We study the dynamics of a single collective excitation in a cold ensemble of
atoms coupled to a one-dimensional waveguide. The coupling between the atoms
and the photonic modes provides a coherent and a dissipative dynamics for this
collective excitation. While the dissipative part accounts for the collectively
enhanced and directed emission of photons, we find a remarkable universal
dynamics for increasing atom numbers exhibiting several revivals under the
coherent part. While this phenomenon provides a limit on the intrinsic
dephasing for such a collective excitation, a setup is presented, where this
remarkable universal dynamics can be explored.Comment: Main text: 5 pages, 3 figures, Supplement Material: 10 pages, 1
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