  Hybridizing collective spin excitations and a cavity with high cooperativity
provides a new research subject in the field of cavity quantum electrodynamics
and can also have potential applications to quantum information. Here we report
an experimental study of cavity quantum electrodynamics with ferromagnetic
magnons in a small yttrium-iron-garnet (YIG) sphere at both cryogenic and room
temperatures. We observe for the first time a strong coupling of the same
cavity mode to both a ferromagnetic-resonance (FMR) mode and a magnetostatic
(MS) mode near FMR in the quantum limit. This is achieved at a temperature ~ 22
mK, where the average microwave photon number in the cavity is less than one.
At room temperature, we also observe strong coupling of the cavity mode to the
FMR mode in the same YIG sphere and find a slight increase of the damping rate
of the FMR mode. These observations reveal the extraordinary robustness of the
FMR mode against temperature. However, the MS mode becomes unobservable at room
temperature in the measured transmission spectrum of the microwave cavity
containing the YIG sphere. Our numerical simulations show that this is due to a
drastic increase of the damping rate of the MS mode.
