  Atoms coupled to cavities provide an exciting playground for the study of
fundamental interactions of atoms mediated through a common channel. Many of
the applications of cavity-QED and cold-atom experiments more broadly, suffer
from limitations caused by the transient nature of an atomic loading cycle. The
development of continuous operation schemes is necessary to push these systems
to the next level of performance. Here we present a machine designed to produce
a continuous flux of collimated atoms that traverse an optical cavity. The
atom-light interaction is enhanced by a fast-decaying cavity optimal for
studying phenomena where atomic properties dominate. We demonstrate the
transition to a collective strong coupling regime heralded by a normal-mode
splitting. We observe a second phase with a binary normal-mode splitting born
from an offset in the mean velocity of the atoms. Inverting the atomic ensemble
in the collective strong coupling regime, we measure continuous optical gain.
This work sets the stage for studying threshold conditions for continuous
collective phenomena, such as continuous superradiant lasing.
