  We study the energy level structure of the Tavis-Cumming model applied to an
ensemble of independent magnetic spins $s=1/2$ coupled to a variable number of
photons. Rabi splittings are calculated and their distribution is analyzed as a
functin of photon number $n_{\rm max}$ and spin system size $N$. A sharp
transition in the distribution of the Rabi frequency is found at $n_{\rm
max}\approx N$. The width of the Rabi frequency spectrum diverges as $\sqrt{N}$
at this point. For increased number of photons $n_{\rm max}>N$, the Rabi
frequencies converge to a value proportional to $\sqrt{n_{\rm max}}$. This
behavior is interpreted as analogous to the classical spin resonance mechanism
where the photon is treated as a classical field and one resonance peak is
expected. We also present experimental data demonstrating cooperative, magnetic
strong coupling between a spin system and photons, measured at room
temperature. This points towards quantum computing implementation with magnetic
spins, using cavity quantum-electrodynamics techniques.
