  Lasing and steady state superradiance are two phenomena that may appear at
first glance to be distinct. In a laser, phase information is maintained by a
macroscopic intracavity light field, and the robustness of this phase is what
leads to the coherence of the output light. In contrast, the coherence of
steady-state superradiant systems derives from the macroscopic collective
dipole of a many-atom ensemble. In this paper, we develop a quantum theory that
connects smoothly between these two extreme limits. We show that lasing and
steady-state superradiance should be thought of as the two extreme limits of a
continuous crossover. The properties of systems that lie in the superradiance,
lasing, and crossover parameter regions are compared. We find that for a given
output intensity a narrower linewidth can be obtained by operating closer to
the superradiance side of the crossover. We also find that the collective phase
is robust against cavity frequency fluctuations in the superradiant regime and
against atomic level fluctuations in the lasing regime.
