  We study the transmission spectra of ultracold rubidium atoms coupled to a
high-finesse optical cavity. Under weak probing with pi-polarized light, the
linear response of the system is that of a collective spin with multiple levels
coupled to a single mode of the cavity. By varying the atom number, we change
the collective coupling of the system. We observe the change in transmission
spectra when going from a regime where the collective coupling is much smaller
than the separation of the atomic levels to a regime where both are of
comparable size. The observations are in good agreement with a reduced model we
developed for our system.
