Dynamics of multiple atoms in one-dimensional fields

We analyze the dynamics of a set of two-level atoms coupled to the electromagnetic environment within a waveguide. This problem is often tackled by assuming a weak coupling between the atoms and the environment as well as the associated Markov approximation. We show that the accuracy of such an approximation may be more limited than in the single-atom case and may also be strongly determined by the presence of collective effects produced by atom-atom interactions. To this aim, we solve the full problem with exact diagonalization and also the time-dependent density matrix renormalization group method, and we compare the result to that obtained within a weak-coupling master equation and with the Dicke approximation. Finally, we study the dynamics of the entanglement within the system when considering several interatomic distances and atomic frequencies.