Normal-mode splitting with large collective cooperativity

We report the observation of normal-mode splitting of the atom-cavity dressed states in both the fluorescence and transmission spectra for large atom number and observe subnatural linewidths in this regime. We also implement a method of utilizing the normal-mode splitting to observe Rabi oscillations on the Rb-87 ground state hyperfine clock transition. We demonstrate a large collective cooperativity, C=1.2x10(4), which, in combination with large atom number, N similar to 2x10(5), offers the potential to realize an absolute phase sensitivity better than that achieved by state-of-the-art atomic fountain clocks or inertial sensors operating near the quantum projection noise limit.