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We investigate the onset of chaos in a periodically kicked Dicke model (KDM),using the out-of-time-order correlator (OTOC) as a diagnostic tool, in both theoscillator and the spin subspaces. In the large spin limit, the classicalHamiltonian map is constructed, which allows us to investigate thecorresponding phase space dynamics and to compute the Lyapunov exponent. Weshow that the growth rate of the OTOC for the canonically conjugate coordinatesof the oscillator is able to capture the Lyapunov exponent in the chaoticregime. The onset of chaos is further investigated using the saturation valueof the OTOC, that can serve as an alternate indicator of chaos in a genericinteracting quantum system. This is also supported by a system independenteffective random matrix model. We further identify the quantum scars in KDM anddetect their dynamical signature by using the OTOC dynamics. The relevance ofthe present study in the context of ongoing cold atom experiments is alsodiscussed.

Fingerprint of chaos and quantum scars in kicked Dicke model: An out-of-time-order correlator study