Four-level superradiant laser with full atomic cooperativity

We investigate a four-level superradiant laser whose intensity is proportional to N2 and whose linewidth scales as 1/N2. In the absence of spontaneous emissions, we derive the stationary solutions of the atomic full cooperativity, analyze their stabilities, and find the corresponding irreducible representation based on group U(4). We also investigate the spectra of the phase and amplitude fluctuations of the fields inside and outside the cavity and find that the amplitude fluctuations of the output fields cannot be squeezed in the low-frequency limit, which is completely different from the three-level superradiant laser system. Finally, we consider the stationary solutions corresponding to the partial cooperativity due to the symmetry breaking of U(4) induced by the atomic spontaneous emissions.