We show that dephasing of individual atoms destroys the superradiance transition of the Dicke model, but that adding individual decay toward the spin down state can restore this transition. To demonstrate this, we present a method to give an exact solution for the N atom problem with individual dephasing which scales polynomially with N. By comparing finite size scaling of our exact solution to a cumulant expansion, we confirm the destruction and restoration of the superradiance transition hold in the thermodynamic limit.
The spontaneous coherent radiation from thin crystal films of
n layers is studied. By treating each layer as a unit and by employing the method of multiple-time-scale expansion, exact solutions for such systems, with no restriction on the value $\frac{{\ensuremath{\lambda}}_{0}}{d}$, are found. Here ${\ensuremath{\lambda}}_{0}$ is the characteristic radiation wavelength and
d is the average interparticle spacing. In the limit $\frac{{\ensuremath{\lambda}}_{0}}{d}\ensuremath{\gg}1$, it is seen that there exist correlated states of the film which are exact analog of Dicke's superradiant states. The decay rate for the superradiant states is roughly enhanced by a factor of $n{(\frac{{\ensuremath{\lambda}}_{0}}{d})}^{2}$ compared to the single-atom decay rate ${\ensuremath{\gamma}}_{s}$.