  Recently, the out-of-time-ordered correlator (OTOC) has gained much attention
as an indicator of quantum chaos. In the semi-classical limit, its exponential
growth rate resembles the classical Lyapunov exponent. The quantum-classical
correspondence has been supported for the one-body chaotic systems as well as
realistic systems with interactions, as in the Dicke model, a model of
multi-two-level atoms and cavity field interactions. To this end, we calculate
the OTOC for different variations of the Dicke model in an open quantum system
setting. The connection between the superradiant phase transition of the Dicke
model and the OTOC is studied. Further, we establish a relation between the
OTOC and the second-order coherence function. This becomes important for the
experimental studies of the OTOC and quantum chaos in the models of quantum
optics.
