High Cooperativity Cavity QED with Magnons at Microwave Frequencies
  Using a sub-millimetre sized YIG (Yttrium Iron Garnet) sphere mounted in a magnetic field-focusing cavity, we demonstrate an ultra-high cooperativity of $10^5$ between magnon and photon modes at millikelvin temperatures and microwave frequencies. The cavity is designed to act as a magnetic dipole by using a novel multiple-post approach, effectively focusing the cavity magnetic field within the YIG crystal with a filling factor of 3%. Coupling strength (normal-mode splitting) of 2 GHz, (equivalent to 76 cavity linewidths or $0.3$ Hz per spin), is achieved for a bright cavity mode that constitutes about 10% of the photon energy and shows that ultra-strong coupling is possible in spin systems at microwave frequencies. With straight forward optimisations we demonstrate that with that this system has the potential to reach cooperativities of $10^7$, corresponding to a normal mode splitting of 5.2 GHz and a coupling per spin approaching 1 Hz. We also observe a three-mode strong coupling regime between a dark cavity mode and a magnon mode doublet pair, where the photon-magnon and magnon-magnon couplings (normal-mode splittings) are 143 MHz and 12.5 MHz respectively, with HWHM bandwidth of about 0.5 MHz. 
Maxim Goryachev, Warrick G. Farr, Daniel L. Creedon, Yaohui Fan,   Mikhail Kostylev and Michael E. Tobar
quant-ph cond-mat.mtrl-sci