  We demonstrate quantum signatures of deterministic nonlinear dynamics in the
transition to superradiance of a generalized open Dicke model with different
coupling strengths for the co- and counter-rotating light-matter interaction
terms. A first-order phase transition to coexisting normal and superradiant
phases is observed, corresponding with the emergence of switching dynamics
between these two phases, driven by quantum fluctuations. We show that this
phase coexistence gives rise to a hysteresis loop also for the quantum
mechanical system. Additionally, a transition to a superradiant oscillatory
phase can be observed clearly in quantum simulations.
