  We study the quantum dynamics of a spin ensemble coupled to cavity photons.
Recently, related experimental results have been reported, showing the
existence of the strong coupling regime in such systems. We study the
eigenenergy distribution of the multi-spin system (following the Tavis-Cummings
model) which shows a peculiar structure as a function of the number of cavity
photons and of spins. We study how this structure causes changes in the
spectrum of the admittance in the linear response theory, and also the
frequency dependence of the excited quantities in the stationary state under a
probing field. In particular, we investigate how the structure of the higher
excited energy levels changes the spectrum from a double-peak structure (the
so-called vacuum field Rabi splitting) to a single peak structure. We also
point out that the spin dynamics in the region of the double-peak structure
corresponds to recent experiments using cavity ringing while in region of the
single peak structure, it corresponds to the coherent Rabi oscillation in a
driving electromagnetic filed. Using a standard Lindblad type mechanism, we
study the effect of dissipations on the line width and separation in the
computed spectra. In particular, we study the relaxation of the total spin in
the general case of a spin ensemble in which the total spin of the system is
not specified. The theoretical results are correlated with experimental
evidence of the strong coupling regime, achieved with a spin 1/2 ensemble.
