  Recently, the hybridization of microwave-frequency cavity modes with
collective spin excitations attracted large interest for the implementation of
quantum computation protocols, which exploit the transfer of information among
these two physical systems. Here, we investigate the interaction among the
magnetization precession modes of a small YIG sphere and the MW electromagnetic
modes, resonating in a tridimensional aluminum cavity. In the strong coupling
regime, anti-crossing features were observed in correspondence of various
magnetostatic modes, which were excited in a magnetically saturated sample.
Time-resolved studies show evidence of Rabi oscillations, demonstrating
coherent exchange of energy among photons and magnons modes. To facilitate the
analysis of the standing spin-wave patterns, we propose here a new procedure,
based on the introduction of a novel functional variable. The resulting easier
identification of magnetostatic modes can be exploited to investigate, control
and compare many-levels hybrid systems in cavity- and opto-magnonics research.
