  As the name indicates, a periodic orbit is a solution for a dynamical system
that repeats itself in time. In the regular regime, periodic orbits are stable,
while in the chaotic regime, they become unstable. The presence of unstable
periodic orbits is directly associated with the phenomenon of quantum scarring,
which restricts the degree of delocalization of the eigenstates and leads to
revivals in the dynamics. Here, we study the Dicke model in the superradiant
phase and identify two sets of fundamental periodic orbits. This experimentally
realizable atom-photon model is regular at low energies and chaotic at high
energies. We study the effects of the periodic orbits in the structure of the
eigenstates in both regular and chaotic regimes and obtain their quantized
energies. We also introduce a measure to quantify how much scarred an
eigenstate gets by each family of periodic orbits and compare the dynamics of
initial coherent states close and away from those orbits.
