Cooperative fluorescence from N coherently driven two-level atoms

Considers a system of N coherently driven two-level atoms contained in a volume with dimensions much smaller than a wavelength. The atoms may decay by a completely cooperative mechanism which conserves (J2), alternatively they may decay by a mechanism which fails to conserve (J2). The steady-state behaviour in each case is determined using the single-atom solutions together with two limiting approximations: (a) complete atomic correlation, (b) no atomic correlation. In case (a) a behaviour characteristic of a second-order phase transition is obtained while in case (b) a first-order phase transition results.