Subradiant-to-Subradiant Phase Transition in the Bad Cavity Laser

We show that the onset of steady-state superradiance in a bad cavity laser is preceded by a dissipative phase transition between two distinct phases of steady-state subradiance. The transition is marked by a nonanalytic behavior of the cavity output power and the mean atomic inversion, as well as a discontinuity in the variance of the collective atomic inversion. In particular, for repump rates below a critical value, the cavity output power is strongly suppressed and does not increase with the atom number, while it scales linearly with atom number above this value. Remarkably, we find that the atoms are in a macroscopically entangled steady state near the critical region with a vanishing fraction of unentangled atoms in the large atom number limit.