Recently, strong coupling regimes of BEC atoms inside an

optical cavity and superconducting qubits, quantum dots, electron spins inside a micro-wave circuit cavity were achieved experimentally. The strong coupling regimes in all these systems can be described by the Dicke model.  Here we study the cavity transmission and  Fluorescence spectra by solving the Dicke model by $ 1/ N $ expansion. In the normal state, we find a $ \sqrt{N} $ behavior of the collective Rabi splitting consistent with the experimental data. Inside the superradiant phase, we identify a high frequency mode and also an emergent quantum phase diffusion mode with a corresponding Berry phase at a finite $ N $ and determine their corresponding spectral weights. We also work out many remarkable experimental consequences of this quantum phase mode such as its low frequency, high spectral weight, consecutive

photons plateaus, photon number squeezing properties and photon statistics. We argue that recent experimental advances in both cold atoms and semiconductor systems should motivate a new emerging interdisciplinary field of quantum optics and quantum phases which can be dubbed as " Strongly correlated quantum optics".