Trapping of coherence and entanglement in photonic band-gaps

We investigate the coherence trapping of a two-level atom transversally interacting with a reservoir with a photonic band-gap structure function. We then focus on the multipartite entanglement dynamics via genuinely multipartite concurrence among N independent atoms each locally coupled with its own reservoir. By considering the Lorentzian width and the system size, we find that for the resonant and near-resonant conditions, the increase of Lorentzian width and the decrease of system size can lead to the occurrence of coherence trapping and entanglement trapping. By choosing the multipartite GHZ state as atomic initial state, we show that the multipartite entanglement may exhibit entanglement sudden death depending on the initial condition and the system size. In addition, we also analyze how the crossover behaviors of two dynamical regimes are influenced by the Lorentzian width and the weight ratio, in terms of the non-Markovianity.