Suppressing and restoring the Dicke superradiance transition by dephasing and decay

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 holds in the thermodynamic limit.