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 function of photon number $n_{\text{max}}$ and spin system size $N$. A sharp transition in the distribution of the Rabi frequency is found at $n_{\text{max}}\approx N$. The width of the Rabi frequency spectrum diverges as $\sqrt{N}$ at this point. For increased number of photons $n_{\text{max}}>N$, the Rabi frequencies converge to a value proportional to $\sqrt{n_{\text{max}}}$. 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 toward quantum computing implementation with magnetic spins, using cavity quantum-electrodynamics techniques.

• Received 8 April 2010

DOI:https://doi.org/10.1103/PhysRevB.82.024413