  We study the quantum dynamics of many-body arrays of two-level atoms in a
driven cavity subject to collective decay and interactions mediated by the
cavity field. We work in the bad cavity limit accessible, for example, using
long-lived electronic clock states of alkaline earth atoms, for which the bare
atomic linewidth is much less than the cavity linewidth. In the absence of
interactions, our system reduces to previously studied models of collective
fluorescence. We show that while interactions do not qualitatively change the
steady state properties, they lead to a drastic change in the dynamical
properties. We find that, for some interval of driving strengths, the system
shows two very distinct types of transient behaviors that depend on the initial
state of the system. In particular, there is a parameter regime where the
system features oscillatory dynamics with a period of oscillation that becomes
much shorter than the duration of the overall transient dynamics as the atom
number increases. We use both mean field and exact numerical calculations of
the quantum system to investigate the dynamics.
