fabry-Perot cavity and modify the Free Spectral Range (FSR). We reach the superstrong coupling regime, where spin-photon coupling strength is larger than FSR, with coupling strength in the 1.1 to 1.5 GHz range.