  We analyze the interaction of a nanomagnet with a single photonic mode of a
microcavity in a fully quantum-mechanical treatment and find that exceptionally
large quantum-coherent magnet-photon coupling can be achieved. Coupling terms
in excess of several THz are predicted to be achievable in a spherical cavity
of ~1 mm radius with a nanomagnet of ~100 nm radius and ferromagnetic resonance
frequency of ~200 GHz. Eigenstates of the magnet-photon system correspond to
entangled states of spin orientation and photon number, in which over 10^5
values of each quantum number are represented; conversely initial (coherent)
states of definite spin and photon number evolve dynamically to produce large
oscillations in the microwave power (and nanomagnet spin orientation), and are
characterized by exceptionally long dephasing times.
