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 non-analytic behavior of the mean atomic inversion and the cavity output power, and a discontinuity in the variance of the collective atomic inversion. Remarkably, we find that the atoms are in a macroscopic entangled steady state near the critical region with a vanishing fraction of unentangled atoms in the large atom number limit.