Quantum quench dynamics in Dicke superradiance models

We study the quantum quench dynamics in an extended version of the Dicke model where an additional parameter allows a smooth transition to the integrable Tavis-Cummings regime. We focus on the influence of various quantum phases and excited-state quantum phase transitions (ESQPTs) on the survival probability of the initial state. We show that, depending on the quench protocol, an ESQPT can either stabilize the initial state or, on the contrary, speed up its decay to the equilibrated regime. Quantum chaos smears out the manifestations of ESQPTs in quench dynamics, therefore significant effects can only be observed in integrable or weakly chaotic settings. Similar features are present also in the post-quench dynamics of some observables.