Hysteresis in the spectrum for cooperative resonance fluorescence

Analytic results for the fluorescent spectrum arising in the cooperative interaction of a population of two-level atoms, driven by resonant laser radiation with the electromagnetic field are presented. The bistability and hysteresis characterising single-time atomic averages are evidenced explicitly as this spectrum is viewed throughout a hysteresis cycle. In the region of bistability full support is given to the designation of a cooperative and a non-cooperative branch. Spectral features reveal linewidths associated with cooperative and non-cooperative atomic decay rates respectively. A dominant feature is strong coherent scattering throughout the cooperative region, fully supporting an identification of this problem with super-radiant phenomena. Linewidth narrowing is predicted in the vicinity of both instabilities.