  We propose a realization of two remarkable effects of Dicke physics in
quantum simulation of light-matter many-body interactions with artificial
quantum systems. These effects are a superradiant decay of an ensemble of
qubits and the opposite radiation trapping effect. We show that both phenomena
coexist in the crossover regime of a "moderately bad" single-mode cavity
coupled to the qubit subsystem. Depending on the type of the initial state and
on the presence of multipartite entanglement in it, the dynamical features can
be opposite resulting either in the superradiance or in the radiation trapping
despite of the fact that the initial state contains the same number of excited
qubits. The difference originates from the symmetrical or nonsymmetrical
character of the initial wave function of the ensemble, which corresponds to
indistinguishable or distinguishable emitters. We argue that a coexistence of
both effects can be used in dynamical quantum simulators to demonstrate
realization of Dicke physics, effects of multipartite quantum entanglement, as
well as quantum interference and thus to deeply probe quantum nature of these
artificial quantum systems.
